Black Hole Entropy Research Articles

Quantum tunneling of fermions from kerr-like black holes within topologically massive gravity

In the framework of 3-D general relativity, this study explores a Kerr-like black hole solution with a focus on its causal structure and particle dynamics, employing Penrose diagrams to elucidate the spacetime geometry. The research investigates the behavior pf particles in the vicinity of the event horizon, analyzing their trajectories and potential fates, including the influence of the black hole’s rotation and gravitational effects. The Dirac equation is solved in this curved spacetime using “WKB approximation”, allowing the computation of the Hawking temperature and unveiling quantum effects associated with black hole geometries in three dimensions. Moreover, the phenomenon of superradiance is explored, highlighting the mechanisms through with the rotational energy and angular momentum of the black hole are extracted. This phenomenon provides deeper insights into energy transfer processes and the stability of such black hole solutions. The research contributes to a better understanding of black hole thermodynamics, particularly in lower-dimensional gravitational settings, and offers a comprehensive analysis of energy exchange processes. By integrating classical and quantum perspectives, this study enhances the comprehension of particle dynamics, quantum field behavior, and thermodynamic properties of black holes, enriching the broader field of lower-dimensional gravitational models and their implications for fundamental physics.

Thermodynamics of Charged Acoustic Black Hole: Heat Engine

Thermodynamics of Charged Acoustic Black Hole: Heat Engine

Topological classification of critical points for hairy black holes in Lovelock gravity

In various fields of mathematical research, the Brouwer degree is a potent tool for topological analysis. By using the Brouwer degree defined in one-dimensional space, we interpret the equation of state for temperature in black hole thermodynamics, T=T(V,xi), as a spinodal curve, with its derivative defining a new function f. The sign of the slope of f indicates the topological charge of the black hole’s critical points, and the total topological charge can be deduced from the asymptotic behavior of the function f. We analyze a spherical hairy black hole within the framework of Lovelock gravity, paying particular attention to the topological structure of black hole thermodynamics under Gauss–Bonnet gravity. Here, the sign of the scalar hair parameter influences the topological classification of uncharged black holes. When exploring the thermodynamic topological properties of hairy black holes under cubic Lovelock gravity, we find that the spherical hairy black hole reproduces the thermodynamic topological classification results seen under Gauss–Bonnet gravity.

Weyl cohomology and the conformal anomaly in the presence of torsion

Using cohomological methods, we identify both trivial and nontrivial contributions to the conformal anomaly in the presence of vectorial torsion in d=2,4 dimensions. In both cases, our analysis considers two scenarios: one in which the torsion vector transforms in an affine way, i.e., it is a gauge potential for Weyl transformations, and the other in which it is invariant under the Weyl group. An important outcome for the former case in both d=2,4 is the presence of anomalies of a “mixed” nature in relation to the classification of Deser and Schwimmer. For invariant torsion in d=4, we also find a new type of anomaly which we dub Ψ-anomaly. Taking these results into account, we integrate the different anomalies to obtain renormalized anomalous effective actions. Thereafter, we recast such actions in the covariant nonlocal and local forms, the latter being easier to work with. Along the way, we pause to comment on the physical usefulness of these effective actions, in particular to obtain renormalized energy–momentum tensors and thermodynamics of 2d black holes.

Schottky Anomaly of the Kalb-Ramond-de Sitter Spacetime

In the theory of gravity, the spontaneous breaking of Lorentz symmetry due to the non-minimal coupling between the Kalb-Ramond field and Einstein gravity results in the existence of exactly static and spherically symmetric black hole solutions related to the Lorentz violating parameter. Based on the consideration of the interaction between the black hole and cosmological horizons, this paper studies the thermodynamic properties of Kalb-Ramond-de Sitter (KR-dS) spacetime. The Smarr relation expressed by equivalent thermodynamic quantities is found, and it is proved that the equivalent thermodynamic quantities of the KR-dS spacetime satisfy the universal Euler's theorem. It is discovered that the heat capacity of the KR-dS spacetime with respect to the ratio of the two horizons and the variation curve of the heat capacity with effective temperature possess the characteristics of Schottky specific heat. Moreover, the black hole and the cosmological horizon in the equivalent thermodynamic system are regarded as two different energy levels, and the heat capacity of the KR-dS spacetime is discussed using the general form given by the ordinary two-level system. It is found that the heat capacity of KR-dS spacetime described by equivalent thermodynamic quantities not only conforms to the characteristics of Schottky specific heat but also is consistent with the heat capacity of the ordinary two-level system. This result reflects that when the cosmological constant and the charged carried in the KR-dS spacetime remain unchanged, the heat capacity of the system can be represented by a universal two-level system. By comparing the maximum value of the heat capacity curves, the number of microscopic particles between the two horizons can be estimated, which reflects the quantum properties of the KR-dS spacetime. These studies will open a new perspective to probe the thermodynamics of black holes.

