Generalisation for regular black holes on general relativity to f(R) gravity

The central theme of this thesis is the study and analysis of black hole mimickers. The concept of a black hole mimicker is introduced, and various mimicker spacetime models are examined within the framework of classical general relativity. The mimickers examined fall into the classes of regular black holes and traversable wormholes under spherical symmetry. The regular black holes examined can be further categorised as static spacetimes, however the traversable wormhole is allowed to have a dynamic (non-static) throat. Astrophysical observables are calculated for a recently proposed regular black hole model containing an exponential suppression of the Misner-Sharp quasi-local mass. This same regular black hole model is then used to construct a wormhole via the "cut-and-paste" technique. The resulting wormhole is then analysed within the Darmois-Israel thin-shell formalism, and a linearised stability analysis of the (dynamic) wormhole throat is undertaken. Yet another regular black hole model spacetime is proposed, extending a previous work which attempted to construct a regular black hole through a quantum "deformation" of the Schwarzschild spacetime. The resulting spacetime is again analysed within the framework of classical general relativity. In addition to the study of black hole mimickers, I start with a brief overview of the theory of special relativity where a new and novel result is presented for the combination of relativistic velocities in general directions using quaternions. This is succeed by an introduction to concepts in differential geometry needed for the successive introduction to the theory of general relativity. A thorough discussion of the concept of spacetime singularities is then provided, before analysing the specific black hole mimickers discussed above.

Construction of regular black holes in general relativity

Physical Review D ◽

10.1103/physrevd.94.124027 ◽

2016 ◽

Vol 94 (12) ◽

Cited By ~ 73

Author(s):

Zhong-Ying Fan ◽

Xiaobao Wang

Keyword(s):

Black Holes ◽

General Relativity ◽

Regular Black Holes

Traversable Wormholes, Regular Black Holes, and Black-Bounces

10.26686/wgtn.17136212 ◽

2021 ◽

Author(s):

◽

Alexander Simpson

Keyword(s):

Black Holes ◽

General Relativity ◽

Black Hole ◽

Einstein Equations ◽

Time Dependent ◽

Alternative Theories Of Gravity ◽

Regular Black Hole ◽

Traversable Wormhole ◽

Regular Black Holes ◽

Traversable Wormholes

Various spacetime candidates for traversable wormholes, regular black holes, and ‘black-bounces’ are presented and thoroughly explored in the context of the gravitational theory of general relativity. All candidate spacetimes belong to the mathematically simple class of spherically symmetric geometries; the majority are static (time-independent as well as nonrotational), with a single dynamical (time-dependent) geometry explored. To the extent possible, the candidates are presented through the use of a global coordinate patch – some of the prior literature (especially concerning traversable wormholes) has often proposed coordinate systems for desirable solutions to the Einstein equations requiring a multi-patch atlas. The most interesting cases include the so-called ‘exponential metric’ – well-favoured by proponents of alternative theories of gravity but which actually has a standard classical interpretation, and the ‘black-bounce’ to traversable wormhole case – where a metric is explored which represents either a traversable wormhole or a regular black hole, depending on the value of the newly introduced scalar parameter a. This notion of ‘blackbounce’ is defined as the case where the spherical boundary of a regular black hole forces one to travel towards a one-way traversable ‘bounce’ into a future reincarnation of our own universe. The metric of interest is then explored further in the context of a time-dependent spacetime, where the line element is rephrased with a Vaidya-like time-dependence imposed on the mass of the object, and in terms of outgoing/ingoing EddingtonFinkelstein coordinates. Analysing these candidate spacetimes extends the pre-existing discussion concerning the viability of non-singular black hole solutions in the context of general relativity, as well as contributing to the dialogue on whether an arbitrarily advanced civilization would be able to construct a traversable wormhole.

On Regular Black Holes at Finite Temperature

Advances in High Energy Physics ◽

10.1155/2020/5712084 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

S. C. Ulhoa ◽

E. P. Spaniol ◽

R. Gomes ◽

A. F. Santos ◽

A. E. Santana

Keyword(s):

Black Holes ◽

General Relativity ◽

Event Horizon ◽

Finite Temperature ◽

Casimir Effect ◽

First Law Of Thermodynamics ◽

Regular Black Holes ◽

Thermo Field Dynamics ◽

Gravitational Entropy ◽

Boltzmann Law

The Thermo Field Dynamics (TFD) formalism is used to investigate the regular black holes at finite temperature. Using the Teleparalelism Equivalent to General Relativity (TEGR), the gravitational Stefan-Boltzmann law and the gravitational Casimir effect at zero and finite temperature are calculated. In addition, the first law of thermodynamics is considered. Then, the gravitational entropy and the temperature of the event horizon of a class of regular black holes are determined.

