Spacetimes admitting appropriate spatial homothetic Killing vectors are called spatially homothet... more Spacetimes admitting appropriate spatial homothetic Killing vectors are called spatially homothetic spacetimes. Such spacetimes conform to the fact that gravity has no length-scale for matter inhomogeneities. The matter density for such spacetimes is (spatially) arbitrary and the matter generating the spacetime admits any equation of state. Spatially homothetic spacetimes necessarily possess energy-momentum fluxes. We first discuss spherically symmetric and axially symmetric examples of such spacetimes that do not form naked singularities for regular initial data. We then consider the most general spatially homothetic spacetime and show that the Cosmic Censorship Hypothesis is equivalent to the statement that gravity has no length-scale for matter properties.
We discuss here the significance of the generalization of the newtonian concept of force by that ... more We discuss here the significance of the generalization of the newtonian concept of force by that of a transformation of a certain Standard Borel Space of cardinality c of the continuum as the "cause" behind motions of material bodies that are representable as Borel measurable subsets of this space. This generalization forms the basis for a Universal Theory of Relativity in which, importantly, the fundamental physical constants can only arise from mutual relationships of the so-defined physical bodies. This Universal Relativity also has the potential to explain the quantum nature of the physical world.
In this letter, we outline an inhomogeneous model of the Big Bang cosmology. For the inhomogeneou... more In this letter, we outline an inhomogeneous model of the Big Bang cosmology. For the inhomogeneous spacetime used here, the universe originates in the infinite past as the one dominated by vacuum energy and ends in the infinite future as the one consisting of "hot and relativistic" matter. The spatial distribution of matter in the considered inhomogeneous spacetime is arbitrary. Hence, observed structures can arise in this cosmology from suitable "initial" density contrast. Different problems of the standard model of Big Bang cosmology are also resolved in the present inhomogeneous model. This inhomogeneous model of the Big Bang Cosmology predicts "hot death" for the universe.
In this work, we outline a new general relativistic cosmology. In this cosmology, the universe or... more In this work, we outline a new general relativistic cosmology. In this cosmology, the universe originates in the infinite past from sparsely distributed neutral matter and ends in the infinite future as a hot, relativistic plasma. The spatial distribution of matter on the "initial" hyper-surface is arbitrary. Hence, observed structures can arise in this cosmology from suitable "initial" density contrast. The red-shifts of different objects in this cosmology are indicative of their different states of collapse and need not possess any correlation to their distance from the observer. Further, the microwave background radiation arises in this cosmology as thermalized radiation from all the radiating matter in the universe. This cosmology predicts that the temperature of the microwave background increases with time. Thus, any conclusive evidence that the temperature of the Microwave Background Radiation was more in the past can falsify this cosmology.
In this paper, we consider the problems of spherical gravitational collapse and accretion using a... more In this paper, we consider the problems of spherical gravitational collapse and accretion using a spherically symmetric, spatially homothetic spacetime, that is, as an exact solution [7] of the field equations of general relativity. Properties of matter like its equation of state determine whether the collapse becomes unstoppable or not since the spacetime under consideration admits any equation of state for matter in it. We can therefore describe the formation of a semi-stable object here. A black hole may form in the unstoppable gravitational collapse and/or accretion but only as an infinite red-shift surface that is, however, not a null hyper-surface. Therefore, spherical, astrophysical black holes will always be of this type. This result will have important implications for observational astrophysics and other considerations in General Relativity based on the conception of black hole as a null hyper-surface.
We consider a spherically symmetric, Petrov-type D, spacetime with hyper-surface orthogonal, radi... more We consider a spherically symmetric, Petrov-type D, spacetime with hyper-surface orthogonal, radial, homothetic Killing vector. In this work, some general properties of this spacetime for nonsingular and non-degenerate data are presented. We also present the source-free electromagnetic fields in this spacetime. We then discuss general astrophysical relevance of the results obtained for this spacetime.
In this note, we discuss the significance of the general principle of relativity for a physical t... more In this note, we discuss the significance of the general principle of relativity for a physical theory that abandons the newtonian concept of force and, hence, uses an entirely different conception for the "cause" behind motions of material bodies.
It is well-known [1] that all black hole solutions of General Relativity are of Petrov-type D. It... more It is well-known [1] that all black hole solutions of General Relativity are of Petrov-type D. It may thus be expected that the spacetime of physically realizable spherical gravitational collapse is also of Petrov-type D. We show that a radially homothetic spacetime, ie, a spherically symmetric spacetime with hyper-surface orthogonal, radial, homothetic Killing vector, is of Petrov-type D. As has been argued in , it is a spacetime of physically realizable spherical collapse.
We show that the existence of appropriate spatial homothetic Killing vectors is directly related ... more We show that the existence of appropriate spatial homothetic Killing vectors is directly related to the separability of the metric functions for axially symmetric spacetimes. The density profile for such spacetimes is (spatially) arbitrary and admits any equation of state for the matter in the spacetime. When used for studying axisymmetric gravitational collapse, such solutions do not result in a locally naked singularity.