Holographic thermodynamics of a charged AdS black hole with a global monopole

By regarding the Newton constant G N and cosmological constant Λ as variables, in this paper we study the thermodynamics and phase transition of the Reissner-Nordstr öm anti-de Sitter (RN-AdS) black hole with a global monopole within the framework of AdS/CFT correspondence. We find interesting critical phenomena and phase behavior in the (grand) canonical ensembles of fixed ( Q˜,V,C ), ( Φ˜,V,C ) and ( Q˜,V,μ ). When the other parameters are fixed, the free energy decreases with the global monopole increases. In the ( Q˜,V,C ) ensemble, the range of the unstable region decreases with the increase of the global monopole. In the ( Φ˜,V,C ) ensemble, when Φ˜<Φc , the free energy appears as two branches, where the upper and lower branches correspond to low and high entropy, respectively. When ( Q˜,V,μ ) is fixed, a new zero-order phase transition occurs in the high-entropy phase and the low-entropy phase at certain μ-dependent temperatures. When μ increases to a certain value, this zero-order phase transition disappears. This certain value is negatively related to the magnitude of the global monopole. Finally, we find that p−V criticality does not appear with the change of global monopole. Therefore, it is important to note that the CFT states of charged black holes with global monopoles do not correspond to van der Waals fluids. Finally, we find that charged black holes with global monopoles can better reflect thermodynamic phase transitions and critical phenomena under the AdS/CFT correspondence. By adjusting the change of the global monopole, the thermodynamic phase transition will also change.

Thermodynamics of black holes featuring primary scalar hair

In this work, we embark on the thermodynamic investigation concerning a family of primary charged black holes within the context of shift and parity symmetric Beyond Horndeski gravity. Employing the Euclidean approach, we derive the functional expression for the free energy and derive the first thermodynamic law, offering a methodology to address the challenge of extracting the thermal quantities in shift-symmetric scalar tensor theories characterized by linear time dependence in the scalar field. Following the formal analysis, we provide some illustrative examples focusing on the thermal evaporation of these objects. Published by the American Physical Society 2024

Thermal stability and phase transitions of static magnetic charged black holes in the background of perfect fluid-type dark matter: Analysis of crucial thermodynamic parameters and P–V criticality along with higher-order entropy corrections

This work focuses on the analysis of P–V criticality for several entropy corrections of uncorrected zeroth entropy of the static magnetic charged black hole embedded in perfect fluid-type dark matter. During the study of P–V criticality, critical points up to several orders are found out. However, the critical points for distinct orders are found to occur at distinct values of the radius of the event horizon. We have resolved the physical significance of those critical points. Further, we have observed that P–V curve wise characteristics do not follow Boyle’s law for some corrections of entropy but it pursues Boyle’s law if we modify the zeroth entropy in some different ways. Physical significance of this phenomenon is also discussed. Again, the heat capacity of the charged black hole for corrected entropies is calculated. Significantly, several phase transitions are observed after plotting those data. We have also investigated how these phase transitions affect the structure of the black hole. Besides, study of free energy and Hawking temperature gives different important cuspidal nodes. The physical significance of these cusps is also discussed. Finally, we obtained an explicit scenario of the phase evolution and stability of the concerned investigated black hole embedded in dark matter.

