The Schwarzschild Solution

2021 ◽  
pp. 162-199
Keyword(s):  
Schwarzschild Solution

Field equations in the neighbourhood of a particle in a conformal theory of gravitation. II

1969 ◽  
Vol 313 (1512) ◽  
pp. 71-82 ◽  
Keyword(s):  
Local Geometry ◽  
Field Equations ◽  
Schwarzschild Solution ◽  
Conformal Theory ◽  
Conformally Invariant ◽  
Coordinate Singularity ◽  
Previous Solution ◽  
Theory Of Gravitation ◽  
Spherically Symmetric Metric ◽  
Radial Variable

The field equations in the neighbourhood of a particle for a spherically symmetric metric in the conformal theory of gravitation put forward by Hoyle & Narlikar are examined. As the theory is conformally invariant, one can use different but physically equivalent conformal frames to study the equations. Previously these equations were studied in a conformal frame which, though suitable far away from the isolated particle, turns out not to be suitable in the neighbourhood of the particle. In the present paper a solution in a conformal frame is obtained that is suitable for considering regions near the particle. The solution thus obtained differs from the previous one in several respects. For example, it has no coordinate singularity for any non-zero value of the radial variable, unlike the previous solution or the Schwarzschild solution. It is also shown with the use of this solution that in this theory distant matter has an effect on local geometry.

scholarly journals Corners of gravity: the case of gravity as a constrained BF theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Remigiusz Durka ◽  
Jerzy Kowalski-Glikman
Keyword(s):  
Cosmological Constant ◽  
Boundary Structure ◽  
Schwarzschild Solution ◽  
Bf Theory ◽  
Theory Of Gravity

Abstract Following recent works on corner charges we investigate the boundary structure in the case of the theory of gravity formulated as a constrained BF theory. This allows us not only to introduce the cosmological constant, but also explore the influence of the topological terms present in the action of this theory. Established formulas for charges resemble previously obtained ones, but we show that they are affected by the presence of the cosmological constant and topological terms. As an example we discuss the charges in the case of the AdS-Schwarzschild solution and we find that the charges give correct values.

Universally stable black holes

2017 ◽  
Vol 26 (12) ◽  
pp. 1743024 ◽  
Author(s):  
Pablo Bueno ◽  
Pablo A. Cano
Keyword(s):  
Black Holes ◽  
Infinite Family ◽  
High Order ◽  
Schwarzschild Solution ◽  
Unitary Evolution ◽  
Thermodynamic Behavior ◽  
Hilbert Action

We argue that, when certain higher-curvature corrections are added to the four-dimensional Einstein–Hilbert action, black holes become stable below certain mass. We show this to be the case for an infinite family of ghost-free theories involving terms of arbitrarily high order in curvature. The thermodynamic behavior of the new black holes is universal for arbitrary values of the couplings, with the only exception of the Schwarzschild solution itself, which is recovered when all the couplings are set to zero. For this class of theories, the issue of non-unitary evolution is inexistent, as black holes never evaporate completely.

PHYSICAL ASPECTS OF SOLITONS IN (4+1) GRAVITY

1995 ◽  
Vol 04 (05) ◽  
pp. 639-659 ◽  
Author(s):  
ANDREW BILLYARD ◽  
PAUL S. WESSON ◽  
DIMITRI KALLIGAS
Keyword(s):  
Physical Properties ◽  
Extra Dimension ◽  
Dimensional Case ◽  
Schwarzschild Solution ◽  
Circular Orbits ◽  
Know How ◽  
Fifth Dimension ◽  
Klein Theory ◽  
Limiting Case ◽  
Kaluza Klein

The augmentation of general relativity’s spacetime by one or more dimensions is described by Kaluza-Klein theory and is within testable limits. Should an extra dimension be observable and significant, it would be beneficial to know how physical properties would differ from “conventional” relativity. In examining the class of five-dimensional solutions analogous to the four-dimensional Schwarzschild solution, we examine where the origin to the system is located and note that it can differ from the four-dimensional case. Furthermore, we study circular orbits and find that the 5D case is much richer; photons can have stable circular orbits in some instances, and stable orbits can exist right to the new origin in others. Finally, we derive both gravitational and inertial masses and find that they do not generally agree, although they can in a limiting case. For all three examinations, it is possible to obtain the four-dimensional results in one limiting case, that of the Schwarzschild solution plus a flat fifth dimension, and that the differences between 4D and 5D occur when the fifth dimension obtains any sort of significance.