Gravity does not provide any scale for matter properties. We argue that this is also the implicat... more Gravity does not provide any scale for matter properties. We argue that this is also the implication of Mach's hypothesis of the relativity of inertia. The most general spacetime compatible with this property of gravity is that admitting three, independent spatial homothetic Killing vectors generating an arbitrary function of each one of the three spatial coordinates. The matter properties for such a spacetime are (spatially) arbitrary and the matter generating the spacetime admits any equation of state. This is also the most general spacetime containing the weak gravity physics in its entirety. This spacetime is machian in that it is globally degenerate for anti-machian situations such as vacuum, a single matter particle etc. and, hence, has no meaning in the absence of matter.
We argue that a particular spacetime, a spherically symmetric spacetime with hyper-surface orthog... more We argue that a particular spacetime, a spherically symmetric spacetime with hyper-surface orthogonal, radial, homothetic Killing vector, is a physically meaningful spacetime that describes the problem of spherical gravitational collapse in its full "physical" generality.
We show that all known naked singularities in spherically symmetric self-similar spacetimes arise... more We show that all known naked singularities in spherically symmetric self-similar spacetimes arise as a result of singular initial matter distribution. This is a result of the peculiarity of the coordinate transformation that takes these spacetimes into a separable form. Therefore, these examples of naked singularities are of no apparent consequence to astrophysical observations or theories.
If space is indistinguishable from the extension of a physical body, as is Descartes's conception... more If space is indistinguishable from the extension of a physical body, as is Descartes's conception, then transformations of space become transformations of physical bodies. Every point of space then has properties of physical bodies in some suitable non-singular sense of average over the space. Every point of space is then thinkable as a non-singular point particle possessing such (averaged) physical properties. Then, the location of such a point particle is, relative to another (similar) point particle, indeterminate over the extension of the physical body. Further, transformations of the space may "move" such a point particle in relation to another such point particle. These notions then provide a non-probabilistic explanation of Heisenberg's indeterminacy relations.
I summarize here the logic that leads us to a program for the Theory of the Total Field in Einste... more I summarize here the logic that leads us to a program for the Theory of the Total Field in Einstein's sense. The purpose is to show that this theory is a logical culmination of the developments of (fundamental) physical concepts and, hence, to initiate a discussion of these issues.
Spacetimes admitting appropriate spatial homothetic Killing vectors are called spatially homothet... more Spacetimes admitting appropriate spatial homothetic Killing vectors are called spatially homothetic spacetimes. Such spacetimes conform to the fact that gravity has no length-scale for matter inhomogeneities. The matter density for such spacetimes is (spatially) arbitrary and the matter generating the spacetime admits any equation of state. Spatially homothetic spacetimes necessarily possess energy-momentum fluxes. We first discuss spherically symmetric and axially symmetric examples of such spacetimes that do not form naked singularities for regular initial data. We then consider the most general spatially homothetic spacetime and show that the Cosmic Censorship Hypothesis is equivalent to the statement that gravity has no length-scale for matter properties.
We discuss here the significance of the generalization of the newtonian concept of force by that ... more We discuss here the significance of the generalization of the newtonian concept of force by that of a transformation of a certain Standard Borel Space of cardinality c of the continuum as the "cause" behind motions of material bodies that are representable as Borel measurable subsets of this space. This generalization forms the basis for a Universal Theory of Relativity in which, importantly, the fundamental physical constants can only arise from mutual relationships of the so-defined physical bodies. This Universal Relativity also has the potential to explain the quantum nature of the physical world.
In this letter, we outline an inhomogeneous model of the Big Bang cosmology. For the inhomogeneou... more In this letter, we outline an inhomogeneous model of the Big Bang cosmology. For the inhomogeneous spacetime used here, the universe originates in the infinite past as the one dominated by vacuum energy and ends in the infinite future as the one consisting of "hot and relativistic" matter. The spatial distribution of matter in the considered inhomogeneous spacetime is arbitrary. Hence, observed structures can arise in this cosmology from suitable "initial" density contrast. Different problems of the standard model of Big Bang cosmology are also resolved in the present inhomogeneous model. This inhomogeneous model of the Big Bang Cosmology predicts "hot death" for the universe.
In this work, we outline a new general relativistic cosmology. In this cosmology, the universe or... more In this work, we outline a new general relativistic cosmology. In this cosmology, the universe originates in the infinite past from sparsely distributed neutral matter and ends in the infinite future as a hot, relativistic plasma. The spatial distribution of matter on the "initial" hyper-surface is arbitrary. Hence, observed structures can arise in this cosmology from suitable "initial" density contrast. The red-shifts of different objects in this cosmology are indicative of their different states of collapse and need not possess any correlation to their distance from the observer. Further, the microwave background radiation arises in this cosmology as thermalized radiation from all the radiating matter in the universe. This cosmology predicts that the temperature of the microwave background increases with time. Thus, any conclusive evidence that the temperature of the Microwave Background Radiation was more in the past can falsify this cosmology.