First order corrections to black hole thermodynamics: A simple approach enhanced

First order corrections to black hole thermodynamics: A simple approach enhanced

Particle motion and thermal fluctuations of charged AdS black holes surrounded by exotic fluid with modified Chaplygin equation of state

This study explores the intricate relationships between thermodynamic properties and particle dynamics of charged AdS black holes, emphasizing the impacts of charge Q and higher-order corrections, particularly the parameter β, which is a modified Chaplygin gas parameter. Our analysis of entropy reveals that smaller black holes exhibit decreasing entropy variations with increased β, while larger black holes display a complex behavior characterized by initial entropy increases followed by decreases as the horizon radius expands. The Helmholtz free energy analysis suggests that higher-order corrections significantly modify energy behavior, indicating potential phase transitions influenced by gravitational forces, with increasing β values counteracting instability linked to larger charges. Internal energy assessments show an evolving stability of black holes, transitioning from negative to positive values as entropy increases, while also highlighting the destabilizing effects of electric charge. The specific heat analysis illustrates a complex thermal stability regime, where a rise in specific heat with increasing Q correlates with greater stability. However, critical points of instability arise with higher B values, where B is the BH model parameter. Moreover, the trajectories of particles around non-rotating charged black holes reveal that lower parameters result in unbounded motion. In contrast, higher parameters tend to restrict particles closer to the event horizon. Collectively, these findings underscore the complex interplay among charge, higher-order corrections, and stability in black hole thermodynamics, shedding light on the fundamental mechanisms governing black hole behavior and paving the way for future explorations using advanced models and simulations.

Holographic thermodynamics of BTZ black holes and Tsallis entropy

This paper presents a detailed study of the thermodynamics of charged BTZ black holes using the conformal holographic extended thermodynamics formalism and Tsallis statistics. The cornerstone of our thermodynamic framework is the re-scaling of CFT by the conformal factor, which is considered a thermodynamic parameter. Here, the AdS radius is distinct from the CFT radius, allowing for independent variations of the central charge and volume. Our analysis revealed that the thermodynamic behavior of charged BTZ black holes in three dimensions is characterized by the stability and absence of phase transitions, contrasting with the behavior of four-dimensional black holes. The central charge of CFT notably influences the thermal evolution of these black holes, with a smaller central charge leading to faster thermal processes. Additionally, the temperature of large black holes is proportional to their entropy. By incorporating Tsallis statistics into our study, we found that the stability of black holes depends on the Tsallis parameter. Black holes are always stable when the Tsallis parameter is less than 2. However, if this parameter is greater than 2, a first-order phase transition occurs between small stable and large unstable. Overall, our findings contribute to a deeper understanding of the holographic thermodynamics of lower-dimensional black holes and the impact of non-extensive statistics on their physical properties.

Thermal chemistry of Anti-de-Sitter black holes in Kalb-Ramond gravity

In this paper, we investigate the thermodynamic properties and emission energy of Anti-de-Sitter (AdS) black holes within the framework of Kalb-Ramond gravity. By analyzing the modified Einstein equations with the inclusion of the antisymmetric Kalb-Ramond tensor field, we explore the changes in key thermodynamic quantities such as temperature, entropy, and specific heat, alongside the emission energy spectrum associated with Hawking radiation. The study reveals novel thermal behaviors and energy emission patterns compared to standard AdS black holes, particularly highlighting the influence of the Kalb-Ramond field on black hole stability and phase transitions. Furthermore, we examine the role of the Kalb-Ramond field in modifying the emission energy. Our findings provide deeper insights into black hole thermodynamics, the emission process, and the broader role of antisymmetric fields in gravitational physics. Different paths for test particles near black holes are determined by their distance from the innermost stable circular orbit, which plays a crucial role in this study. The unique behavior of particles impacted by mass and rotational momentum is highlighted by the fact that particles within the innermost stable circular orbits tend to converge toward the singularity, but particles outside tend to diverge toward infinity.

