This paper and the others in the series challenges the standard model of the effects of gravitati... more This paper and the others in the series challenges the standard model of the effects of gravitational lensing on observations at large distances. We show that due to the cumulative effect of lensing, areas corresponding to an observed solid angle can be quite different than would be estimated from the corresponding Friedmann-Lemaître model, even when averaged over large angular scales. This paper concentrates on the specific example of spherically symmetric but spatially inhomogeneous dust universes, the Lemaître-Tolman-Bondi models, and shows that radial lensing significantly distorts the area distance-redshift and density-redshift relations in these exact solutions compared with the standard ones for Friedmann-Lemaître models. Thus inhomogeneity may introduce significant errors into distance estimates based on the standard FL relations, even after all-sky averaging. In addition a useful new gauge choice is presented for these models, solving the problem of locating the past null c...
In this paper we show in a covariant and gauge invariant way that in general relativity, tidal fo... more In this paper we show in a covariant and gauge invariant way that in general relativity, tidal forces are actually a hidden form of gravitational waves. This must be so because gravitational effects cannot occur faster than the speed of light. Any two body gravitating system, where the bodies are orbiting around each other, may generate negligible gravitational waves, but it is via these waves that non-negligible tidal forces (causing shape distortions) act on these bodies. Although the tidal forces are caused by the electric part of the Weyl tensor, we transparently show that some small time varying magnetic part of the Weyl tensor with non zero curl must be present in the system that mediates the tidal forces via gravitational wave type effects. The outcome is a new test of whether gravitational effects propagate at the speed of light.
FQXI Essay for Wandering Towards a Goal Essay contest. 1 Physics vs Biology How can a universe th... more FQXI Essay for Wandering Towards a Goal Essay contest. 1 Physics vs Biology How can a universe that is ruled by natural laws give rise to aims and intentions? The key difference between physics and biology is function or purpose. There is no purpose in the existence of the Moon or an electron or in a collision of two gas particles.
Transactions of the Royal Society of South Africa, 2021
Significant challenges exist globally regarding literacy teaching and learning. To address these ... more Significant challenges exist globally regarding literacy teaching and learning. To address these challenges, key features of how the brain works should be taken into account. First, perception is an active process based in detection of errors in hierarchical predictions of sensory data and action outcomes. Reading is a particular case of this non-linear predictive process. Second, emotions play a key role in underlying cognitive functioning, including oral and written language. Negative emotions undermine motivation to learn. Third, there is not the fundamental difference between listening/speaking and reading/writing often alleged on the basis of evolutionary arguments. Both are socio-cultural practices that are driven through the communication imperative of the social brain. Fourth, both listening and reading are contextually occurring pyscho-social practices of understanding, shaped by current knowledge and cultural contexts and practices. Fifth, the natural operation of the brain is not rule-based, as is supposed in the standard view of linguistics: it is prediction, based on statistical pattern recognition. This all calls into question narrow interpretations of the widely quoted "Simple View of Reading", which argues that explicit decoding is the necessary route to comprehension. One of the two neural routes to reading does not involve such explicit decoding processes, and can be activated from the earliest years. An integrated view of brain function reflecting the non-linear contextual nature of the reading process implies that an ongoing focus on personal meaning and understanding from the very beginning provides positive conditions for learning all aspects of reading and writing.
This article reviews the properties and limitations associated with the existence of particle, vi... more This article reviews the properties and limitations associated with the existence of particle, visual, and event horizons in cosmology in general and in inflationary universes in particular, carefully distinguishing them from `Hubble horizons'. It explores to what extent one might be able to probe conditions beyond the visual horizon (which is close in size to the present Hubble radius), thereby showing that visual horizons place major limits on what are observationally testable aspects of a multiverse, if such exists. Indeed these limits largely prevent us from observationally proving a multiverse either does or does not exist. We emphasize that event horizons play no role at all in observational cosmology, even in the multiverse context, despite some claims to the contrary in the literature.
We review current theoretical cosmology, including fundamental and mathematical cosmology and phy... more We review current theoretical cosmology, including fundamental and mathematical cosmology and physical cosmology (as well as cosmology in the quantum realm), with an emphasis on open questions.
