scholarly journals Higher Dimensional Rotating Black Hole Solutions in Quadratic f(R) Gravitational Theory and the Conserved Quantities

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 358
Author(s):  
Gamal G. L. Nashed ◽  
Kazuharu Bamba
Keyword(s):  
Black Hole ◽  
Gravitational Theory ◽  
Thermodynamic Quantities ◽  
Conserved Quantities ◽  
Dimensional Parameter ◽  
Dimensional Spacetime ◽  
Higher Dimensional ◽  
Physics Of Black Holes ◽  
The Stability ◽  
Black Hole Solutions

We explore the quadratic form of the f(R)=R+bR2 gravitational theory to derive rotating N-dimensions black hole solutions with ai,i≥1 rotation parameters. Here, R is the Ricci scalar and b is the dimensional parameter. We assumed that the N-dimensional spacetime is static and it has flat horizons with a zero curvature boundary. We investigated the physics of black holes by calculating the relations of physical quantities such as the horizon radius and mass. We also demonstrate that, in the four-dimensional case, the higher-order curvature does not contribute to the black hole, i.e., black hole does not depend on the dimensional parameter b, whereas, in the case of N>4, it depends on parameter b, owing to the contribution of the correction R2 term. We analyze the conserved quantities, energy, and angular-momentum, of black hole solutions by applying the relocalization method. Additionally, we calculate the thermodynamic quantities, such as temperature and entropy, and examine the stability of black hole solutions locally and show that they have thermodynamic stability. Moreover, the calculations of entropy put a constraint on the parameter b to be b<116Λ to obtain a positive entropy.

scholarly journals Charged spherically symmetric Taub–NUT black hole solutions in $f(R)$ gravity

2020 ◽  
Vol 2020 (4) ◽  
Author(s):  
G G L Nashed ◽  
Kazuharu Bamba
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Free Energy ◽  
Black Hole Solution ◽  
Energy Conditions ◽  
Thermodynamic Quantities ◽  
Spherically Symmetric ◽  
Dimensional Parameter ◽  
Charged Black Holes ◽  
Black Hole Solutions

Abstract $f(R)$ theory is a modification of Einstein’s general relativity which has provided many interesting results in cosmology and astrophysics. To derive a black hole solution in this theory is difficult due to the fact that it contains fourth-order differential equations. In this study, we use the first reliable deviation from general relativity which is given by the quadratic form of $f(R)=R+\beta R^2$, where $\beta$ is a dimensional parameter. We calculate the energy conditions of charged black holes and show that they are all satisfied for the Taub–NUT spacetime. Finally, we study some thermodynamic quantities such as entropy, temperature, specific heat, and Gibbs free energy. The calculations of heat capacity and free energy show that the charged Taub–NUT black hole has positive values, which means that it has thermal stability.

Lovelock black holes in the presence of nonlinear electrodynamics

2015 ◽  
Vol 24 (06) ◽  
pp. 1550040 ◽  
Author(s):  
Seyed Hossein Hendi
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Nonlinear Electrodynamics ◽  
Thermodynamic Quantities ◽  
De Sitter ◽  
Maxwell Theory ◽  
Hole Radius ◽  
Higher Dimensional ◽  
Effective Cosmological Constant ◽  
Black Hole Solutions

In this paper, we consider third-order Lovelock–Maxwell gravity with additional (Fμν Fμν)2 term as a nonlinearity correction of the Maxwell theory. We obtain black hole solutions with various horizon topologies (and various number of horizons) in which their asymptotical behavior can be flat or anti-de Sitter with an effective cosmological constant. We investigate the effects of Lovelock and electrodynamic corrections on properties of the solutions. Then, we restrict ourselves to asymptotically flat solutions and calculate the conserved and thermodynamic quantities. We check the first law of thermodynamics for these black hole solutions and calculate the heat capacity to analyze stability. Although higher dimensional black holes in Einstein gravity are unstable, here we look for suitable constraints on the black hole radius to find thermally stable black hole solutions.

scholarly journals Superradiant instability of D-dimensional Reissner–Nordström-anti-de Sitter black hole mirror system

2017 ◽  
Vol 26 (13) ◽  
pp. 1750141 ◽  
Author(s):  
Yang Huang ◽  
Dao-Jun Liu ◽  
Xin-Zhou Li
Keyword(s):  
Black Hole ◽  
Threshold Value ◽  
Scalar Fields ◽  
Scalar Perturbation ◽  
De Sitter ◽  
Charged Scalar ◽  
Dimensional Spacetime ◽  
Higher Dimensional ◽  
The Stability ◽  
Degree Of Instability

