Black Holes In Massive Gravity Research Articles

Topological dyonic black holes of massive gravity with generalized quasitopological electromagnetism

In this paper we investigate new dyonic black holes of massive gravity sourced by generalized quasitopological electromagnetism in arbitrary dimensions. We begin by deriving the exact solution to the field equations defining these black holes and look at how graviton’s mass, dimensionality parameter, and quasitopological electromagnetic field affect the horizon structure of anti-de Sitter dyonic black holes. We also explore the asymptotic behaviour of the curvature invariants at both the origin and infinity to analyze the geometric structure of the resultant black holes. We also compute the conserved and thermodynamic quantities of these dyonic black holes with the help of established techniques and known formulas. After investigating the relevancy of first law, we look at how various parameters influence the local thermodynamic stability of resultant black hole solution. We also examine how thermal fluctuations affect the local stability of dyonic black holes in massive gravity. Finally, we study the shadow cast of the black hole.

Thermodynamics and optical properties of phantom AdS black holes in massive gravity

Motivated by high interest in Lorentz invariant massive gravity models known as dRGT massive gravity, we present an exact phantom black hole solution in this theory of gravity and discuss the thermodynamic structure of the black hole in the canonical ensemble. Calculating the conserved and thermodynamic quantities, we check the validity of the first law of thermodynamics and the Smarr relation in the extended phase space. In addition, we investigate both the local and global stability of these black holes and show how massive parameters affect the regions of stability. We extend our study to investigate the optical features of the black holes such as the shadow geometrical shape, energy emission rate, and deflection angle. Also, we discuss how these optical quantities are affected by massive coefficients. Finally, we consider a massive scalar perturbation minimally coupled to the background geometry of the black hole and examine the quasinormal modes by employing the WKB approximation.

Gauss-bonnet modification to Hawking evaporation of AdS black holes in massive gravity

Gauss-bonnet modification to Hawking evaporation of AdS black holes in massive gravity

Complexity growth of BTZ black hole in massive gravity with a null string

In this paper, we investigate the complexity growth of the tensionless limit of string in the neutral BTZ black hole horizon in massive gravity. When the string approaches the horizon, we observe a novel phenomenon for the Nambu–Goto action growth that produces significant difference from tensile string geometry. The string’s tension is then suggested to partially contribute to the growth of the action. We also argue a potential proposal that reconstructs the complexity from the renormalization group (RG) flow.

Thermal fluctuations of (non)linearly charged BTZ black hole in massive gravity

In this paper, we consider a charged BTZ black hole in asymptotically AdS spacetime of massive gravity to study the effect of the thermal fluctuations on the black hole thermodynamics. We consider the Einstein–Born–Infeld solution and investigate critical points and stability. We also compare the results with the case of Einstein–Maxwell solutions. Besides, we find that thermal fluctuations, which appear as a logarithmic term in the entropy, affect the stability of the black hole and change the phase transition point. Moreover, we study the geometrical thermodynamics and find that the behavior of the linear Maxwell solution is the same as the nonlinear one.

Holographic Einstein rings of an AdS black hole in massive gravity

In the context of holography, the Einstein ring of an AdS black hole (BH) in massive gravity (MG) is depicted. An oscillating Gaussian source on one side of the AdS boundary propagates in bulk, and we impose a response function to explain it. Using a wave optics imaging system, we obtain the optical appearance of the Einstein ring. Our research reveals that the ring can change into a luminosity-deformed ring or light spots depending on the variation of parameters and observational positions. When observers are positioned at the north pole, the holographic profiles always appear as a ring with concentric stripe surroundings, and a bright ring appears at the location of the photon sphere of the BH. To investigate the distinct features of the MG AdS BH from previous studies, we discussed the relation between the temperature T and the event horizon  ue , which shows the decaying behavior with the increasing values of the event horizon  ue , when the graviton parameter m is fixed. These in turn influence the behavior of the response function and the Einstein ring. For example, the amplitude of the lensed response function |〈O〉| increases with the increasing values of the graviton parameter m, for the fixed value of the horizon ue . On the other hand, the amplitude of the lensed response function |〈O〉| decreases with the increasing values of the horizon  ue , for the fixed value of graviton parameter m. These differences are also reflected in the Einstein ring, where the intensities and the locations of the Einstein ring significantly vary according to the numerical values of the involved parameters. These findings are also observed in the brightness profiles and the best fit comparison between the results obtained by wave optics and geometric optics for different values of graviton parameter m. In this perspective, our study contributes to a better understanding of the analytical studies of holographic theory, which can be used to evaluate different types of BHs for a fixed wave source and optical system.

Structure of 3D gravastars in the context of massive gravity

In this paper, we investigate a new model of (2+1)−dimensional (3D) gravitational vacuum stars (gravastars) with an isotropic matter distribution anti-de Sitter (AdS) spacetime in the context of massive gravity. For this purpose, we explore free singularity models with a specific equation of state. Using Mazur-Mottola's approach, we predict 3D gravastars as alternatives to BTZ black holes in massive gravity. We find analytical solutions to the interior of gravastars free of singularities and event horizons. For a thin shell containing an ultra-relativistic stiff fluid, we discuss length, energy, and entropy. In conclusion, the parameter of massive gravity plays a significant role in predicting the proper length, energy contents and entropy and parameters of gravastars.