In this paper, we consider the problems of spherical gravitational collapse and accretion using a... more In this paper, we consider the problems of spherical gravitational collapse and accretion using a spherically symmetric, spatially homothetic spacetime, that is, as an exact solution [7] of the field equations of general relativity. Properties of matter like its equation of state determine whether the collapse becomes unstoppable or not since the spacetime under consideration admits any equation of state for matter in it. We can therefore describe the formation of a semi-stable object here. A black hole may form in the unstoppable gravitational collapse and/or accretion but only as an infinite red-shift surface that is, however, not a null hyper-surface. Therefore, spherical, astrophysical black holes will always be of this type. This result will have important implications for observational astrophysics and other considerations in General Relativity based on the conception of black hole as a null hyper-surface.
We consider a spherically symmetric, Petrov-type D, spacetime with hyper-surface orthogonal, radi... more We consider a spherically symmetric, Petrov-type D, spacetime with hyper-surface orthogonal, radial, homothetic Killing vector. In this work, some general properties of this spacetime for nonsingular and non-degenerate data are presented. We also present the source-free electromagnetic fields in this spacetime. We then discuss general astrophysical relevance of the results obtained for this spacetime.
In this note, we discuss the significance of the general principle of relativity for a physical t... more In this note, we discuss the significance of the general principle of relativity for a physical theory that abandons the newtonian concept of force and, hence, uses an entirely different conception for the "cause" behind motions of material bodies.
It is well-known [1] that all black hole solutions of General Relativity are of Petrov-type D. It... more It is well-known [1] that all black hole solutions of General Relativity are of Petrov-type D. It may thus be expected that the spacetime of physically realizable spherical gravitational collapse is also of Petrov-type D. We show that a radially homothetic spacetime, ie, a spherically symmetric spacetime with hyper-surface orthogonal, radial, homothetic Killing vector, is of Petrov-type D. As has been argued in , it is a spacetime of physically realizable spherical collapse.
We show that the existence of appropriate spatial homothetic Killing vectors is directly related ... more We show that the existence of appropriate spatial homothetic Killing vectors is directly related to the separability of the metric functions for axially symmetric spacetimes. The density profile for such spacetimes is (spatially) arbitrary and admits any equation of state for the matter in the spacetime. When used for studying axisymmetric gravitational collapse, such solutions do not result in a locally naked singularity.
Gravity does not provide any scale for matter properties. We argue that this is also the implicat... more Gravity does not provide any scale for matter properties. We argue that this is also the implication of Mach's hypothesis of the relativity of inertia. The most general spacetime compatible with this property of gravity is that admitting three, independent spatial homothetic Killing vectors generating an arbitrary function of each one of the three spatial coordinates. The matter properties for such a spacetime are (spatially) arbitrary and the matter generating the spacetime admits any equation of state. This is also the most general spacetime containing the weak gravity physics in its entirety. This spacetime is machian in that it is globally degenerate for anti-machian situations such as vacuum, a single matter particle etc. and, hence, has no meaning in the absence of matter.
We argue that a particular spacetime, a spherically symmetric spacetime with hyper-surface orthog... more We argue that a particular spacetime, a spherically symmetric spacetime with hyper-surface orthogonal, radial, homothetic Killing vector, is a physically meaningful spacetime that describes the problem of spherical gravitational collapse in its full "physical" generality.
We show that all known naked singularities in spherically symmetric self-similar spacetimes arise... more We show that all known naked singularities in spherically symmetric self-similar spacetimes arise as a result of singular initial matter distribution. This is a result of the peculiarity of the coordinate transformation that takes these spacetimes into a separable form. Therefore, these examples of naked singularities are of no apparent consequence to astrophysical observations or theories.
If space is indistinguishable from the extension of a physical body, as is Descartes's conception... more If space is indistinguishable from the extension of a physical body, as is Descartes's conception, then transformations of space become transformations of physical bodies. Every point of space then has properties of physical bodies in some suitable non-singular sense of average over the space. Every point of space is then thinkable as a non-singular point particle possessing such (averaged) physical properties. Then, the location of such a point particle is, relative to another (similar) point particle, indeterminate over the extension of the physical body. Further, transformations of the space may "move" such a point particle in relation to another such point particle. These notions then provide a non-probabilistic explanation of Heisenberg's indeterminacy relations.
I summarize here the logic that leads us to a program for the Theory of the Total Field in Einste... more I summarize here the logic that leads us to a program for the Theory of the Total Field in Einstein's sense. The purpose is to show that this theory is a logical culmination of the developments of (fundamental) physical concepts and, hence, to initiate a discussion of these issues.
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Papers by Sanjay Wagh