Comment on “Generic rotating regular black holes in general relativity coupled to nonlinear electrodynamics”

Physical Review D ◽

10.1103/physrevd.96.128502 ◽

2017 ◽

Vol 96 (12) ◽

Cited By ~ 10

Author(s):

Manuel E. Rodrigues ◽

Ednaldo L. B. Junior

Keyword(s):

Black Holes ◽

General Relativity ◽

Nonlinear Electrodynamics ◽

Regular Black Holes

Comment on “Construction of regular black holes in general relativity”

Physical Review D ◽

10.1103/physrevd.96.128501 ◽

2017 ◽

Vol 96 (12) ◽

Cited By ~ 16

Author(s):

Kirill A. Bronnikov

Keyword(s):

Black Holes ◽

General Relativity ◽

Regular Black Holes

Test particle orbits around regular black holes in general relativity combined with nonlinear electrodynamics

Physical Review D ◽

10.1103/physrevd.101.104045 ◽

2020 ◽

Vol 101 (10) ◽

Cited By ~ 6

Author(s):

Javlon Rayimbaev ◽

Marcos Figueroa ◽

Zdeněk Stuchlík ◽

Bakhtinur Juraev

Keyword(s):

Black Holes ◽

General Relativity ◽

Test Particle ◽

Nonlinear Electrodynamics ◽

Regular Black Holes ◽

Particle Orbits

Mimicking Black Holes in General Relativity

10.26686/wgtn.14361101 ◽

2021 ◽

Author(s):

Thomas Berry

Keyword(s):

Black Holes ◽

General Relativity ◽

Black Hole ◽

Thin Shell ◽

Classical General Relativity ◽

Regular Black Hole ◽

Regular Black Holes ◽

Traversable Wormholes ◽

Hole Model ◽

Linearised Stability

The central theme of this thesis is the study and analysis of black hole mimickers. The concept of a black hole mimicker is introduced, and various mimicker spacetime models are examined within the framework of classical general relativity. The mimickers examined fall into the classes of regular black holes and traversable wormholes under spherical symmetry. The regular black holes examined can be further categorised as static spacetimes, however the traversable wormhole is allowed to have a dynamic (non-static) throat. Astrophysical observables are calculated for a recently proposed regular black hole model containing an exponential suppression of the Misner-Sharp quasi-local mass. This same regular black hole model is then used to construct a wormhole via the "cut-and-paste" technique. The resulting wormhole is then analysed within the Darmois-Israel thin-shell formalism, and a linearised stability analysis of the (dynamic) wormhole throat is undertaken. Yet another regular black hole model spacetime is proposed, extending a previous work which attempted to construct a regular black hole through a quantum "deformation" of the Schwarzschild spacetime. The resulting spacetime is again analysed within the framework of classical general relativity. In addition to the study of black hole mimickers, I start with a brief overview of the theory of special relativity where a new and novel result is presented for the combination of relativistic velocities in general directions using quaternions. This is succeed by an introduction to concepts in differential geometry needed for the successive introduction to the theory of general relativity. A thorough discussion of the concept of spacetime singularities is then provided, before analysing the specific black hole mimickers discussed above.

Traversable Wormholes, Regular Black Holes, and Black-Bounces

10.26686/wgtn.17136212.v1 ◽

2021 ◽

Author(s):

◽

Alexander Simpson

Keyword(s):

Black Holes ◽

General Relativity ◽

Black Hole ◽

Einstein Equations ◽

Time Dependent ◽

Alternative Theories Of Gravity ◽

Regular Black Hole ◽

Traversable Wormhole ◽

Regular Black Holes ◽

Traversable Wormholes

Various spacetime candidates for traversable wormholes, regular black holes, and ‘black-bounces’ are presented and thoroughly explored in the context of the gravitational theory of general relativity. All candidate spacetimes belong to the mathematically simple class of spherically symmetric geometries; the majority are static (time-independent as well as nonrotational), with a single dynamical (time-dependent) geometry explored. To the extent possible, the candidates are presented through the use of a global coordinate patch – some of the prior literature (especially concerning traversable wormholes) has often proposed coordinate systems for desirable solutions to the Einstein equations requiring a multi-patch atlas. The most interesting cases include the so-called ‘exponential metric’ – well-favoured by proponents of alternative theories of gravity but which actually has a standard classical interpretation, and the ‘black-bounce’ to traversable wormhole case – where a metric is explored which represents either a traversable wormhole or a regular black hole, depending on the value of the newly introduced scalar parameter a. This notion of ‘blackbounce’ is defined as the case where the spherical boundary of a regular black hole forces one to travel towards a one-way traversable ‘bounce’ into a future reincarnation of our own universe. The metric of interest is then explored further in the context of a time-dependent spacetime, where the line element is rephrased with a Vaidya-like time-dependence imposed on the mass of the object, and in terms of outgoing/ingoing EddingtonFinkelstein coordinates. Analysing these candidate spacetimes extends the pre-existing discussion concerning the viability of non-singular black hole solutions in the context of general relativity, as well as contributing to the dialogue on whether an arbitrarily advanced civilization would be able to construct a traversable wormhole.