Topological classification and black hole thermodynamics

One of the new methods that can be used to study the thermodynamics, critical points of a system based on a topological approach is the study of topological charges using Duan’s ϕ-mapping method. In this article, we will attempt to use this method to study three different black holes, each with different coefficients in their metric function, in order to determine the class of critical points, these black holes have in terms of phase transition. Through this analysis, we found that the Euler–Heisenberg black hole has two different topological classes, and the parameter “a” added to the metric function by QED plays an important role in this classification. While a black hole with a non-linear electrodynamic field, despite having an electromagnetic parameter, which is added to its metric function, has only one topological class, and its “α” parameter has no effect on the number of critical points and topological class. Finally, the Yang–Mills black hole in massive gravity will have a different number of critical points, depending on the coefficient “ci”, which is related to massive gravity and leads to different topological classes. However, this black hole exhibits the same phase structure in all cases.

Dynamic phase transition of black holes in massive gravity

The dynamical properties of small-large black hole phase transition in dRGT non-linear massive gravity theory are studied based on the underlying free energy landscape. The free energy landscape is constructed by specifying the Gibbs free energy to every state, and the free energy profile is used to study the different black hole phases. The small-large black hole states are characterized by probability distribution functions and the kinetics of phase transition are described by the Fokker–Planck equation. Further, a detailed study of the first passage process is presented which describes the dynamics of phase transitions. Finally, we have investigated the effect of mass and topology on the dynamical properties of phase transitions of black holes in dRGT non-linear massive gravity theory.

Topological classes of higher-dimensional black holes in massive gravity

In this paper, we study topological numbers for five-, six- and seven-dimensional anti-de Sitter black holes in the ghost-free massive gravity. We find that when the black holes are charged, they have the same topological number. The topological numbers for the uncharged black holes are 0 or 1, and the specific values are determined by the values of the black holes’ parameters. Since k and c_ 0^2c_2 m^2 appear together in the generalized free energy in the form of k +c_ 0^2c_2 m^2 , where k characterizes the horizon curvature and c_2 m^2 is the coefficient of the second term of massive potential associated with the graviton mass, this result is applicable to the black holes with the spherical, Ricci flat or hyperbolic horizons. This work shows that the parameters of the ghost-free massive gravity play an important role in topological classes of black holes.

Thermodynamics of black holes in massive gravity with holography

For the black hole thermodynamics under the modified gravity model, there is a very controversial issue of whether coupling parameters can be treated as thermodynamic quantities. There is currently no clear consensus. In this study, we want to develop a criterion for this issue with the help of holography under the de Rham, Gabadadze and Tolley (dRGT) massive gravity theory. We find that the extensive properties of black hole thermodynamics can be used to constrain this issue and at this point, the black hole can also appear interesting thermodynamic phase transition. The proposal of the additive constraint may be applied to many other modified gravity models.

Spherical Particle Orbits around a Rotating Black Hole in Massive Gravity

In this paper, we present a rotating de Rham–Gabadadze–Tolley black hole with a positive cosmological constant under massive gravity, achieved by applying a modified Newman–Janis algorithm. The black hole exhibited stable orbits of constant radii, prompting a numerical study of the behavior of the solutions to a nonic equation governing the radii of planar orbits around the black hole. Additionally, we investigated the stability of orbits near the event horizon and provide a comprehensive analytical examination of the solutions to the angular equations of motion. This was followed by a simulation of some spherical particle orbits around the black hole.

Weak gravity conjecture, black branes and violations of universal thermodynamics relation

The universal thermodynamic relations between corrections to entropy and extremality for various black hole solutions, like rotating-AdS black holes, charged black holes, rotating black holes in massive gravity, etc., have been studied by modifying general relativity. In this paper, we consider a number of the black brane in different structures, such as black brane solution in Rastall AdS massive gravity, Einstein–Yang–Mills AdS black brane solution in massive gravity, and general anisotropic black brane in Horava–Lifshitz gravity. Then, we study universal thermodynamic relations by using a small constant correction added to the action. We conclude that black brane violates the universal thermodynamic relations. In other words, these universal thermodynamic relations are not valid in the black brane structure.

Exponential corrected thermodynamics of Born–Infeld BTZ black holes in massive gravity

It is known that entropy of black hole gets correction at quantum level. Universally, these corrections are logarithmic and exponential in nature. We analyze the impacts of these quantum corrections on thermodynamics of Born–Infeld BTZ black hole in massive gravity by considering both such kinds of correction. We do comparative analysis of corrected thermodynamics with their equilibrium values. Here, we find that the exponential correction yields to the second point of the first-order phase transition. Also, quantum correction affects significantly the Helmholtz free energy of larger black holes. We study the equation of state for the exponential corrected black hole to obtain a leading order virial expansion.

