Holes In dRGT Massive Gravity Research Articles

Dilatonic black holes in dRGT massive gravity

Motivated by high interest in Lorentz invariant massive gravity models known as the dRGT massive gravity, we discuss the dRGT massive gravity including the coupling term between dilaton scalar field and massive graviton, and present static and spherically symmetric solutions of dilatonic black holes in four and higher dimensional spacetime. Later, we investigate phase structure of these black hole solutions, and discover that the dilatonic black hole could possess two horizons, extreme and naked singularity black holes for the suitably parameters values. Calculating the conserved and thermodynamic quantities, we check the validity of the first law of thermodynamics.

Greybody factors for massive scalar field emitted from black holes in dRGT massive gravity

Greybody factors are transmission probabilities of the Hawking radiation, which are emitted from black holes and can be obtained from the gravitational potential of black holes. The de Rham, Gabadadze, and Tolly (dRGT) massive gravity is one of the gravity theories that modified general relativity. In this paper, we investigate the greybody factor from the massive scalar field in both the asymptotically dS and the AdS spacetime using the WKB and the rigorous bound methods. We found that the greybody factor depends on the shape of the potential as found in quantum mechanics. The higher the potential barrier, the lower the amount of the greybody factor. Interestingly, for the low multipole case, we found that there exists a critical mass which provides the maximum bound of the greybody factor. This is a crucial feature of the massive scalar field on the greybody factor from the black holes in both the asymptotically dS and the AdS spacetime.

Black holes in dRGT massive gravity with the signature of EHT observations of M87*

The recent Event Horizon Telescope (EHT) observations of the M87* have led to a surge of interest in studying the shadow of black holes. Besides, investigation of time evolution and lifetime of black holes helps us to veto/restrict some theoretical models in gravitating systems. Motivated by such exciting properties, we study optical features of black holes, such as the shadow geometrical shape and the energy emission rate in modified gravity. We consider a charged AdS black hole in dRGT massive gravity and look for criteria to restrict the free parameters of the theory. The main goal of this paper is to compare the shadow of the mentioned black hole in a rotating case with the EHT data to obtain the allowed regions of the model parameters. Therefore, we employ the Newman-Janis algorithm to build the rotating counterpart of static solution in dRGT massive gravity. We also calculate the energy emission rate for the rotating case and discuss how the rotation factor and other parameters affect the emission of particles around the black holes.

Analysis of accretion disk around a black hole in dRGT massive gravity

We show the analysis of a thin accretion disk around a static and spherically symmetric black hole in dRGT massive gravity. We present the accretion disk analysis in a gravitational theory with a nonzero graviton mass. Also, we study the event horizons of the black hole and we calculate the equations of motion and effective potential. In the following, we obtain the specific energy, specific angular momentum, and angular velocity of the particles which move in circular orbits. In addition, we plot the effective potentials for two cases and we show the locations of stable circular orbits. At last, we show the possibility of constraining the parameter space of dRGT massive gravity by the astrophysical gamma-ray bursts.

Thermodynamic properties of Bardeen black holes in dRGT massive gravity

The Bardeen black hole solution is the first spherically symmetric regular black hole based on the Sakharov and Gliner proposal which is a modification of the Schwarzschild black hole. We present the Bardeen black hole solution in the presence of the de Rham, Gabadaadze, and Tolly (dRGT) massive gravity, which is regular everywhere in the presence of a nonlinear source. The obtained solution reduces to the Bardeen black hole in the absence of a massive gravity parameter, and the Schwarzschild black hole when magnetic charge g = 0. We investigated the thermodynamic quantities, that is, mass (M), temperature (T), entropy (S), and free energy (F), in terms of the horizon radius for both canonical and grand canonical ensembles. We checked the local and global stability of the obtained solution by studying the heat capacity and free energy. The heat capacity changes sign at r = rc. The black hole is thermodynamically stable with a positive heat capacity C > 0 (i.e., globally preferred with negative free energy F < 0). In addition, we studied the phase structure of the obtained solution in both ensembles.

Quasinormal modes of black holes in dRGT massive gravity ‎ under electromagnetic perturbations

Upon semi-analytical and numerical methods, the quasinormal frequencies of dRGT massive black holes under electromagnetic perturbation are calculated and the dynamical stability of these black holes is investigated. The effect of graviton’s mass on the frequencies is investigated and it is shown that the WKB approximation is valid not only for but also only for low-mass gravitons.

