On super-massive objects without event horizon

Starting with the conceptual foundation of general relativity (GR) - equivalence principle, space-time geometry and special relativity, I train cross hairs on two characteristic predictions of GR - black holes and gravitational waves. These two consequences of GR have played a significant role in relativistic astrophysics, e.g. compact X-ray sources, quasars, blazars, coalescing binary pulsars, etc. With quantum theory wedded to GR, particle production from vacuum becomes a generic feature whenever event horizons are present. In this paper, I shall briefly discuss the fate of a `black hole atom' when Hawking radiation is taken into account. In the context of gravitational waves, I shall focus on the possible consequences of gravitational and electromagnetic radiation from highly magnetized and rapidly spinning white dwarfs. The discovery of RX J0648.0-4418 system - a WD in a binary with mass slightly over 1.2 $ M_{\odot}$, and rotating with spin period as short as 13.2 s, provides an impetus to revisit the problem of WD spin evolution due to energy loss.

2009

Cosmological observations indicate that the Einstein equation may not be entirely correct to describe gravity. However, numerous modifications of these equations usually do not affect foundations of the theory. In this paper two important issue that lead to a substantial revision of the theory are considered : 1. The significance of relativity of space-time geometry with respect to measuring instruments for theory of gravitation. 2. The gauge transformations of the field variables in correct theory of gravitation.

2001

It has shown that Einstein General Relativity can be expressed covariantly in a bi-metric spacetime context[1], without the uncertainties which arise from the effects of gravitational energy-momentum pseudotensors. We construct a new bi-metric General Relativity theory of gravitation in curved spacetime[2] , based on a new physical paradigm, which allows the operational procedure of local spacetime measurements in general spacetime frames of reference to be defined in a similar manner as that for local spacetime measurements in inertial Special Relativistic spacetime frames. The paradigm[3] accomplishes this by using the Principle of Equivalence to define the symmetric metric tensor of curved spacetime as an exponential function of a symmetric gravitational potential tensor. Since the metric tensor in the new bi-metric General Relativity theory is an exponential function of the gravitational potential tensor, we find that requiring the matter geodesic equations of motion to have an N-body interactive form implies that the gravitational potential tensor must obey a superposition principle. This requirement uniquely determines the field equations for the gravitational potential tensor in the theory. The structure of these field equations imply that , in addition to the matter energy-momentum tensor, a gravitational field stress-energy tensor appears in the right member of the Einstein field equations. A unique prediction of the new bi-metric General Relativity theory is that massive compact astrophysical objects have no event horizons and can manifest the existence of intrinsic dipole magnetic fields which can affect their accretion disks. [1] Rosen, N., (1963), Annals of Physics, vol 22, pg 1 [2] Leiter, D.J., and Robertson ,S.L., LANL, arXiv.org, eprint, gr-qc/0101025 [3] Yilmaz , H., (1981), International Journal of Theo. Phys., vol 21, No's,10/11, pg 871

2006

The black hole paradigm (BHP) is based on an implicit assumption that the collapse occurs quickly not only on proper times of falling particles, but on world time also, and that information about that is retarded only. According to general relativity (GR) in a static field there is a global simultaneity of events, the proper times are slowed down with respect to world time absolutely and these facts are confirmed experimentally by clocks long-term located at different heights. Therefore, the basic assumption of BHP is incompatible with GR, the collapse occurs not quickly, but it needs in really infinity world time. For a falling particle at any finite world time moment its corresponding proper time moment is insufficient for reaching the gravitational radius of the source. As the result, in GR real horizons and physical singularities do not exist, the black holes never be formed. Instead of the black holes GR predicts the gravitationally-frozen states of matter in superdense and supermassive objects. Particles inside of any compact object are frozen by the strong gravitational field so that the time dilation is finite, but maximal at the center and minimal on the surface. In cosmology this fact solves the problem of an initial singularity, in astrophysics allows one to construct a theory of superdense stars, quasars and AGN, in particle physics leads to the ultraviolet finiteness of quantum fields, including quantum gravity.

arXiv (Cornell University), 2012

We study some exact and approximate solutions of Einstein's equations that can be used to describe the gravitational field of astrophysical compact objects in the limiting case of slow rotation and slight deformation. First, we show that none of the standard models obtained by using Fock's method can be used as an interior source for the approximate exterior Kerr solution. We then use Fock's method to derive a generalized interior solution, and also an exterior solution that turns out to be equivalent to the exterior Hartle-Thorne approximate solution that, in turn, is equivalent to an approximate limiting case of the exact Quevedo-Mashhoon solution. As a result we obtain an analytic approximate solution that describes the interior and exterior gravitational field of a slowly rotating and slightly deformed astrophysical object.