scholarly journals Black Hole Interior from Loop Quantum Gravity

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Leonardo Modesto
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Event Horizon ◽  
Loop Quantum Gravity ◽  
Planck Scale ◽  
Semiclassical Analysis ◽  
Schwarzschild Solution ◽  
Quantum Black Hole ◽  
Minimum Value ◽  
Black Hole Interior

We calculate modifications to the Schwarzschild solution by using a semiclassical analysis of loop quantum black hole. We obtain a metric inside the event horizon that coincides with the Schwarzschild solution near the horizon but that is substantially different at the Planck scale. In particular, we obtain a bounce of theS2sphere for a minimum value of the radius and that it is possible to have another event horizon close to ther=0point.

scholarly journals Emergent GUP from modified Hawking radiation in Einstein–NED theory

2020 ◽  
Vol 98 (8) ◽  
pp. 801-809
Author(s):  
S. Hamid Mehdipour
Keyword(s):  
Hawking Radiation ◽  
Lagrangian Density ◽  
General Procedure ◽  
Generalized Uncertainty Principle ◽  
Energy Condition ◽  
Intrinsic Property ◽  
Hawking Temperature ◽  
Nonlinear Electrodynamics ◽  
Uncertainty Relations ◽  
Schwarzschild Solution

We present a general procedure for constructing exact black hole (BH) solutions with a magnetic charge in the context of nonlinear electrodynamics (NED) theory as well as in the coherent state approach to noncommutative geometry (NCG). In this framework, the Lagrangian density for a noncommutative Hayward BH is obtained and the weak energy condition is satisfied. The noncommutative Hayward solution depends on two kind of charges, without which the Schwarzschild solution is applicable. Moreover, to find a link between the BH evaporation and uncertainty relations, we may calculate the Hawking temperature and find the effect of the Lagrangian density of BHs on the Hawking radiation. Therefore, a generalized uncertainty principle (GUP) emerges from the modified Hawking temperature in Einstein–NED theory. The origin of this GUP is the combined influence of a nonlinear magnetic source and an intrinsic property of the manifold associated with a fictitious charge. Finally, we find that there is an upper bound on the Lagrangian uncertainty of the BHs that is caused by the NED field and (or) the fictitious charge.

scholarly journals Embedding spherical spacelike slices in a Schwarzschild solution

2005 ◽  
Vol 23 (2) ◽  
pp. 539-547 ◽  
Author(s):  
Niall Ó Murchadha ◽  
Krzysztof Roszkowski
Keyword(s):  
Schwarzschild Solution

A HAMILTONIAN TREATMENT OF FIVE-DIMENSIONAL KALUZA–KLEIN GRAVITY

2000 ◽  
Vol 09 (04) ◽  
pp. 445-458 ◽  
Author(s):  
W. N. SAJKO
Keyword(s):  
Total Mass ◽  
Soliton Solutions ◽  
Schwarzschild Solution ◽  
Coordinate Dependence ◽  
Klein Theory ◽  
The One ◽  
Induced Matter ◽  
Classical Derivation ◽  
Area Law ◽  
Kaluza Klein

We give a Hamiltonian treatment of 5D vacuum Kaluza–Klein theory that is unrestricted in the extra coordinate dependence. When the extra coordinate dependence is removed from the 5D metric we recover the Hamiltonian for gravity and electromagetism nonminimally coupled to a scalar field. The energies of 5D uncharged and charged soliton solutions are calculated via the Hamiltonian and are identified with the total mass. The expressions for the total mass are shown to agree with the sum of scalar and gravitational masses calculated from the scalar-tensor induced matter in 4D. A semi-classical derivation of the temperature for the uncharged solitons is calculated and it is shown that the only nontrivial member of the 5D class is the 4D Schwarzschild solution trivially embedded in 5D, and therefore the entropy obeys the one-quarter area law.

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