Black Hole Entropy Research Articles

Latent Stochastic Differential Equations for Modeling Quasar Variability and Inferring Black Hole Properties

Quasars are bright and unobscured active galactic nuclei (AGN) thought to be powered by the accretion of matter around supermassive black holes at the centers of galaxies. The temporal variability of a quasar’s brightness contains valuable information about its physical properties. The UV/optical variability is thought to be a stochastic process, often represented as a damped random walk described by a stochastic differential equation (SDE). Upcoming wide-field telescopes such as the Rubin Observatory Legacy Survey of Space and Time (LSST) are expected to observe tens of millions of AGN in multiple filters over a ten year period, so there is a need for efficient and automated modeling techniques that can handle the large volume of data. Latent SDEs are machine learning models well suited for modeling quasar variability, as they can explicitly capture the underlying stochastic dynamics. In this work, we adapt latent SDEs to jointly reconstruct multivariate quasar light curves and infer their physical properties such as the black hole mass, inclination angle, and temperature slope. Our model is trained on realistic simulations of LSST ten year quasar light curves, and we demonstrate its ability to reconstruct quasar light curves even in the presence of long seasonal gaps and irregular sampling across different bands, outperforming a multioutput Gaussian process regression baseline. Our method has the potential to provide a deeper understanding of the physical properties of quasars and is applicable to a wide range of other multivariate time series with missing data and irregular sampling.

Generalized Freudenthal duality for rotating extremal black holes

Freudenthal duality (FD) is a non-linear symmetry of the Bekenstein-Hawking entropy of extremal dyonic black holes (BHs) in Maxwell-Einstein-scalar theories in four space-time dimensions realized as an anti-involutive map in the symplectic space of electric-magnetic BH charges. In this paper, we generalize FD to the class of rotating (stationary) extremal BHs, both in the under- and over-rotating regime, defining a (generalized) rotating FD (generally, non-anti-involutive) map (RFD), which also acts on the BH angular momentum. We prove that the RFD map is unique, and we compute the explicit expression of its non-linear action on the angular momentum itself. Interestingly, in the non-rotating limit, RFD bifurcates into the usual, non-rotating FD branch and into a spurious branch, named “golden” branch, mapping a non-rotating (static) extremal BH to an under-rotating (stationary) extremal BH, in which the ratio between the angular momentum and the non-rotating entropy is the square root of the golden ratio. Finally, we investigate the possibility of inducing transitions between the under- and over- rotating regimes by means of RFD, obtaining a no-go result.

Normal modes of the stretched horizon: a bulk mechanism for black hole microstate level spacing

In 1984, ’t Hooft famously used a brickwall (aka stretched horizon) to compute black hole entropy up to a numerical pre-factor. This calculation is sometimes interpreted as due to the entanglement of the modes across the horizon, but more operationally, it is simply an indirect count of the semi-classical modes trapped between the stretched horizon and the angular momentum barrier. Because the calculation was indirect, it needed both the mass and the temperature of the black hole as inputs, to reproduce the area. A more conventional statistical mechanics calculation should be able to get the entropy, once the ensemble is specified (say via the energy, in a microcanonical setting). In this paper, we explicitly compute black hole normal modes in various examples, numerically as well as (in various regimes) analytically. The explicit knowledge of normal modes allows us to reproduce both the Hawking temperature as well as the entropy, once the charges are specified, making this a conventional statistical mechanics calculation. A quasi-degeneracy in the angular quantum numbers is directly responsible for the area scaling of the entropy, and is the key distinction between the Planckian black body calculation (volume scaling) and the ’t Hooftian calculation (area scaling). We discuss the (rotating) BTZ case in detail and match the thermodynamic quantities exactly. Schwarzschild and Kerr normal modes are discussed in less detail using near-horizon approximations. Our calculations reveal a new hierarchy in the angular quantum numbers, which we speculate is related to string theory.

Effects of the new type of extended uncertainty principle on Van der Waals black hole thermodynamics: A theoretical and deep learning approach

In this paper, we study the Van der Waals black holes (the case [Formula: see text]) in the anti-de Sitter space under the effect of the linear extended uncertainty principle (EUP). The analysis was undertaken using deep learning by employing physics-informed neural networks in addition to the semi-classical approach, we have calculated the thermal quantities, including mass, volume, temperature, entropy, and Gibbs free energy. Additionally, we visually depict the effects of the EUP-term on the thermodynamic properties of the studied black holes.

Thin-shell gravastar in a noncommutative BTZ geometry

In this paper, we build a thin-shell gravastar model within a noncommutative BTZ geometry. For this, we consider a noncommutative BTZ metric in the inner region and a geometry associated with a BTZ solution in the outer region, joined by the generalized join technique. After investigating the inner spacetime, surface and outer spacetime, we observe that there is a surface energy density and surface pressure, such as to make gravastar stable. This effect persists even when the cosmological constant is zero. Besides, we found a bound for the noncommutativity parameter. In addition, we examine the thermodynamics of the noncommutative BTZ black hole in Schwarzschild-type form in three-dimensional spacetime. We also check the stability condition by calculating the specific heat capacity, as well as for the formation of black hole remnants.