Greybody factors of black holes in dRGT massive gravity coupled with nonlinear electrodynamics

In the context of the dRGT massive gravity coupled with nonlinear electrodynamics, we present new dRGT black hole solutions. Together with the thermodynamical properties of the solutions, we study the greybody factor of the corresponding black hole solution. To this end, we compute the rigorous bound on the greybody factor for the obtained dRGT black holes. The obtained results are graphically represented for different values of the theory’s physical parameters. Our analysis shows that the charged dRGT black holes of nonlinear electrodynamics evaporate quicker than the charged dRGT black holes originated from linear electrodynamics.

Thermodynamic properties of higher-dimensional dS black holes in dRGT massive gravity

On the basis of the state parameter of de Sitter space-time satisfying the first law of thermodynamics, we can derive some effective thermodynamic quantities. When the temperature of the black hole horizon is equal to that of the cosmological horizon, we think that the effective temperature of the space-time should have the same value. Using this condition, we obtain a differential equation of the entropy of the de Sitter black hole in the higher-dimensional de Rham, Gabadadze and Tolley (dRGT) massive gravity. Solving the differential equation, we obtain the corrected entropy and effective thermodynamic quantities of the de Sitter black hole. The results show that for multi-parameter black holes, the entropy satisfied differential equation is invariable with different independent state parameters. Therefore, the entropy of higher-dimensional dS black holes in dRGT massive gravity is only a function of the position of the black hole horizon, and is independent of other state parameters. It is consistent with the corresponding entropy of the black hole horizon and the cosmological horizon. The thermodynamic quantities of self-consistent de Sitter space-time are given theoretically, and the equivalent thermodynamic quantities have the second-order phase transformation similar to AdS black hole, but unlike AdS black hole, the equivalent temperature of de Sitter space-time has a maximum value. By satisfying the requirement of thermodynamic equilibrium and stability of space-time, the conditions for the existence of dS black holes in the universe are obtained.

Holographic complexity of Born\u2013Infeld black holes

In this paper, according to CA duality, we study complexity growth of Born–Infeld (BI) black holes. As a comparison, we study action growth of dyonic black holes in Einstein–Maxwell gravity at the beginning. We study action growth of electric BI black holes in dRGT massive gravity, and find BI black holes in massive gravity complexify faster than the Einstein gravity counterparts. We study action growth of the purely electric and magnetic Einstein–Born–Infeld (EBI) black holes in general dimensions and the dyonic EBI black holes in four-dimensions, and find the manners of action growth are different between electric and magnetic EBI black holes. In all the gravity systems we considered, we find action growth rates vanish for the purely magnetic black holes, which is unexpected. In order to ameliorate the situation, we add the boundary term of matter field to the action and discuss the outcomes of the addition.

Modified fermion tunneling from higher-dimensional charged AdS black hole in massive gravity

The tunneling behavior of fermions with half-integral spin from a higher dimensional charged anti-de Sitter (AdS) black hole in de Rham, Gabadadze and Tolley (dRGT) massive gravity is investigated via a modified Hamilton–Jacobi equation. The results demonstrate that the modified thermodynamic quantities not only are related to the properties of the higher dimensional charged AdS black hole in dRGT massive gravity but also depend on the parameter beta , the coupling constant sigma and the mass of emitted particles m. In addition, the modified Hawking temperature is higher than the original temperature; hence, the effect of MDR can significantly enhance the evolution of the black hole. Besides, our results can be verified using the modified Stefan–Boltzmann law.

Phase transitions and geothermodynamics of black holes in dRGT massive gravity

In this paper, we study the thermodynamics and geothermodynamics of spherical black hole solutions in dRGT massive gravity in a new extended phase space. Inspire by the work of Kastor et al. (Class Quantum Gravity 26:195011, 2009), by interpreting the graviton mass as a thermodynamical variable, we propose a first law of thermodynamics which include a mass term and establish a new Smarr Formula. Then, we perform a thermodynamical analysis to reveal the existence of a critical behavior for black holes in dRGT massive gravity with two different critical points through canonical and grand canonical ensembles. To consolidate these results, we make use of the thermodynamical geometry formalism, with the HPEM and the Gibbs free energy metrics, to derive the singularities of Ricci scalar curvatures and show that they coincide with those of the capacities. The effect of different values of the spacetime parameters on the stability conditions is also discussed.