This is the first of a series of papers extending a Gauge Invariant and Covariant (GIC) treatment... more This is the first of a series of papers extending a Gauge Invariant and Covariant (GIC) treatment of kinetic theory in curved space-times to a treatment of Cosmic Background Radiation (CBR) temperature anisotropies arising from inhomogeneities in the early universe. This paper deals with algebraic issues, both generically and in the context of models linearised about Robertson-Walker geometries. The approach represents radiation anisotropies by Projected Symmetric and Trace-Free tensors. The Angular correlation functions for the mode coefficients are found in terms of these quantities, following the Wilson-Silk approach, but derived and dealt with in GIC form. The covariant multipole and mode-expanded angular correlation functions are related to the usual treatments in the literature. The GIC mode expansion is related to the coordinate approach by linking the Legendre functions to the Projected Symmetric Trace-free representation, using a covariant addition theorem for the tensors to generate the Legendre Polynomial recursion relation. This paper lays the foundation for further papers in the series, which use this formalism in a GIC approach to develop solutions of the Boltzmann and Liouville equations for the CBR before and after decoupling, thus providing a unified GIC derivation of the variety of approaches to CBR anisotropies in the current literature. 1
Transactions of the Royal Society of South Africa, 2021
Significant challenges exist globally regarding literacy teaching and learning. To address these ... more Significant challenges exist globally regarding literacy teaching and learning. To address these challenges, key features of how the brain works should be taken into account. First, perception is an active process based in detection of errors in hierarchical predictions of sensory data and action outcomes. Reading is a particular case of this non-linear predictive process. Second, emotions play a key role in underlying cognitive functioning, including oral and written language. Negative emotions undermine motivation to learn. Third, there is not the fundamental difference between listening/speaking and reading/writing often alleged on the basis of evolutionary arguments. Both are socio-cultural practices that are driven through the communication imperative of the social brain. Fourth, both listening and reading are contextually occurring pyscho-social practices of understanding, shaped by current knowledge and cultural contexts and practices. Fifth, the natural operation of the brain is not rule-based, as is supposed in the standard view of linguistics: it is prediction, based on statistical pattern recognition. This all calls into question narrow interpretations of the widely quoted "Simple View of Reading", which argues that explicit decoding is the necessary route to comprehension. One of the two neural routes to reading does not involve such explicit decoding processes, and can be activated from the earliest years. An integrated view of brain function reflecting the non-linear contextual nature of the reading process implies that an ongoing focus on personal meaning and understanding from the very beginning provides positive conditions for learning all aspects of reading and writing.
There has been much controversy over weak and strong emergence in physics and biology. As pointed... more There has been much controversy over weak and strong emergence in physics and biology. As pointed out by Phil Anderson in many papers, the existence of broken symmetries is the key to emergence of properties in much of solid state physics. By carefully distinguishing between different types of symmetry breaking and tracing the relation between broken symmetries at micro and macro scales, I demonstrate that the emergence of the properties of metals and semiconductors is a case of strong emergence. This is due to the existence of quasiparticles such as phonons. A second key case where symmetry breaking leads to strong emergence is the existence of the various arrows of time. Related arguments extend to demonstrating strong emergence in molecular biology, in this case due to the existence of time dependent constraint terms in the underlying Hamiltonian. Additionally I show that the processes of evolutionary emergence of living systems is also a case of strong emergence. A useful result emerges: standard physics theories and the emergent theories arising out of them are all effective theories that are equally valid.
We review current theoretical cosmology, including fundamental and mathematical cosmology and phy... more We review current theoretical cosmology, including fundamental and mathematical cosmology and physical cosmology (as well as cosmology in the quantum realm), with an emphasis on open questions.
Commonly used Acronyms used in this paper include: Cold dark matter (CDM). Cosmic microwave backg... more Commonly used Acronyms used in this paper include: Cold dark matter (CDM). Cosmic microwave background (CMB). Einstein field equations (EFE). Friedmann-Lemaítre-Robertson-Walker (FLRW). Gravitational waves (GW). General Relativity (GR). Large scale structure (LSS). Linear perturbation theory (LPT). Loop quantum cosmology (LQC). Loop quantum gravity (LQG). Primordial gravitational waves (PGW). Primordial non-Gaussianities (PNG). Quantum gravity (QG). 2 Except in the degenerate cases of spacetimes of constant curvature (de Sitter, anti-de Sitter and Minkowski spacetimes). Such universe models do not correspond to the real Universe, which has preferred world lines everywhere [1].
