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 $r = r_c$. 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.
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 $d\geq6$-dimensional spacetime when the coupling coefficients $c_i m^2$ of massive potential satisfy some …
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…
In this paper, we study the thermodynamics and geothermodynamics of spherical black hole solutions in dRGT massive gravity in a new extended phase space. Inspired by the work of Kastor et al. [1], 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 …
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 higherdimensional de Rham, Gabadadze and Tolley (dRGT) massive gravity. Solving the differential equation, we obtain the corrected entropy and effective therm…
Thermodynamics of Bardeen AdS black holes has attracted a great deal of attentions due to its intrinsic complications and rich phase structures. However, the entropy and thermodynamic volume are incorrect in some literatures. In this paper we revisit the thermodynamics of Bardeen AdS black holes and provide the correct entropy and thermodynamic volume. Furthermore, thermodynamic geometries are a powerful tool to probe the microstructure of black holes. Based on the Hessian matrix of black hole mass, we introduce a thermodynamic metric and give its scalar curvature in Weinhold's geometry. The c…
We discuss the first law of thermodynamics of Bardeen black hole. The presence of magnetic monopole charge modifies the energy and we define the temperature of the system accordingly. We introduce a lower cut-off to the space time by introducing a spherical surface, which can be identified with the event horizon. The corresponding temperature is identified with Hawking temperature. The entropy is assumed to obey the area law and we confirm this by calculating the statistical entropy by using brick wall model.
Instead of the work \cite{1} which in according to the Lovelock theorem it could not applicable for all types of 4D curved spacetimes of Einstein Gauss Bonnet (EGB) gravity, authors of the work \cite{2} applied break of diffeomorphism property to present a consistent EGB gravity theory. In this work we use the latter model by adding a nonlinear electromagnetic field lagrangian density to study affects of GB coupling constant into the thermodynamic phase transition and Joule Thomson (JT) adiabatic expansion of a 4D $dS/AdS$ GB Bardeen black hole.
The phase transition of a Bardeen black hole is studied by considering Ehrenfest's equations. The thermodynamic variables such as entropy, potential and heat capacity are calculated from the first law of thermodynamics for black holes. That no discontinuity in entropy and potential of the black holes means that the first order phase transition will not generate for the Bardeen black holes. However, the divergence of heat capacity at constant potential and satisfaction of the Ehrenfest's equations indicates that the second order phase transition of Bardeen black hole will appear.
We first study the thermodynamics of Bardeen-AdS black hole by the $T$-$r_{h}$ diagram, where T is the Hawking temperature and $r_{h}$ is the radius of event horizon. The cut-off radius which is the minimal radius of the thermodynamical stable Bardeen black hole can be got, and the cut-off radius is the same with the result of the heat capacity analysis. Moreover, by studying the parameter $g$, which is interpreted as a gravitationally collapsed magnetic monopole arising in a specific form of non-linear electrodynamics, in the Bardeen black hole, we can get a critical value $g_{m}$ and differe…
In this paper we present a Bardeen solution surrounded by a cloud of strings fluid. We show how this model has the same event horizon characteristic as the Bardeen solution, however, the parameter of the strings make the solution singular at the origin. We also analyze the solution from a thermodynamic point of view. We calculate the system's state function, enthalpy; the temperature; and the other potentials; as a function of entropy. By analyzing the thermodynamic coefficients, we show that the solution presents three distinct phases, two of which are stable and one unstable. These three pha…
In this paper, we discuss remnants of the Bardeen regular black hole motivated by using the concept of thermal fluctuations. First, we derive the equilibrium values of various thermodynamic quantities like entropy, Hawking temperature, pressure, internal energy, Helmholtz free energy and Gibbs free energy in the non-extended phase space. We then discuss geometrothermodynamics (GTD) of Bardeen black hole to study its stability. Next, we estimate the size of black hole remnant in terms of some known parameters of the black hole solution. Motivated by the fact that estimation of size, characteris…
We find an exact spherically symmetric regular Bardeen-like solutions by considering the coupling between Einstein-Gauss-Bonnet theory and nonlinear electrodynamics (NED) in five-dimensional spacetime. These solutions, with an additional parameter $g$ apart from the mass $M$, represent black holes with Cauchy and event horizons, extremal black holes with degenerate horizons or no black holes in the absence of the horizons, and encompasses as a special case Boulware-Deser black holes which can be recovered in the absence of magnetic charge ($g=0$). Owing to the NED corrected black hole, the the…
