Schwarzschild Field of a Proper Time Oscillator

Hawking–Bekenstein entropy formula seems to tell us that no quantum degrees of freedom can reside in the interior of a black hole. We suggest that this is a consequence of the fact that the volume of any interior sphere of finite surface area simply vanishes. Obviously, this is not the case in general relativity. However, we show that such a phenomenon does occur in various gravitational theories which admit a spontaneously induced general relativity. In such theories, due to a phase transition (one-parameter family degenerates) which takes place precisely at the would-have-been horizon, the recovered exterior Schwarzschild solution connects, by means of a self-similar transition profile, with a novel "hollow" interior exhibiting a vanishing spatial volume and a locally varying Newton constant. This constitutes the so-called "hollowgraphy" driven holography.

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Asymptotically flat vacuum solution in modified theory of Einstein’s gravity

The European Physical Journal C ◽

10.1140/epjc/s10052-019-7396-x ◽

2019 ◽

Vol 79 (10) ◽

Author(s):

Surajit Kalita ◽

Banibrata Mukhopadhyay

Keyword(s):

General Relativity ◽

Vacuum Solution ◽

Compact Objects ◽

Schwarzschild Solution ◽

Asymptotically Flat ◽

Symmetric Vacuum ◽

Theory Of Gravity ◽

Bound Orbits ◽

Vacuum Spacetime ◽

The Universe

Abstract A number of recent observations have suggested that the Einstein’s theory of general relativity may not be the ultimate theory of gravity. The f(R) gravity model with R being the scalar curvature turns out to be one of the best bet to surpass the general relativity which explains a number of phenomena where Einstein’s theory of gravity fails. In the f(R) gravity, behaviour of the spacetime is modified as compared to that of given by the Einstein’s theory of general relativity. This theory has already been explored for understanding various compact objects such as neutron stars, white dwarfs etc. and also describing evolution of the universe. Although researchers have already found the vacuum spacetime solutions for the f(R) gravity, yet there is a caveat that the metric does have some diverging terms and hence these solutions are not asymptotically flat. We show that it is possible to have asymptotically flat spherically symmetric vacuum solution for the f(R) gravity, which is different from the Schwarzschild solution. We use this solution for explaining various bound orbits around the black hole and eventually, as an immediate application, in the spherical accretion flow around it.

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Collisional Stellar Dynamics in General Relativity: An Overview

Symposium - International Astronomical Union ◽

10.1017/s0074180900147539 ◽

1985 ◽

Vol 113 ◽

pp. 323-325

Author(s):

Henry E. Kandrup

Keyword(s):

General Relativity ◽

Statistical Mechanics ◽

Stellar Dynamics ◽

Classical General Relativity ◽

Point Mass ◽

Radiative Effects ◽

Equilibrium Statistical Mechanics ◽

Covariant Approach ◽

Non Equilibrium

Recently, Israel and Kandrup (1984; Kandrup 1984 a,b,c,d) have formulated a new, manifestly covariant approach to non-equilibrium statistical mechanics in classical general relativity. The object here is to indicate how that formalism may be used to construct a theory of ‘collisional’ stellar dynamics, valid for a collection of point mass stars in the limit that incoherent radiative effects may be neglected.

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Strategies of motion under the black hole horizon

International Journal of Modern Physics D ◽

10.1142/s0218271820300037 ◽

2020 ◽

Vol 29 (03) ◽

pp. 2030003

Author(s):

A. V. Toporensky ◽

O. B. Zaslavskii

Keyword(s):

General Relativity ◽

Black Hole ◽

First Principles ◽

Proper Time ◽

Black Hole Horizon ◽

Schwarzschild Metric ◽

Peculiar Velocity ◽

Peculiar Velocities ◽

Visible Part ◽

Methodological Paper

In this methodological paper, we consider two problems an astronaut faces under the black hole horizon in the Schwarzschild metric. (1) How to maximize the survival proper time. (2) How to make a visible part of the outer universe as large as possible before hitting the singularity. Our consideration essentially uses the concept of peculiar velocities based on the “river model.” Let an astronaut cross the horizon from the outside. We reproduce from the first principles the known result that point (1) requires that an astronaut turn off the engine near the horizon and follow the path with the momentum equal to zero. We also show that point (2) requires maximizing the peculiar velocity of the observer. Both goals (1) and (2) require, in general, different strategies inconsistent with each other that coincide at the horizon only. The concept of peculiar velocities introduced in a direct analogy with cosmology and its application for the problems studied in this paper can be used in advanced general relativity courses.