Probing inside a charged hairy black hole in massive gravity

In this paper, we investigate the internal structure of a charged hairy black hole solution in the non-linear massive gravity. We first consider the impact of various configurations of massive gravity on the condensate operator and then probe the black hole interior dynamics. Like a standard holographic superconductor system, just below the critical temperature, the interior evolves through several distinct epochs, including a collapse of the Einstein-Rosen bridge, Josephson oscillations of the scalar field, and finally a Kasner (or Kasner inversion) cosmology. However, for the large massive gravity parameter, we see distinguishing features for the interior dynamics. In this regime, at a given temperature, the Einstein-Rosen bridge collapse and subsequent Josephson oscillations epochs completely disappear from the interior dynamics and the final Kasner cosmology epoch starts exactly after the would-be inner horizon and the system does not experience the Kasner inversion epoch.

Phase transition grade and microstructure of AdS black holes in massive gravity

Considering that under the framework of the massive gravity theory, the interaction between the mass gravitons and Schwarzschild black hole (BH) could make it carry a scalar charge, the phase transition process caused by this scalar charge is investigated in this analysis. The phase transition grade and microstructure of those BHs are investigated from both macroscopic and microscopic points of view. From the macroscopic point of view, it is found that Ehrenfest equations are satisfied at the phase transition critical point, which implies that the phase transition grade of those BHs is second-order. Based on the BH molecules model and Landau continuous phase transition theory, the phase transition of those BHs from the microcosmic point of view is analyzed. The critical exponents obtained from the two perspectives are consistent. By investigating the Ruppeiner geometry, the microstructure feature of those BHs is revealed. These results suggest that the phase transition of BH in massive gravity is a standard second-order phase transition at the critical point, and the microscopic details of those BHs are different from the Reissner–Nordström AdS BH in standard Einstein gravity.

Thermodynamics of novel black holes in massive gravity coupled to nonlinear electrodynamics

By introducing a static and spherically symmetric geometry, we have solved the coupled electromagnetic and gravitational field equations in the presence of both, massive gravitons and nonlinear electrodynamics. The exact solutions show that massive gravity theory admits two novel classes of nonlinearly charged asymptotically AdS black holes. The black holes’ electric charge, mass, and other thermodynamic quantities have been calculated. Then, by use of a Smarr-type mass formula, it has been proved that the thermodynamical first law is valid for both the new massive black hole solutions. The black hole local stability has been investigated by use of the canonical ensemble and geometrical methods, separately. Through comparison of the results, we found that they are compatible provided that the HEPM or QII thermodynamic metrics are used. Global stability and Hawking–Page phase transition points have been studied by use of the grand canonical ensemble method and regarding the Gibbs free energy of the black holes.

Phase equilibrium and microstructure of topological AdS black holes in massive gravity * *Supported in part by the National Natural Science Foundation of China (11705106, 11705107, 12075143), Science and Technology Innovation Project of Shanxi Higher Education (2016173) and the Doctoral Sustentation Fund of Shanxi Datong University

In order to clearly understand the gravitational theory through the thermal properties of the black hole, it is important to further investigate the first-order phase transition of black holes. In this paper, we adopt different conjugate variables ( , , , and ) and apply Maxwell's equal-area law to study the phase equilibrium of a topological black hole in massive gravity. The condition and latent heat of phase transition are displayed as well as the coexistent curve of . The result shows that the phase transition of this system is the high/low electric potentials one, not only the large/small black holes one. We also analyze the effect of the model's parameters on phase transition. Furthermore we introduce a new order parameter to probe the microstructure of this system. This work will provide the theoretical basis to study the phase structure of topological black holes in massive gravity and to further explore the gravitational theory.

Five-dimensional Yang–Mills black holes in massive gravity’s rainbow

In this paper, we will analyze a five-dimensional Yang–Mills black hole solution in massive gravity’s rainbow. We will also investigate the flow of such a solution with scale. Then, we will discuss the scale dependence of the thermodynamics for this black hole. In addition, we study the criticality in the extended phase space by treating the cosmological constant as the thermodynamics pressure of this black hole solution. Moreover, we will use the partition function for this solution to obtain corrections to the thermodynamics of this system and examine their key role in the behavior of corrected solutions.

Entanglement entropy and Page curve of black holes with island in massive gravity

By applying the island rule proposed recently, we compute the entanglement entropy of Hawking radiation and study the Page curve for the eternal black holes in massive gravity. We investigate for both the neutral and charged black holes which the corresponding results of Schwarzschild and Reissner–Nordström black holes are restored in the limit of massless graviton. We show for the neutral and non-extremal charged black holes that the island is not formed at the early times of the evaporation and hence the entanglement entropy increases linearly in time. However, for the extremal charged black hole, the calculation of the entanglement entropy at the early times without the island is ill-defined because the metric is divergent at the curvature singularity. This implies that new physics in the UV region must be taken into account to make the metric behaving smoothly at the very short distances. At the late times, with the emergence of one island near the event horizon, the entanglement entropy is saturated by the Bekenstein–Hawking entropy of black holes. In addition, we analyze the impact of massive gravity parameters on the size of island, the entanglement entropy, the Page time, and the scrambling time in detail.