The $P$-$V$ phase transition and critical behavior in the extended phase space of asymptotic Anti-de Sitter (AdS) black holes have been widely investigated, in which four critical exponents around critical point are found to be consistent with values in the mean field theory. Recently, another critical exponent $ν$ related to divergent correlation length at critical point is proposed by using thermodynamic curvature scalar $R_N$ in the charged AdS black hole. In this paper, we develop a method to investigate the divergent behavior of $R_N$ at critical point, and find that the divergent behavio…
In this article, we present a study on thermodynamics of a class of regular black holes. Such a class includes Bardeen and Hayward regular black holes. We obtained thermodynamic quantities like the Hawking temperature, entropy, and heat capacity for the entire class. As part of an effort to indicate some physical observable to distinguish regular black holes from singular black holes, we suggest that regular black holes are colder than singular black holes. Besides, contrary to the Schwarzschild black hole, that class of regular black holes may be thermodynamically stable. From a generalized u…
We analyze certain aspects of BTZ black holes in massive theory of gravity. The black hole solution is obtained by using the Vainshtein and dRGT mechanism, which is asymptotically AdS with an electric charge. We study the Hawking radiation using the tunneling formalism as well as analyze the black hole chemistry for such system. Subsequently, we use the thermodynamic pressure-volume diagram to explore the efficiency of the Carnot heat engine for this system. Some of the important features arising from our solution include the non-existence of quantum effects, critical Van der Walls behaviour, …
Motivated by recent developments of black hole thermodynamics in de Rham, Gabadadze and Tolley(dRGT) massive gravity, we study the critical behaviors of four-dimensional topological Anti-de Sitter(AdS) black holes in the presence of Born-Infeld nonlinear electrodynamics by treating the cosmological constant as pressure and the corresponding conjugate quantity is interpreted as thermodynamic volume. It shows that besides the Van der Waals-like SBH/LBH phase transitions appears, the so-called reentrant phase transitions (RPTs) are also observed when the coupling coefficients $c_i m^2$ of massive…
We investigate the effect of massive graviton on the holographic thermalization process. Before doing this, we first find out the generalized Vaidya-AdS solutions in the de Rham-Gabadadze-Tolley (dRGT) massive gravity by directly solving the gravitational equations. Then, we study the thermodynamics of these Vaidya-AdS solutions by using the Minsner-Sharp energy and unified first law, which also shows that the massive gravity is in a thermodynamic equilibrium state. Moreover, we adopt the two-point correlation function at equal time to explore the thermalization process in the dual field theor…
In this paper we study AdS-Schwarzschild black holes in four and five dimensions in dRGT minimally coupled to a cloud of strings and investigate the effects of this string cloud on the thermodynamics of the black holes. It is observed that the entropy of the string cloud and massive terms does not affect the black hole entropy. The observations about four dimensions indicate that the massive term in the presence of external string cloud can not exhibit Van der Waals like behavior for AdS-Schwarzschild black holes and therefore there is only the Hawking-Page phase transition. In contrast, in fi…
In the context of Black Hole Chemistry (BHC), holographic phase transitions of asymptotically anti-de Sitter (AdS) charged topological black holes (TBHs) in massive gravity coupled to Power Maxwell Invariant (PMI) electrodynamics are discussed in the grand canonical (fixed $U(1)$ potential, $Φ$) ensemble. Considering all higher-order graviton's self-interactions of (dRGT) massive gravitational field theory in arbitrary dimensions, exact TBH solutions are derived, the explicit form of the on-shell action is computed, and the associated thermodynamic quantities in the Grand Canonical Ensemble (G…
Dynamical solutions are always of interest to people in gravity theories. We derive a series of generalized Vaidya solutions in the $n$-dimensional de Rham-Gabadadze-Tolley (dRGT) massive gravity with a singular reference metric. Similar to the case of the Einstein gravity, the generalized Vaidya solution can describe shining/absorbing stars. Moreover, we also find a more general Vaidya-like solution by introducing a more generic matter field than the pure radiation in the original Vaidya spacetime. As a result, the above generalized Vaidya solution is naturally included in this Vaidya-like so…