These lecture notes have been prepared as a rapid introduction to Einstein's General Theory of Relativity. Consequently, I have restricted to the standard four dimensional, metric theory of gravity with no torsion. A basic exposure to geometrical notions of tensors, their algebra and calculus, Riemann-Christoffel connection, curvature tensors, etc has been presupposed being covered by other lecturers. Given the time constraint, the emphasis is on explaining the concepts and the physical ideas. Calculational details and techniques have largely been given reference to. The First two lectures discuss the arguments leading to the beautiful synthesis of the idea of space-time geometry, the relativity of observers and the phenomenon of gravity. Heuristic 'derivations' of the Einstein Field equations are presented and some of their mathematical properties are discussed. The (simplest) Schwarzschild solution is presented. The next lecture discusses the standard solar system tests of Einstein's theory. The fourth lecture returns to static, spherically symmetric solutions namely the interiors of stars. This topic is discussed both to illustrate how non-vacuum solutions are constructed, how the Einstein's gravity affects stellar equilibria and hold out the possibility of complete, un-stoppable gravitational collapse. The concept of a black hole is introduced via the example of the Schwarzschild solution with the possibility of a physical realization justified by the interior solution. The fifth lecture describes the Kerr-Newman family of black holes. More general (nonstationary) black holes are defined and the laws of black hole mechanics are introduced. Their analogy with the laws of thermodynamics is discussed. This topic is of importance because it provides an arena from where the glimpses of interaction of GR and quantum theory can be hoped for. The cosmos is too large and too real to be ignored. So the last lecture is devoted to a view of the standard cosmology. Some additional material is included in an appendix. A collection of exercises meant for practice are also included.

2018

A general theory of relativity is formulated without Einstein's equation. Einstein's tensor ties the space metric to the stress-energy tensor of a gravitational field. A homogeneous isotropic field metric is under consideration. In particular, the metric for a homogeneous isotropic universe possesses the anticipated density of our own universe. The speed of time progression at a distance from the observer slows according to an acceleration law asymptotically equal to Hubble's Law. A continuous field is homogeneous within the limits of small domains. This makes it possible to write a metric for a general continuous field and the single parameter given by the wave equation. The Schwarzschild problem has a continuous solution for r > 0. This solution approaches the Schwarzschild solution beyond the Schwarzschild radius and a second solution is obtained from the Schwarzschild problem-a stationary, expulsive, self-consistent field.

Many previous attempts have been undertaken to produce a singularity-free solution to the black hole problem. This effort included many " Bardeen black hole " models, as well as quantum mechanical, and string theory models. The present paper describes a new solution based on a relativistic extension of Newton-Galileo physics, termed Information Relativity theory. For a purely gravitational, spherical black hole, the theory yields a black hole radius that equals the Schwarzschild radius, but without an interior singularity. Moreover, for a typical galaxy with a supermassive black hole residing at its center, the model produces a simple expression for the galaxy's dynamics in its dependence on redshift. According to the emerging dynamics, a galaxy's supermassive black hole is part of a binary system, together with a naked singularity at redshift z = 2-1/2 ≈ 0.707, suspected to be a quasar with extreme velocity offsets or an active galactic nucleus (AGN). Another redshift, z ≈ 2.078, is also predicted to be associated with quasars and AGNs. The derived results are contrasted with observational data and with a recent ΛCDM model. Taken together, the produced galaxy dynamics and the aforementioned results could shed some light on the role of supermassive black holes in the evolution of the galaxies in which they reside. The success of Information Relativity in reproducing the Schwarzschild radius of black holes, together with previous successful predictions of the phenomena of light bending, gravitational redshift, dark matter, and dark energy, attest the possibility of constructing a simple cosmology, based only on physical variables, without the notion of space time and its geodesics.

2015

A new integration condition for Einstein’s field equations is found in the static case of a spherical body with mass density ()rρ and radius R. Taking the metric as 2 2 2 2 2 2d d d ds e c t e r e rν λ σ = − − Ω, with 2d ( d) / = ×r r rΩ, the condition is 0ν + σ =. It allows the metric functions ( , ,)ν λ σ to be expressed in terms of a single potential function,Φ, which satisfies a Poisson-type equation with Euclidian coefficients. The source of the field is entirely located inside the body and contains explicitly the gravitational energy. The integration condition may be interpreted in terms of a gauge condition of a generalized De Donder-Rosen-Fock type. Among the characteristic features of the potentialΦ, we point out the compliance with the point-like black hole and with the existence of a finite pressure for.constρ = and R → ∞ , namely 2 / 2p c = ρ. Thus, a solution of the famous Seeliger’s Paradox, of the divergent cosmical pressure, is given in the framework of General Relat...