This is the first of a series of papers extending a Gauge Invariant and Covariant (GIC) treatment... more This is the first of a series of papers extending a Gauge Invariant and Covariant (GIC) treatment of kinetic theory in curved space-times to a treatment of Cosmic Background Radiation (CBR) temperature anisotropies arising from inhomogeneities in the early universe. This paper deals with algebraic issues, both generically and in the context of models linearised about Robertson-Walker geometries . The approach represents radiation anisotropies by Projected Symmetric and Trace-Free tensors. The Angular correlation functions for the mode coefficients are found in terms of these quantities, following the Wilson-Silk approach, but derived and dealt with in GIC form. The covariant multipole and mode-expanded angular correlation functions are related to the usual treatments in the literature. The GIC mode expansion is related to the coordinate approach by linking the Legendre functions to the Projected Symmetric Trace-free representation, using a covariant addition theorem for the tensors to generate the Legendre Polynomial recursion relation. This paper lays the foundation for further papers in the series, which use this formalism in a GIC approach to develop solutions of the Boltzmann and Liouville equations for the CBR before and after decoupling, thus providing a unified GIC derivation of the variety of approaches to CBR anisotropies in the current literature.
General relativity is a cornerstone of modern physics, and is of major importance in its applicat... more General relativity is a cornerstone of modern physics, and is of major importance in its applications to cosmology. Plebanski and Krasinski are experts in the field and in this 2006 book they provide a thorough introduction to general relativity, guiding the reader through complete derivations of the most important results. Providing coverage from a unique viewpoint, geometrical, physical and astrophysical properties of inhomogeneous cosmological models are all systematically and clearly presented, allowing the reader to follow and verify all derivations. For advanced undergraduates and graduates in physics and astronomy, this textbook will enable students to develop expertise in the mathematical techniques necessary to study general relativity.
Commonly used Acronyms used in this paper include: Cold dark matter (CDM). Cosmic microwave backg... more Commonly used Acronyms used in this paper include: Cold dark matter (CDM). Cosmic microwave background (CMB). Einstein field equations (EFE). Friedmann-Lemaítre-Robertson-Walker (FLRW). Gravitational waves (GW). General Relativity (GR). Large scale structure (LSS). Linear perturbation theory (LPT). Loop quantum cosmology (LQC). Loop quantum gravity (LQG). Primordial gravitational waves (PGW). Primordial non-Gaussianities (PNG). Quantum gravity (QG). 2 Except in the degenerate cases of spacetimes of constant curvature (de Sitter, anti-de Sitter and Minkowski spacetimes). Such universe models do not correspond to the real Universe, which has preferred world lines everywhere [1].
We model massive dark objects in galactic nuclei as spherically symmetric static naked singularit... more We model massive dark objects in galactic nuclei as spherically symmetric static naked singularities in the Einstein massless scalar field theory and study the resulting gravitational lensing in detail. Based on whether or not a naked singularity is covered within a photon sphere we classify naked singularities into two kinds: weakly naked ͑those contained within at least one photon sphere͒ and strongly naked ͑those not contained within any photon sphere͒. The qualitative features of gravitational lensing due to a weakly naked singularity are similar to those due to a Schwarzschild black hole ͑these give rise to one Einstein ring but no radial critical curve͒. However, the gravitational lensing due to a strongly naked singularity is qualitatively different from that due to a Schwarzschild black hole; a strongly naked singularity gives rise to either two or nil Einstein ring͑s͒ and one radial critical curve. A light ray passing close to a photon sphere of a black hole or a weakly naked singularity goes around its photon sphere once, twice, or many times ͑before reaching an observer͒ depending upon the impact parameter and thus gives rise to a sequence of theoretically infinite number of relativistic images, which are highly demagnified. A strongly naked singularity produces no relativistic images.
