scholarly journals Integrability of particle motion and scalar field propagation in Kerr-(anti-) de Sitter black hole spacetimes in all dimensions

2005 ◽  
Vol 72 (12) ◽  
Author(s):  
Muraari Vasudevan ◽  
Kory A. Stevens
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Particle Motion ◽  
De Sitter ◽  
Black Hole Spacetimes

Cylindrically symmetric unimodular f(R) black holes

2021 ◽  
pp. 2150101
Author(s):  
Hüseyi̇n Aydın ◽  
Meli̇s Ulu Dog̃ru
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Equations Of Motion ◽  
Energy Conditions ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
De Sitter ◽  
Field Equations ◽  
Black Hole Spacetimes ◽  
Cylindrically Symmetric

In this paper, we examine massless scalar field by using unimodular [Formula: see text] theory. It is taken into account unimodular and cylindrically symmetric spacetime which provides convenience in researching black hole. The field equations in unimodular [Formula: see text] theory for given spacetime with massless scalar field and additional Bianchi identities are solved. Cylindrically symmetric anti-de Sitter (AdS)–Schwarzschild-like and AdS–Reissner–Nordström-like black hole spacetimes are achieved. Equations of motion are derived by using Hamiltonian. Orbits of massless test particles are depicted. Obtained line element asymptotically converges to dS/AdS spacetime. Weak and strong energy conditions of the massless scalar field are obtained with Raychaudhuri equations in unimodular [Formula: see text] theory. Also, stiff fluid interpretation of scalar field is reviewed.

scholarly journals Quasi-normal modes and the area spectrum of a near extremal de Sitter black hole with conformally coupled scalar field

2015 ◽  
Vol 30 (11) ◽  
pp. 1550057 ◽  
Author(s):  
Sharmanthie Fernando
Keyword(s):  
Black Hole ◽  
Wave Equation ◽  
Scalar Field ◽  
Normal Modes ◽  
Type Equation ◽  
Area Spectrum ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
De Sitter ◽  
Quasi Normal Mode

In this paper, we have studied a black hole in de Sitter space which has a conformally coupled scalar field in the background. This black hole is also known as the MTZ black hole. We have obtained exact values for the quasi-normal mode (QNM) frequencies under massless scalar field perturbations. We have demonstrated that when the black hole is near-extremal, that the wave equation for the massless scalar field simplifies to a Schrödinger type equation with the well-known Pöschl–Teller potential. We have also used sixth-order WKB approximation to compute QNM frequencies to compare with exact values obtained via the Pöschl–Teller method for comparison. As an application, we have obtained the area spectrum using modified Hods approach and show that it is equally spaced.

scholarly journals THE REAL SCALAR FIELD EQUATION FOR NARIAI BLACK HOLE IN THE 5D SCHWARZSCHILD–DE SITTER BLACK STRING SPACE

2007 ◽  
Vol 22 (24) ◽  
pp. 4451-4465 ◽  
Author(s):  
MOLIN LIU ◽  
HONGYA LIU ◽  
CHUNXIAO WANG ◽  
YONGLI PING
Keyword(s):  
Black Hole ◽  
Field Equation ◽  
Scalar Field ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
De Sitter ◽  
Black String ◽  
Transmission Coefficients ◽  
Scalar Field Equation ◽  
Continuous Potential

The Nariai black hole, whose two horizons are lying close to each other, is an extreme and important case in the research of black hole. In this paper we study the evolution of a massless scalar field scattered around in 5D Schwarzschild–de Sitter black string space. Using the method shown by Brevik and Simonsen (2001) we solve the scalar field equation as a boundary value problem, where real boundary condition is employed. Then with convenient replacement of the 5D continuous potential by square barrier, the reflection and transmission coefficients (R, T) are obtained. At last, we also compare the coefficients with the usual 4D counterpart.

The entropy evolution of a Schwarzschild–(Anti) de Sitter black hole

2020 ◽  
Vol 29 (07) ◽  
pp. 2050048
Author(s):  
Xin-Yang Wang ◽  
Yi-Ru Wang ◽  
Wen-Biao Liu
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Scalar Field ◽  
Hawking Radiation ◽  
Dynamical Variable ◽  
De Sitter ◽  
The One ◽  
Definition Of ◽  
Spherically Symmetry ◽  
Interior Volume

Based on the definition of the interior volume of spherically symmetry black holes, the interior volume of Schwarzschild–(Anti) de Sitter black holes is calculated. It is shown that with the cosmological constant ([Formula: see text]) increasing, the changing behaviors of both the position of the largest hypersurface and the interior volume for the Schwarzschild–Anti de Sitter black hole are the same as the Schwarzschild–de Sitter black hole. Considering a scalar field in the interior volume and Hawking radiation with only energy, the evolution relation between the scalar field entropy and Bekenstein–Hawking entropy is constructed. The results show that the scalar field entropy is approximately proportional to Bekenstein–Hawking entropy during Hawking radiation. Meanwhile, the proportionality coefficient is also regarded as a constant approximately with the increasing [Formula: see text]. Furthermore, considering [Formula: see text] as a dynamical variable, the modified Stefan–Boltzmann law is proposed which can be used to describe the variation of both the mass and [Formula: see text] under Hawking radiation. Using this modified law, the evolution relation between the two types of entropy is also constructed. The results show that the coefficient for Schwarzschild–de Sitter black holes is closer to a constant than the one for Schwarzschild–Anti de Sitter black holes during the evaporation process. Moreover, we find that for Hawking radiation carrying only energy, the evolution relation is a special case compared with the situation that the mass and [Formula: see text] are both considered as dynamical variables.