Thermodynamic Aspects of Higher-Dimensional Black Holes in Einstein Gauss-Bonnet Gravity Through Exponential Entropy

Abstract We assume exponential corrections to the entropy of $5D$ charged AdS&amp;#xD;black hole solutions, which are derived within the framework of&amp;#xD;Einstein Gauss-Bonnet gravity and nonlinear electrodynamics.&amp;#xD;Additionally, we consider two distinct versions of $5D$ charged AdS&amp;#xD;black holes by setting the parameters $q\rightarrow0$ and&amp;#xD;$k\rightarrow0$ (where $q$ represents charge, $k$ is the non-linear&amp;#xD;parameter). We investigate these black holes in the extended phase&amp;#xD;space, where the cosmological constant is interpreted as pressure,&amp;#xD;and demonstrate the first law of black hole thermodynamics. The&amp;#xD;focus extends to understanding the thermal stability or instability,&amp;#xD;as well as identifying first and second-order phase transitions.&amp;#xD;This exploration is carried out through the analysis of various&amp;#xD;thermodynamic quantities, including heat capacity at constant&amp;#xD;pressure, Gibbs free energy, Helmholtz free energy, and the trace of&amp;#xD;the Hessian matrix. In order to visualize phase transitions,&amp;#xD;identify critical points, analyzing stability and provide&amp;#xD;comprehensive analysis, we have made the contour plot of the&amp;#xD;mentioned thermodynamic quantities and observed that our results are&amp;#xD;very much consistent. These investigations are conducted within the&amp;#xD;context of exponentially corrected entropies, providing valuable&amp;#xD;insights into the intricate thermodynamic behavior of these $5D$&amp;#xD;charged AdS black holes under different parameter limits.

Freudenthal duality in conformal field theory

Rotational Freudenthal duality (RFD) relates two extremal Kerr-Newman (KN) black holes (BHs) with different angular momenta and electric-magnetic charges, but with the same Bekenstein-Hawking entropy. Through the Kerr/CFT correspondence (and its KN extension), a four-dimensional, asymptotically flat extremal KN BH is endowed with a dual thermal, two-dimensional conformal field theory (CFT) such that the Cardy entropy of the CFT is the same as the Bekenstein-Hawking entropy of the KN BH itself. Using this connection, we study the effect of the RFD on the thermal CFT dual to the KN extremal (or doubly-extremal) BH. We find that the RFD maps two different thermal, two-dimensional CFTs with different temperatures and central charges, but with the same asymptotic density of states, thereby matching the Cardy entropy. We also discuss the action of the RFD on doubly-extremal rotating BHs, finding a spurious branch in the non-rotating limit, and determining that for this class of BH solutions the image of the RFD necessarily over-rotates.

Specific heats for quantum BTZ black holes in extended thermodynamics

It was shown recently that extended black hole thermodynamics, where the cosmological constant is a dynamical variable, giving rise to a pressure p and its conjugate volume V, can be given a natural setting in the context of braneworld models. We study the specific heat capacities Cp(T) and CV(T) of the quantum version of the Bañados, Teitelboim, and Zanelli (BTZ) black hole that lives in the induced gravity theory on the brane. There are multiple branches of solutions, and we explore and characterize key features of the possible behavior. We identify and study a critical point in the space of solutions where both specific heats diverge. In the regime of weak backreaction where we are close to an ordinary theory of gravity, the black hole is “subentropic,” but as backreaction is increased we note that there are parts of parameter space that has regions where it is “superentropic.” While a study of the sign of the specific heats does not always show a corresponding instability (conjectured in the literature), the presence of strong backreaction makes interpretation unclear. Published by the American Physical Society 2024

The fate for the interior content of a Black Hole from one-quarter entropy area-law

In this paper we continue investigations concerning the physical nature of the black hole entropy. In particular, in order to depict massless excitations (gravitons) leading to the one-quarter entropy area law, we use a mechanical statistical approach. As a first result, we obtain that, starting with a radiation field, we cannot exactly obtain the one-quarter factor in entropy area law. In the aforementioned framework, the correct black hole entropy is obtained only in the case where the internal temperature Ti, proportional to the Bekenstein-Hawking one, is such that Ti→0. As a consequence, according to other similar proposals in the literature, only a kind of Bose–Einstein condensate (BEC) can exactly support the black hole entropy.