We develop a new approach to local nonlinear effects in cosmic microwave background anisotropies,... more We develop a new approach to local nonlinear effects in cosmic microwave background anisotropies, and discuss the qualitative features of these effects. New couplings of the baryonic velocity to radiation multipoles are found, arising from nonlinear Thomson scattering effects. We also find a new nonlinear shear effect on small angular scales. The full set of evolution and constraint equations is derived, including the nonlinear generalizations of the radiation multipole hierarchy, and of the dynamics of multi-fluids. These equations govern radiation anisotropies in any inhomogeneous spacetime, but their main application is to second-order effects in a universe that is close to the Friedmann models. Qualitative analysis is given here, and quantitative calculations are taken up in further papers. to appear Phys. Rev. D 59 (1999)
The use of proper \time" to describe classical \spacetimes" which contain both Euclidean and Lore... more The use of proper \time" to describe classical \spacetimes" which contain both Euclidean and Lorentzian regions permits the introduction of smooth (generalized) orthonormal frames. This remarkable fact permits one to describe both a variational treatment of Einstein's equations and distribution theory using straightforward generalizations of the standard treatments for constant signature.
What happens to a star when it dies? This is a very natural astronomical question, and various th... more What happens to a star when it dies? This is a very natural astronomical question, and various theories since the 1930s have been advanced towards answer- ing it. The theories predict supernovae, white dwarf stars, neutron stars and black holes. The first two are now ...
The photon sphere concept in Schwarzschild space-time is generalized to a definition of a photon ... more The photon sphere concept in Schwarzschild space-time is generalized to a definition of a photon surface in an arbitrary space-time. A photon sphere is then defined as an SO(3)xR-invariant photon surface in a static spherically symmetric space-time. It is proved, subject to an energy condition, that a black hole in any such space-time must be surrounded by a photon sphere. Conversely, subject to an energy condition, any photon sphere must surround a black hole, a naked singularity or more than a certain amount of matter. A second order evolution equation is obtained for the area of an SO(3)-invariant photon surface in a general non-static spherically symmetric space-time. Many examples are provided.
This paper and the others in the series challenges the standard model of the effects of gravitati... more This paper and the others in the series challenges the standard model of the effects of gravitational lensing on observations at large distances. We show that due to the cumulative effect of lensing, areas corresponding to an observed solid angle can be quite different than would be estimated from the corresponding Friedmann-Lemaître model, even when averaged over large angular scales. This paper concentrates on the specific example of spherically symmetric but spatially inhomogeneous dust universes, the Lemaître-Tolman-Bondi models, and shows that radial lensing significantly distorts the area distance-redshift and density-redshift relations in these exact solutions compared with the standard ones for Friedmann-Lemaître models. Thus inhomogeneity may introduce significant errors into distance estimates based on the standard FL relations, even after all-sky averaging. In addition a useful new gauge choice is presented for these models, solving the problem of locating the past null c...
In this paper we show in a covariant and gauge invariant way that in general relativity, tidal fo... more In this paper we show in a covariant and gauge invariant way that in general relativity, tidal forces are actually a hidden form of gravitational waves. This must be so because gravitational effects cannot occur faster than the speed of light. Any two body gravitating system, where the bodies are orbiting around each other, may generate negligible gravitational waves, but it is via these waves that non-negligible tidal forces (causing shape distortions) act on these bodies. Although the tidal forces are caused by the electric part of the Weyl tensor, we transparently show that some small time varying magnetic part of the Weyl tensor with non zero curl must be present in the system that mediates the tidal forces via gravitational wave type effects. The outcome is a new test of whether gravitational effects propagate at the speed of light.
FQXI Essay for Wandering Towards a Goal Essay contest. 1 Physics vs Biology How can a universe th... more FQXI Essay for Wandering Towards a Goal Essay contest. 1 Physics vs Biology How can a universe that is ruled by natural laws give rise to aims and intentions? The key difference between physics and biology is function or purpose. There is no purpose in the existence of the Moon or an electron or in a collision of two gas particles.