In this paper, a detailed analysis for superradiant stability of the system composed by a [Formula: see text]-dimensional Reissner–Nordström-anti-de Sitter (RN-AdS) black hole and a reflecting mirror under charged scalar perturbations are presented in the linear regime. It is found that the stability of the system is heavily affected by the mirror radius as well as the mass of the scalar perturbation, AdS radius and the dimension of spacetime. In a higher dimensional spacetime, the degree of instability of the superradiant modes will be severely weakened. Nevertheless, the degree of instability can be magnified significantly by choosing a suitable value of the mirror radius. Remarkably, when the mirror radius is smaller than a threshold value the system becomes stable. We also find that massive charged scalar fields cannot trigger the instabilities in the background of [Formula: see text]-dimensional asymptotically flat RN black hole. For a given scalar charge, a small RN-AdS black hole can be superradiantly unstable, while a large one may be always stable under charged scalar field with or without a reflecting mirror. We also show that these results can be easily expounded and understood with the help of factorized potential analysis.

FERMION PERTURBATIONS IN HIGHER-DIMENSIONAL STRING-THEORY BLACK HOLES

2013 ◽  
Vol 22 (10) ◽  
pp. 1350073
Author(s):  
OWEN PAVEL FERNÁNDEZ PIEDRA ◽  
JOSE BERNAL CASTILLO ◽  
YULIER JIMENEZ SANTANA ◽  
LEOSDAN FIGUEREDO NORIS
Keyword(s):  
Black Hole ◽  
Damping Factor ◽  
Test Field ◽  
Perfect Agreement ◽  
Massless Fermion ◽  
Time Domain Data ◽  
Fermion Fields ◽  
Dimensional Spacetime ◽  
Higher Dimensional ◽  
The Time Domain

In this paper, we report the results of a detailed investigation of the complete time evolution of massless fermion fields propagating in spacetimes of higher-dimensional stringy black hole solutions, obtained from intersecting branes in string/M theory. We write the Dirac equation in D-dimensional spacetime in a form suitable to perform a numerical integration of it, and using a Prony fitting of the time domain data, we determine the quasinormal frequencies that characterize the test field evolution at intermediary times. We also present the results obtained for the quasinormal frequencies using a sixth-order WKB approximation, that are in perfect agreement with the numerical results. The power-law exponents that describe the field relaxation at very late-times are also determined, and we show that they depends upon the dimensionality of spacetime, and are identical to that associated with the relaxation of boson fields for odd dimensions. The dependence of the frequencies and damping factor of the spinor field with the charges of the stringy black hole are studied.

scholarly journals Thermodynamics and reentrant phase transition for logarithmic nonlinear charged black holes in massive gravity

2020 ◽  
Vol 29 (12) ◽  
pp. 2050081
Author(s):  
S. Rajaee Chaloshtary ◽  
M. Kord Zangeneh ◽  
S. Hajkhalili ◽  
A. Sheykhi ◽  
S. M. Zebarjad
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Black Hole ◽  
Quantum Effect ◽  
Massive Gravity ◽  
Nonlinear Electrodynamics ◽  
Model Parameters ◽  
Thermodynamic Quantities ◽  
Field Equations ◽  
Black Hole Solutions

We investigate a new class of [Formula: see text]-dimensional topological black hole solutions in the context of massive gravity and in the presence of logarithmic nonlinear electrodynamics. Exploring higher-dimensional solutions in massive gravity coupled to nonlinear electrodynamics is motivated by holographic hypothesis as well as string theory. We first construct exact solutions of the field equations and then explore the behavior of the metric functions for different values of the model parameters. We observe that our black holes admit the multi-horizons caused by a quantum effect called anti-evaporation. Next, by calculating the conserved and thermodynamic quantities, we obtain a generalized Smarr formula. We find that the first law of black holes thermodynamics is satisfied on the black hole horizon. We study thermal stability of the obtained solutions in both canonical and grand canonical ensembles. We reveal that depending on the model parameters, our solutions exhibit a rich variety of phase structures. Finally, we explore, for the first time without extending thermodynamics phase space, the critical behavior and reentrant phase transition for black hole solutions in massive gravity theory. We realize that there is a zeroth-order phase transition for a specified range of charge value and the system experiences a large/small/large reentrant phase transition due to the presence of nonlinear electrodynamics.

scholarly journals A SLOWLY ROTATING CHARGED BLACK HOLE IN FIVE DIMENSIONS

2006 ◽  
Vol 21 (09) ◽  
pp. 751-757 ◽  
Author(s):  
A. N. ALIEV
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
System Of Equations ◽  
Maxwell System ◽  
Five Dimensions ◽  
Four Dimensions ◽  
Higher Dimensional ◽  
Long Time ◽  
Electrically Charged ◽  
Black Hole Solutions

Black hole solutions in higher dimensional Einstein and Einstein–Maxwell gravity have been discussed by Tangherlini as well as Myers and Perry a long time ago. These solutions are the generalizations of the familiar Schwarzschild, Reissner–Nordström and Kerr solutions of four-dimensional general relativity. However, higher dimensional generalization of the Kerr–Newman solution in four dimensions has not been found yet. As a first step in this direction we shall report on a new solution of the Einstein–Maxwell system of equations that describes an electrically charged and slowly rotating black hole in five dimensions.