Greybody factor for black holes in dRGT massive gravity

In general relativity, greybody factor is a quantity related to the quantum nature of a black hole. A high value of greybody factor indicates a high probability that Hawking radiation can reach infinity. Although general relativity is correct and has been successful in describing many phenomena, there are some questions that general relativity cannot answer. Therefore, general relativity is often modified to attain answers. One of the modifications is the ‘massive gravity’. The viable model of the massive gravity theory belongs to de Rham, Gabadadze and Tolley (dRGT). In this paper, we calculate the gravitational potential for the de Sitter black hole and for the dRGT black hole. We also derive the rigorous bound on the greybody factor for the de Sitter black hole and the dRGT black hole. It is found that the structure of potentials determines how much the rigorous bound on the greybody factor should be. That is, the higher the potential, the lesser the bound on the greybody factor will be. Moreover, we compare the greybody factor derived from the rigorous bound with the greybody factor derived from the matching technique. The result shows that the rigorous bound is a true lower bound because it is less than the greybody factor obtained from the matching technique.

Charged scalar perturbations on charged black holes in de Rham-Gabadadze-Tolley massive gravity

We explore the quasi-stationary profile of massive charged scalar field in a class of charged black hole in dRGT massive gravity. We discuss how the linear term in the metric which is a unique character of the dRGT massive gravity affects structure of the spacetime. Numerical calculations of the quasinormal modes are performed for the charged scalar field in the dRGT black hole background. For asymptotically de Sitter (dS) black hole, an improved asymptotic iteration method is used to obtain the associated quasinormal frequencies. The unstable modes are found for $\ell=0$ case and their corresponding real parts satisfy superradiant condition. For $\ell=2$, the results show that all the de Sitter black holes considered here are stable against a small perturbation. For asymptotically dRGT anti de Sitter (AdS) black hole, unstable modes are found with the frequency satisfying superradiant condition. Effects of massive gravity parameter are discussed. Analytic calculation reveals unique diffusive nature of quasinormal modes in the massive gravity model with the linear term. Numerical results confirm existence of the characteristic diffusive modes in both dS and AdS cases.

Reentrant phase transitions of higher-dimensional AdS black holes in dRGT massive gravity

We study the P–V criticality and phase transition in the extended phase space of anti-de Sitter (AdS) black holes in higher-dimensional de Rham, Gabadadze and Tolley (dRGT) massive gravity, treating the cosmological constant as pressure and the corresponding conjugate quantity is interpreted as thermodynamic volume. Besides the usual small/large black hole phase transitions, the interesting thermodynamic phenomena of reentrant phase transitions (RPTs) are observed for black holes in all dge 6-dimensional spacetime when the coupling coefficients c_i m^2 of massive potential satisfy some certain conditions.

A class of black holes in dRGT massive gravity and their thermodynamical properties

We present exact spherical black hole solutions in de Rham, Gabadadze and Tolley (dRGT) massive gravity for a generic choice of the parameters in the theory, and also discuss the thermodynamical and phase structure of the black hole in both the grand canonical and canonical ensembles (for charged case). It turns out that the dGRT black hole solutions includes the known solutions to the Einstein field equations, such as, the monopole-de Sitter-Schwarzschild ones with the coefficients for the third and fourth terms in the potential and the graviton mass in massive gravity naturally generates the cosmological constant and the global monopole term. Furthermore, we compute the mass, temperature, and entropy of dGRT black hole solutions and also perform thermodynamical stability. It turns out that the presence of the graviton mass completely changes the black hole thermodynamics, and it can provide the Hawking-Page phase transition which is also true for the obtained charged black holes. Interestingly, the entropy of a black hole is unaffected and still obeys area law. In particular, our results, in the limit $m_g \rightarrow 0$, reduced exactly to \emph{vis-$\grave{a}$-vis} the general relativity results.

Bounding the Greybody Factor, Temperature and Entropy of Black Holes in dRGT Massive Gravity

A black hole greybody factor is the quantum quantity of a black hole. It is the fraction of Hawking radiation that can reach spatial infinity. The greybody factor may contain the necessary information to support the theory of quantum gravity. An understanding of the greybody factor helps us gain insight, not only into the nature of the black hole itself, but also into the theory of quantum gravity, which is currently being developed via numerous attempts. In this paper, we calculate the bound on the greybody factor for scalar field emitted from black holes in dRGT massive gravity. The bound on the reflection probability is also determined. Moreover, the effects of massive gravity on the greybody factors are explored. The results show that the bound on the greybody factor for the dRGT black holes is less than the bound for the Schwarzschild-de-Sitter black hole. The Hawking temperature is also calculated, both in the dRGT case and in the Schwarzschild-de-Sitter case. It is found that the Hawking temperature of the dRGT black hole is higher than that of the Schwarzschild-de-Sitter black hole. The increase in the Hawking temperature probably results from the mass of graviton. Finally, the black hole entropy is also determined. We found that the entropy of the Schwarzschild-de-Sitter black hole is more than the entropy of the dRGT black hole.