Transactions of the Royal Society of South Africa, 2021
Significant challenges exist globally regarding literacy teaching and learning. To address these ... more Significant challenges exist globally regarding literacy teaching and learning. To address these challenges, key features of how the brain works should be taken into account. First, perception is an active process based in detection of errors in hierarchical predictions of sensory data and action outcomes. Reading is a particular case of this non-linear predictive process. Second, emotions play a key role in underlying cognitive functioning, including oral and written language. Negative emotions undermine motivation to learn. Third, there is not the fundamental difference between listening/speaking and reading/writing often alleged on the basis of evolutionary arguments. Both are socio-cultural practices that are driven through the communication imperative of the social brain. Fourth, both listening and reading are contextually occurring pyscho-social practices of understanding, shaped by current knowledge and cultural contexts and practices. Fifth, the natural operation of the brain is not rule-based, as is supposed in the standard view of linguistics: it is prediction, based on statistical pattern recognition. This all calls into question narrow interpretations of the widely quoted "Simple View of Reading", which argues that explicit decoding is the necessary route to comprehension. One of the two neural routes to reading does not involve such explicit decoding processes, and can be activated from the earliest years. An integrated view of brain function reflecting the non-linear contextual nature of the reading process implies that an ongoing focus on personal meaning and understanding from the very beginning provides positive conditions for learning all aspects of reading and writing.
This article reviews the properties and limitations associated with the existence of particle, vi... more This article reviews the properties and limitations associated with the existence of particle, visual, and event horizons in cosmology in general and in inflationary universes in particular, carefully distinguishing them from `Hubble horizons'. It explores to what extent one might be able to probe conditions beyond the visual horizon (which is close in size to the present Hubble radius), thereby showing that visual horizons place major limits on what are observationally testable aspects of a multiverse, if such exists. Indeed these limits largely prevent us from observationally proving a multiverse either does or does not exist. We emphasize that event horizons play no role at all in observational cosmology, even in the multiverse context, despite some claims to the contrary in the literature.
We review current theoretical cosmology, including fundamental and mathematical cosmology and phy... more We review current theoretical cosmology, including fundamental and mathematical cosmology and physical cosmology (as well as cosmology in the quantum realm), with an emphasis on open questions.
This is the first of a series of papers extending a Gauge Invariant and Covariant (GIC) treatment... more This is the first of a series of papers extending a Gauge Invariant and Covariant (GIC) treatment of kinetic theory in curved space-times to a treatment of Cosmic Background Radiation (CBR) temperature anisotropies arising from inhomogeneities in the early universe. This paper deals with algebraic issues, both generically and in the context of models linearised about Robertson-Walker geometries. The approach represents radiation anisotropies by Projected Symmetric and Trace-Free tensors. The Angular correlation functions for the mode coefficients are found in terms of these quantities, following the Wilson-Silk approach, but derived and dealt with in GIC form. The covariant multipole and mode-expanded angular correlation functions are related to the usual treatments in the literature. The GIC mode expansion is related to the coordinate approach by linking the Legendre functions to the Projected Symmetric Trace-free representation, using a covariant addition theorem for the tensors to generate the Legendre Polynomial recursion relation. This paper lays the foundation for further papers in the series, which use this formalism in a GIC approach to develop solutions of the Boltzmann and Liouville equations for the CBR before and after decoupling, thus providing a unified GIC derivation of the variety of approaches to CBR anisotropies in the current literature. 1
Transactions of the Royal Society of South Africa, 2021
Significant challenges exist globally regarding literacy teaching and learning. To address these ... more Significant challenges exist globally regarding literacy teaching and learning. To address these challenges, key features of how the brain works should be taken into account. First, perception is an active process based in detection of errors in hierarchical predictions of sensory data and action outcomes. Reading is a particular case of this non-linear predictive process. Second, emotions play a key role in underlying cognitive functioning, including oral and written language. Negative emotions undermine motivation to learn. Third, there is not the fundamental difference between listening/speaking and reading/writing often alleged on the basis of evolutionary arguments. Both are socio-cultural practices that are driven through the communication imperative of the social brain. Fourth, both listening and reading are contextually occurring pyscho-social practices of understanding, shaped by current knowledge and cultural contexts and practices. Fifth, the natural operation of the brain is not rule-based, as is supposed in the standard view of linguistics: it is prediction, based on statistical pattern recognition. This all calls into question narrow interpretations of the widely quoted "Simple View of Reading", which argues that explicit decoding is the necessary route to comprehension. One of the two neural routes to reading does not involve such explicit decoding processes, and can be activated from the earliest years. An integrated view of brain function reflecting the non-linear contextual nature of the reading process implies that an ongoing focus on personal meaning and understanding from the very beginning provides positive conditions for learning all aspects of reading and writing.