CONFORMAL KILLING-YANO TENSOR AND KERR-NUT-DE SITTER SPACETIME UNIQUENESS

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2169-2171 ◽  
Author(s):  
YUKINORI YASUI
Keyword(s):  
Black Hole ◽  
Conformal Killing ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Higher Dimensional ◽  
Dimensional Black Hole ◽  
Rank 2 ◽  
Black Hole Solutions

This paper gives a brief review of recent results on higher dimensional black hole solutions. It is shown that the D-dimensional Kerr-NUT-de Sitter spacetime constructed by Chen-Lü-Pope is the only spacetime admitting a rank-2 conformal Killing-Yano tensor with a certain symmetry.

scholarly journals Superradiant stability of five and six-dimensional extremal Reissner–Nordstrom black holes

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Jia-Hui Huang ◽  
Tian-Tian Cao ◽  
Mu-Zi Zhang
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Numerical Methods ◽  
Effective Potential ◽  
Scalar Perturbation ◽  
Polynomial Equations ◽  
Potential Well ◽  
Massive Scalar ◽  
Higher Dimensional ◽  
The Stability

AbstractWe revisit the superradiant stability of five and six-dimensional extremal Reissner–Nordstrom black holes under charged massive scalar perturbation with a new analytical method. In each case, it is analytically proved that the effective potential experienced by the scalar perturbation has only one maximum outside the black hole horizon and no potential well exists for the superradiance modes. So the five and six-dimensional extremal Reissner–Nordstrom black holes are superradiantly stable. The new method we developed is based on the Descartes’ rule of signs for the polynomial equations. Our result provides a complementary support of previous studies on the stability of higher dimensional extremal Reissner–Nordstrom black holes based on numerical methods.

scholarly journals Stability and phase transition of rotating Kaluza–Klein black holes

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Seyed Hossein Hendi ◽  
Somayeh Hajkhalili ◽  
Mubasher Jamil ◽  
Mehrab Momennia
Keyword(s):  
Black Hole ◽  
Black Hole Solution ◽  
Canonical Ensemble ◽  
Quasinormal Modes ◽  
Scalar Perturbation ◽  
Thermodynamic Quantities ◽  
Resonance Modes ◽  
Maxwell Electrodynamics ◽  
The Stability ◽  
Kaluza Klein

AbstractIn this paper, we investigate the thermodynamics and phase transitions of a four-dimensional rotating Kaluza–Klein black hole solution in the presence of Maxwell electrodynamics. Calculating the conserved and thermodynamic quantities shows that the first law of thermodynamics is satisfied. To find the stable black hole’s criteria, we check the stability in the canonical ensemble by analyzing the behavior of the heat capacity. We also consider a massive scalar perturbation minimally coupled to the background geometry of the four-dimensional static Kaluza–Klein black hole and investigate the quasinormal modes by employing the Wentzel–Kramers–Brillouin (WKB) approximation. The anomalous decay rate of the quasinormal modes spectrum is investigated by using the sixth-order WKB formula and quasi-resonance modes of the black hole are studied with averaging of Padé approximations as well.

Phase transition in decaying black holes

2020 ◽  
Vol 35 (31) ◽  
pp. 2050258
Author(s):  
Aloke Kumar Sinha
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Black Hole ◽  
Phase Transitions ◽  
Quantum Black Hole ◽  
Dimensional Spacetime ◽  
The Stability ◽  
Derivatives Of ◽  
Physical Quantities ◽  
Thermal Stability Of

We had earlier derived the most general criteria for thermal stability of a quantum black hole, with arbitrary number of parameters, in any dimensional spacetime. These conditions appeared in form of a series of inequalities connecting second order derivatives of black hole mass with respect to its parameters. Some black holes like asymptotically flat rotating charged black holes do not satisfy all the stability criteria simultaneously, but do satisfy some of them in certain region of parameter space. They are known as “Quasi Stable” black holes. In this paper, we will show that quasi stable black holes although ultimately decay under Hawking radiation undergo phase transitions. These phase transitions are different from phase transition in ADS Schwarzschild black hole. These are marked by sign changes in certain physical quantities apart from specific heat of the black hole. We will also discuss the changes in the nature of fluctuations of the parameters of these quasi stable black holes with different phases.

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