Gauss–Bonnet AdS planar and spherical black hole thermodynamics and holography

Abstract In this work, we extend the study in Bilic and Fabris (2022 J. High Energy Phys. JHEP11(2022)013) incorporating the AdS/CFT duality to establish a relationship between the local temperatures (Tolman temperatures) of a large (AdS) spherical and a (AdS) planar Schwarzschild black hole near the AdS boundary considering Gauss–Bonnet (GB) curvature correction in the gravitational action. We have shown that the higher curvature corrections appear in the local temperature relationship due to the inclusion of GB term in the bulk. By transforming the metric into Fefferman–Graham form, we have calculated the energy density of the conformal fluid at the boundary. The obtained result contains finite coupling corrections which are holographically induced by the GB curvature correction in the bulk theory. Following the well known approach of fluid/gravity duality, the energy density of the conformal fluid at the boundary is then compared with the black body radiation energy density. This comparison shows that the energy density is proportional to the temperature of the conformal fluid. The temperature of the conformal fluid is then shown to be related to the Tolman temperature of the black hole which then eventually helps us to establish both the Hawking temperature and Tolman temperature relationship between large spherically symmetric and planar Schwarzschild black holes in GB gravity near the AdS boundary.

Riemann surfaces and winding numbers of Rényi phase structure of charged-flat black holes

It’s widely recognized that the free energy landscape captures the essentials of thermodynamic phase transitions. In this work, we extend the findings of [1] by incorporating the nonextensive nature of black hole entropy. Specifically, the connection between black hole phase transitions and the winding number of Riemann surfaces derived through complex analysis is extended to the Rényi entropy framework. This new geometrical and nonextensive formalism is employed to predict the phase portraits of charged-flat black holes within both the canonical and grand canonical ensembles. Furthermore, we elucidate novel relations between the number of sheets comprising the Riemann surface of the Hawking–Page and Van der Waals transitions and the dimensionality of black hole spacetimes. Notably, these new numbers are consistent with those found for charged-AdS black holes in Gibbs–Boltzmann statistics, providing another significant example of the potential connection between the cosmological constant and the nonextensive Rényi parameter.

Corrected thermodynamics and stability of magnetic charged AdS black holes surrounded by quintessence

In this study, we explore the corrected thermodynamics of non-linear magnetic charged anti-de Sitter (AdS) black holes surrounded by quintessence, incorporating thermal fluctuations and deriving the corrected thermodynamic potentials. We analyze the effects of corrections due to thermal fluctuations on various thermodynamic potentials, including enthalpy, Helmholtz free energy, and Gibbs free energy. Our results show significant impacts on smaller black holes, with first-order corrections destabilizing them, while second-order corrections enhance stability with increasing parameter values. The specific heat analysis further elucidates the stability criteria, indicating that the large black holes ensure stability against phase transitions. However, the thermal fluctuations do not affect the physical limitation points as well as the second-order phase transition points of the black hole. Our findings highlight the intricate role of thermal fluctuations in black hole thermodynamics and their influence on stability, providing deeper insights into the behaviour of black holes under corrected thermodynamic conditions.

Probing modified Hawking evaporation with gravitational waves from the primordial black hole dominated universe

It has been recently proposed that Hawking evaporation might slow down after a black hole has lost about half of its mass. Such an effect, called “memory burden”, is parameterized as a suppression in the mass loss rate by negative powers n of the black hole entropy and could considerably extend the lifetime of a black hole. We study the impact of memory burden on the Primordial Black Hole (PBH) reheating scenario. Modified PBH evaporation leads to a significantly longer PBH dominated stage. Requiring that PBHs evaporate prior enough to Big Bang Nucleosynthesis shrinks the allowed PBH mass range. Indeed, we find that for n > 2.5 the PBH reheating scenario is not viable. The frequency of the Gravitational Waves (GWs) induced by PBH number density fluctuations is bound to be larger than about a Hz, while the amplitude of the GW spectrum is enhanced due to the longer PBH dominated phase. Interestingly, we show that, in some models, the slope of the induced GW spectrum might be sensitive to the modifications to Hawking evaporation, proving it may be possible to test the “memory burden” effect via induced GWs. Lastly, we argue that our results could also apply to general modifications of Hawking evaporation.