Considering the negative cosmological constant of an anti-de Sitter (AdS) background as a positive thermodynamic pressure in the extended phase space, we study the thermodynamic behaviors of the regular Hayward-AdS (HAdS) black hole (BH) by investigating $P-\upsilon$ critical and cooling-heating phase transition. We compare the difference of two thermodynamic processes between the HAdS BH and the Bardeen-AdS (BAdS) BH. It is found that the phase transition of the BAdS BH tends to be more the van der Waals (vdW) phase transition. For the cooling-heating phase transition, we find the inversion c…
Our primary goal in this paper is to confirm new universal relations in black hole thermodynamics. We investigate the universal relations by selecting different black holes. First, we obtain the black holes' thermodynamic relations assuming a new minor correction is added to the AdS part of the action. Then we confirm the universal relations by performing a series of direct calculations. It is noteworthy that according to each of the properties related to black holes, a new universal relation can be obtained according to this method. We confirm two different types of these universal relations …
Extended thermodynamics and $P-v$ Criticality of Kalb-Ramond black hole coupled with nonlinear electrodynamics
Inter-University Center of Astronomy and Astrophysics (IUCAA)（大学间天文学与天体物理中心）；Department of Physics, Institute of Applied Science and Humanities, GLA University（GLA大学应用科学与人文学院物理系）；School of Physics, Damghan University（达姆甘大学物理学院）；Department of Physics, K.L.S. College, Magadh University（马加德大学K.L.S.学院物理系）；Indian Institute of Engineering Science and Technology (IIEST)（印度工程科学与技术研究所）；Department of General & Theoretical Physics, L. N. Gumilyov Eurasian National University（L.N. 古米廖夫欧亚国立大学普通与理论物理系）
Regular black holes do not violate the first law of thermodynamics
New Uzbekistan University（新乌兹别克斯坦大学）；Ulugh Beg Astronomical Institute（乌鲁伯格天文研究所）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）；School of Physics, Harbin Institute of Technology（哈尔滨工业大学物理学院）
In this paper we present some stringy corrections to black hole spacetimes emerging from string T-duality. As a first step, we derive the static Newtonian potential by exploiting the relation between the T-duality and the path integral duality. We show that the intrinsic non-perturbative nature of stringy corrections introduce an ultraviolet cutoff known as zero-point length in the path integral duality literature. As a result, the static potential is found to be regular. We use this result to derive a consistent black hole metric for the spherically symmetric, electrically neutral case. It tu…
In this paper, we attempt to further study the heat engine efficiency for the regular black hole (BH) with an anti-de Sitter (AdS) background where the working material is the Hayward-AdS (HAdS) BH. In the extended phase space, we investigate the heat engine efficiency of the HAdS BH by defining the cosmological constant as the thermodynamic pressure $P$ and deriving the mechanical work from the $PdV$ terms. Then, we obtain the relation between the efficiency and the entropy/pressure and plot these function figures. Meanwhile, we compare the relation between the HAdS BH with that of the Bardee…
In this paper we study thermodynamic properties of dense cold $SU(2)$ QCD within lattice simulation with dynamical rooted staggered quarks which in the continuum limit correspond to $N_f=2$ quark flavours. We calculate baryon density, renormalized chiral and diquark condensates for various baryon chemical potentials in the region $μ\in (0,\,2000)$ MeV. It is found, that in the region $μ\in (0,\,540)$ MeV the system is well described by the ChPT predictions. In the region $μ> 540$ MeV the system becomes sufficiently dense and ChPT is no longer applicable to describe lattice data. For chemical p…
In the subject of black hole chemistry, a broad variety of critical phenomena for charged topological black holes (TBHs) with massive gravitons (within the framework of dRGT massive gravity) is discussed in detail. Since critical behavior and nature of possible phase transition(s) crucially depend on the specific choice of ensemble, and, in order to gain more insight into criticality in the massive gravity framework, we perform our analysis in both the canonical (fixed charge, $Q$) and the grand canonical (fixed potential, $Φ$) ensembles. It is shown that, for charged TBHs in the grand canonic…
Horizon-Brightened Acceleration Radiation and Optical Signatures of Generic Regular Black Holes from Nonlinear Electrodynamics
Harbin Institute of Technology（哈尔滨工业大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Tashkent State Technical University（塔什干国立技术大学）；Institute for Advanced Studies, New Uzbekistan University（新乌兹别克斯坦大学高等研究院）；Eastern Mediterranean University（东地中海大学）；Mapúa University（马普阿大学）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）
We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole "exterior entropy" and "radiation entropy." For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various sp…
Holographic explorations of regular black holes in pure gravity
Universidad de Concepción（康塞普西翁大学）；Universidad Nacional de La Plata（拉普拉塔国立大学）；Instituto de Física La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas（拉普拉塔物理研究所，国家科学研究委员会）；Universitat de Barcelona（巴塞罗那大学）；Universidad Nacional Autónoma de México（墨西哥国立自治大学）