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Equations of state of continuous matter in general relativity

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1970.0064 ◽

1970 ◽

Vol 316 (1524) ◽

pp. 1-28 ◽

Cited By ~ 33

Keyword(s):

General Relativity ◽

Equations Of State ◽

Proper Time ◽

World Line ◽

Time Lag ◽

Strain Tensor ◽

Rheological Behaviour ◽

Physical Constant ◽

Temperature History ◽

Lie Derivative

The invariant forms that equations of state of continuous matter may take in general relativity, when the rheological behaviour of matter at any event may depend on previous rheological states through which that matter has passed, are discussed. A complete set of variables, needed in the general case to specify the relevant information about the matter at event x i , is first obtained as a set of space-tensors and then as a set of four-tensors orthogonal to the four-velocity at x i . These variables represent proper measures of deformation history, mechanical-stress history, temperature history, proper-time lag and physical constants of the material. An unambiguous definition is given of a physical constant (tensor) of the material (equation (122)). Elasticity, viscosity, and all possible combinations of these properties are within the scope of the theory. A detailed discussion is included of the processes of differentiation and integration of tensor quantities with respect to proper-time, following a particle along its world-line, such as will occur in equations of state in the general case. A convected integral with respect to proper-time is expressed (in equation (111)) in terms of displacement functions X 'm , which relate events x i and x 'm on the world-line of the same particle (such that x 'm is earlier than x i by an interval of proper-time t—t' ) through equations x 'm = X 'm (x i , t — t' ) . A convected derivative with respect to proper-time is expressed (in equation (82)) in terms of a Lie derivative defined with respect to the velocity vector field. Successive convected differentiation of a finite-strain tensor, defined in relation to an arbitrary reference configuration of a material element, gives rise to a sequence of rate-of-strain tensors.

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Schwarzschild solution from Weyl transverse gravity

Modern Physics Letters A ◽

10.1142/s0217732317500225 ◽

2017 ◽

Vol 32 (03) ◽

pp. 1750022 ◽

Cited By ~ 4

Author(s):

Ichiro Oda

Keyword(s):

General Relativity ◽

Coordinate System ◽

Conformal Transformation ◽

Classical Solutions ◽

Cartesian Coordinate System ◽

Spacetime Dimension ◽

Schwarzschild Solution ◽

Classical Level ◽

Cartesian Coordinate ◽

Volume Preserving

We study classical solutions in the Weyl-transverse (WTDiff) gravity. The WTDiff gravity is invariant under both the local Weyl (conformal) transformation and the volume preserving diffeomorphisms (Diff) (transverse diffeomorphisms (TDiff)) and is known to be equivalent to general relativity at least at the classical level. In particular, we find that in a general spacetime dimension, the Schwarzschild metric is a classical solution in the WTDiff gravity when it is expressed in the Cartesian coordinate system.

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Measurable maximal energy and minimal time interval

Canadian Journal of Physics ◽

10.1139/cjp-2013-0661 ◽

2014 ◽

Vol 92 (10) ◽

pp. 1124-1129 ◽

Cited By ~ 3

Author(s):

Abdel Nasser Tawfik ◽

Eiman Abou El Dahab

Keyword(s):

General Relativity ◽

Large Scale ◽

Generalized Uncertainty Principle ◽

Time Interval ◽

Minimum Mass ◽

Schwarzschild Solution ◽

Maximal Energy ◽

Minimal Time ◽

Shortest Distance ◽

Planck Time

The possibility of finding the measurable maximal energy and the minimal time interval is discussed in different quantum aspects. It is found that the linear generalized uncertainty principle (GUP) approach gives a nonphysical result. Based on large scale Schwarzschild solution, the quadratic GUP approach is utilized. The calculations are performed at the shortest distance, at which the general relativity is assumed to be a good approximation for the quantum gravity and at larger distances, as well. It is found that both maximal energy and minimal time have the order of the Planck time. Then, the uncertainties in both quantities are accordingly bounded. Some physical insights are addressed. Also, the implications on the physics of early Universe and on quantized mass are outlined. The results are related to the existence of finite cosmological constant and minimum mass (mass quanta).

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