There has been much controversy over weak and strong emergence in physics and biology. As pointed... more There has been much controversy over weak and strong emergence in physics and biology. As pointed out by Phil Anderson in many papers, the existence of broken symmetries is the key to emergence of properties in much of solid state physics. By carefully distinguishing between different types of symmetry breaking and tracing the relation between broken symmetries at micro and macro scales, I demonstrate that the emergence of the properties of metals and semiconductors is a case of strong emergence. This is due to the existence of quasiparticles such as phonons. A second key case where symmetry breaking leads to strong emergence is the existence of the various arrows of time. Related arguments extend to demonstrating strong emergence in molecular biology, in this case due to the existence of time dependent constraint terms in the underlying Hamiltonian. Additionally I show that the processes of evolutionary emergence of living systems is also a case of strong emergence. A useful result emerges: standard physics theories and the emergent theories arising out of them are all effective theories that are equally valid.
We review current theoretical cosmology, including fundamental and mathematical cosmology and phy... more We review current theoretical cosmology, including fundamental and mathematical cosmology and physical cosmology (as well as cosmology in the quantum realm), with an emphasis on open questions.
Commonly used Acronyms used in this paper include: Cold dark matter (CDM). Cosmic microwave backg... more Commonly used Acronyms used in this paper include: Cold dark matter (CDM). Cosmic microwave background (CMB). Einstein field equations (EFE). Friedmann-Lemaítre-Robertson-Walker (FLRW). Gravitational waves (GW). General Relativity (GR). Large scale structure (LSS). Linear perturbation theory (LPT). Loop quantum cosmology (LQC). Loop quantum gravity (LQG). Primordial gravitational waves (PGW). Primordial non-Gaussianities (PNG). Quantum gravity (QG). 2 Except in the degenerate cases of spacetimes of constant curvature (de Sitter, anti-de Sitter and Minkowski spacetimes). Such universe models do not correspond to the real Universe, which has preferred world lines everywhere [1].
This is the first of a series of papers extending a Gauge Invariant and Covariant (GIC) treatment... more This is the first of a series of papers extending a Gauge Invariant and Covariant (GIC) treatment of kinetic theory in curved space-times to a treatment of Cosmic Background Radiation (CBR) temperature anisotropies arising from inhomogeneities in the early universe. This paper deals with algebraic issues, both generically and in the context of models linearised about Robertson-Walker geometries . The approach represents radiation anisotropies by Projected Symmetric and Trace-Free tensors. The Angular correlation functions for the mode coefficients are found in terms of these quantities, following the Wilson-Silk approach, but derived and dealt with in GIC form. The covariant multipole and mode-expanded angular correlation functions are related to the usual treatments in the literature. The GIC mode expansion is related to the coordinate approach by linking the Legendre functions to the Projected Symmetric Trace-free representation, using a covariant addition theorem for the tensors to generate the Legendre Polynomial recursion relation. This paper lays the foundation for further papers in the series, which use this formalism in a GIC approach to develop solutions of the Boltzmann and Liouville equations for the CBR before and after decoupling, thus providing a unified GIC derivation of the variety of approaches to CBR anisotropies in the current literature.
General relativity is a cornerstone of modern physics, and is of major importance in its applicat... more General relativity is a cornerstone of modern physics, and is of major importance in its applications to cosmology. Plebanski and Krasinski are experts in the field and in this 2006 book they provide a thorough introduction to general relativity, guiding the reader through complete derivations of the most important results. Providing coverage from a unique viewpoint, geometrical, physical and astrophysical properties of inhomogeneous cosmological models are all systematically and clearly presented, allowing the reader to follow and verify all derivations. For advanced undergraduates and graduates in physics and astronomy, this textbook will enable students to develop expertise in the mathematical techniques necessary to study general relativity.