scholarly journals Energy of test objects on black hole spacetimes: A brief review

2015 ◽  
Vol 24 (14) ◽  
pp. 1550103 ◽  
Author(s):  
Alejandro Corichi
Keyword(s):  
Black Hole ◽  
Asymptotic Region ◽  
Gravitational Potential Energy ◽  
De Sitter ◽  
Conservation Of Energy ◽  
Asymptotically Flat ◽  
Black Hole Spacetimes ◽  
Test Particles ◽  
Exterior Regions ◽  
Test Objects

In this paper, we review the issue of defining energy for test particles on a background stationary spacetime. We revisit different notions of energy as defined by different observers. As is well-known, the existence of a timelike isometry allows for the notion of total conserved energy to be well defined. We use this well-known quantity to show that a gravitational potential energy can be consistently defined. As examples, we study the case of the exterior regions of an asymptotically flat black hole and of the [Formula: see text] Schwarzschild–de Sitter (SdS) case, where an asymptotic region is not available. We then consider the situation in which the test particle is absorbed by the black hole and analyze the energetics in detail. In particular, we show that the notion of horizon energy as defined by the isolated horizons formalism provides a satisfactory notion of energy compatible with the particle’s total conserved energy. With these choices, there is a global conservation of energy. Finally, we comment on a recent proposal to define energy of the black hole as seen by a nearby observer at rest, for which this feature is lost.

scholarly journals Extreme gravitational lensing in vicinity of Schwarzschild-de Sitter black holes

Open Physics ◽  
2007 ◽  
Vol 5 (4) ◽  
Author(s):  
Pavel Bakala ◽  
Petr Čermák ◽  
Stanislav Hledík ◽  
Zdeněk Stuchlík ◽  
Kamila Truparová
Keyword(s):  
Black Hole ◽  
Cosmological Constant ◽  
Gravitational Lensing ◽  
High Performance ◽  
Computer Code ◽  
De Sitter ◽  
Simulation Code ◽  
Black Hole Spacetimes ◽  
Optical Projection ◽  
Free Falling

AbstractWe have developed a realistic, fully general relativistic computer code to simulate optical projection in a strong, spherically symmetric gravitational field. The standard theoretical analysis of optical projection for an observer in the vicinity of a Schwarzschild black hole is extended to black hole spacetimes with a repulsive cosmological constant, i.e, Schwarzschild-de Sitterspacetimes. Influence of the cosmological constant is investigated for static observers and observers radially free-falling from the static radius. Simulations include effects of the gravitational lensing, multiple images, Doppler and gravitational frequency shift, as well as the intensity amplification. The code generates images of the sky for the static observer and a movie simulations of the changing sky for the radially free-falling observer. Techniques of parallel programming are applied to get a high performance and a fast run of the BHC simulation code.

Geometry of Black Holes

2020 ◽  
Author(s):  
Piotr T. Chruściel
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Einstein Equations ◽  
De Sitter ◽  
Black Hole Spacetimes ◽  
Local Coordinates ◽  
The Subject ◽  
Basic Facts ◽  
Kaluza Klein

There exists a large scientific literature on black holes, including many excellent textbooks of various levels of difficulty. However, most of these prefer physical intuition to mathematical rigour. The object of this book is to fill this gap and present a detailed, mathematically oriented, extended introduction to the subject. The first part of the book starts with a presentation, in Chapter 1, of some basic facts about Lorentzian manifolds. Chapter 2 develops those elements of Lorentzian causality theory which are key to the understanding of black-hole spacetimes. We present some applications of the causality theory in Chapter 3, as relevant for the study of black holes. Chapter 4, which opens the second part of the book, constitutes an introduction to the theory of black holes, including a review of experimental evidence, a presentation of the basic notions, and a study of the flagship black holes: the Schwarzschild, Reissner–Nordström, Kerr, and Majumdar–Papapetrou solutions of the Einstein, or Einstein–Maxwell, equations. Chapter 5 presents some further important solutions: the Kerr–Newman–(anti-)de Sitter black holes, the Emperan–Reall black rings, the Kaluza–Klein solutions of Rasheed, and the Birmingham family of metrics. Chapters 6 and 7 present the construction of conformal and projective diagrams, which play a key role in understanding the global structure of spacetimes obtained by piecing together metrics which, initially, are expressed in local coordinates. Chapter 8 presents an overview of known dynamical black-hole solutions of the vacuum Einstein equations.

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