Commonly used Acronyms used in this paper include: Cold dark matter (CDM). Cosmic microwave backg... more Commonly used Acronyms used in this paper include: Cold dark matter (CDM). Cosmic microwave background (CMB). Einstein field equations (EFE). Friedmann-Lemaítre-Robertson-Walker (FLRW). Gravitational waves (GW). General Relativity (GR). Large scale structure (LSS). Linear perturbation theory (LPT). Loop quantum cosmology (LQC). Loop quantum gravity (LQG). Primordial gravitational waves (PGW). Primordial non-Gaussianities (PNG). Quantum gravity (QG). 2 Except in the degenerate cases of spacetimes of constant curvature (de Sitter, anti-de Sitter and Minkowski spacetimes). Such universe models do not correspond to the real Universe, which has preferred world lines everywhere [1].
We model massive dark objects in galactic nuclei as spherically symmetric static naked singularit... more We model massive dark objects in galactic nuclei as spherically symmetric static naked singularities in the Einstein massless scalar field theory and study the resulting gravitational lensing in detail. Based on whether or not a naked singularity is covered within a photon sphere we classify naked singularities into two kinds: weakly naked ͑those contained within at least one photon sphere͒ and strongly naked ͑those not contained within any photon sphere͒. The qualitative features of gravitational lensing due to a weakly naked singularity are similar to those due to a Schwarzschild black hole ͑these give rise to one Einstein ring but no radial critical curve͒. However, the gravitational lensing due to a strongly naked singularity is qualitatively different from that due to a Schwarzschild black hole; a strongly naked singularity gives rise to either two or nil Einstein ring͑s͒ and one radial critical curve. A light ray passing close to a photon sphere of a black hole or a weakly naked singularity goes around its photon sphere once, twice, or many times ͑before reaching an observer͒ depending upon the impact parameter and thus gives rise to a sequence of theoretically infinite number of relativistic images, which are highly demagnified. A strongly naked singularity produces no relativistic images.
We develop a new approach to local nonlinear effects in cosmic microwave background anisotropies,... more We develop a new approach to local nonlinear effects in cosmic microwave background anisotropies, and discuss the qualitative features of these effects. New couplings of the baryonic velocity to radiation multipoles are found, arising from nonlinear Thomson scattering effects. We also find a new nonlinear shear effect on small angular scales. The full set of evolution and constraint equations is derived, including the nonlinear generalizations of the radiation multipole hierarchy, and of the dynamics of multi-fluids. These equations govern radiation anisotropies in any inhomogeneous spacetime, but their main application is to second-order effects in a universe that is close to the Friedmann models. Qualitative analysis is given here, and quantitative calculations are taken up in further papers. to appear Phys. Rev. D 59 (1999)
The use of proper \time" to describe classical \spacetimes" which contain both Euclidean and Lore... more The use of proper \time" to describe classical \spacetimes" which contain both Euclidean and Lorentzian regions permits the introduction of smooth (generalized) orthonormal frames. This remarkable fact permits one to describe both a variational treatment of Einstein's equations and distribution theory using straightforward generalizations of the standard treatments for constant signature.
What happens to a star when it dies? This is a very natural astronomical question, and various th... more What happens to a star when it dies? This is a very natural astronomical question, and various theories since the 1930s have been advanced towards answer- ing it. The theories predict supernovae, white dwarf stars, neutron stars and black holes. The first two are now ...
The photon sphere concept in Schwarzschild space-time is generalized to a definition of a photon ... more The photon sphere concept in Schwarzschild space-time is generalized to a definition of a photon surface in an arbitrary space-time. A photon sphere is then defined as an SO(3)xR-invariant photon surface in a static spherically symmetric space-time. It is proved, subject to an energy condition, that a black hole in any such space-time must be surrounded by a photon sphere. Conversely, subject to an energy condition, any photon sphere must surround a black hole, a naked singularity or more than a certain amount of matter. A second order evolution equation is obtained for the area of an SO(3)-invariant photon surface in a general non-static spherically symmetric space-time. Many examples are provided.
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Papers by George Ellis