Black holes thermodynamics with CFT re-scaling

In this paper, we study the thermodynamic behavior of charged AdS black holes in a conformal holographic extended thermodynamic. Our setup is constructed using a new dictionary that relates AdS black hole quantities to the corresponding dual conformal fields theory (CFT) one, with the conformal factor being treated as a variable thermodynamic. In this thermodynamic study, we investigate the critical phenomena of charged AdS black holes and their relationship to the central charge value, C. Additionally, we examine the phase transitions and black holes stability using the free energy and the heat capacity, respectively. Furthermore, by examining the chemical potential, we establish a criteria that differentiate between quantum and classical black hole’s behaviors. Our setup highlights one of the key findings, namely traditional black hole thermodynamics acts as a boundary between quantum and classical regimes.

Barrow entropy and AdS black holes in RPS thermodynamics

In this paper, we examine the restricted phase space (RPS) thermodynamics for charged AdS black holes by considering the impact of quantum gravity on the event horizon area. The primary aim of this work is to elucidate the influence of quantum gravitational effects on thermodynamic behaviors, critical phenomena, phase transitions, and the stability of black holes. We observe that charged AdS black holes exhibit thermodynamic behavior similar to that of Van der Waals fluids when influenced by quantum gravity. Furthermore, we introduce a novel black hole thermodynamic phenomenon, which we term “resistance of phase transitions”. Our study uncovers a violation of the homogeneity property of the Smarr relation in RPS thermodynamics due to the effects of quantum gravity.

Behaviors of black holes and black strings in M-theory on Calabi–Yau manifolds

In this work, we reconsider the study of black holes and black strings in the compactification of M-theory on a Calabi–Yau three-fold, considered as a complete intersection of hypersurfaces in a product of weighted projective spaces given by [Formula: see text]. Using the [Formula: see text] supergravity formalism in five dimensions, we examine the BPS and non-BPS solutions by wrapping M-branes on appropriate cycles in such a Calabi–Yau geometry. For the black hole case, we compute certain thermodynamical quantities. In particular, we calculate the entropy taking a maximal value corresponding to the ordinary projective space [Formula: see text] with [Formula: see text]. Using extended black hole entropies, we evaluate the temperature involving a minimal value for [Formula: see text]. Then, we approach the stability of the non-BPS black holes via the recombination factor. In the allowed electric charge regions, we show that such states are unstable. For the black string solutions, we calculate the tension taking a minimal value corresponding to [Formula: see text]. Computing the recombination factor, we show that the associated non-BPS black string states are stable in the allowed magnetic charge regions of the moduli space.

Logarithmic correction to BPS black hole entropy from supersymmetric index at finite temperature

It has been argued by Iliesiu, Kologlu and Turiaci in arXiv:2107.09062 that one can compute the supersymmetric index of black holes using black hole geometry carrying finite temperature but a specific complex angular velocity. We follow their prescription to compute the logarithmic correction to the entropy of BPS states in four dimensions, defined as the log of the index of supersymmetric black holes, and find perfect agreement with the previous results for the same quantity computed using the near horizon AdS2 × S2 geometry of zero temperature black holes. Besides giving an independent computation of supersymmetric black hole entropy, this analysis also provides a test of the procedure used previously for computing logarithmic corrections to Schwarzschild and other non-extremal black hole entropy.

Magnetic Black Hole Thermodynamics in an Extended Phase Space with Nonlinear Electrodynamics.

We study Einstein's gravity coupled to nonlinear electrodynamics with two parameters in anti-de Sitter spacetime. Magnetically charged black holes in an extended phase space are investigated. We obtain the mass and metric functions and the asymptotic and corrections to the Reissner-Nordström metric function when the cosmological constant vanishes. The first law of black hole thermodynamics in an extended phase space is formulated and the magnetic potential and the thermodynamic conjugate to the coupling are obtained. We prove the generalized Smarr relation. The heat capacity and the Gibbs free energy are computed and the phase transitions are studied. It is shown that the electric fields of charged objects at the origin and the electrostatic self-energy are finite within the nonlinear electrodynamics proposed.

Tearing down spacetime with quantum disentanglement

A longstanding enigma within AdS/CFT concerns the entanglement entropy of holographic quantum fields in Rindler space. The vacuum of a quantum field in Minkowski spacetime can be viewed as an entangled thermofield double of two Rindler wedges at a temperature T = 1/2π. We can gradually disentangle the state by lowering this temperature, and the entanglement entropy should vanish in the limit T → 0 to the Boulware vacuum. However, holography yields a non-zero entanglement entropy at arbitrarily low T, since the bridge in the bulk between the two wedges retains a finite width. We show how this is resolved by bulk quantum effects of the same kind that affect the entropy of near-extremal black holes. Specifically, a Weyl transformation maps the holographic Boulware states to near-extremal hyperbolic black holes. A reduction to an effective two-dimensional theory captures the large quantum fluctuations in the geometry of the bridge, which bring down to zero the density of entangled states in the Boulware vacuum. Using another Weyl transformation, we construct unentangled Boulware states in de Sitter space.

BTZ black hole in [formula omitted] gravity and thermodynamic properties

In this study, we aim to investigate the rotating Banados-Teitelboim-Zanelli (BTZ) black hole (BH) solution within the framework of modified gravity theories. Notably, our investigation reveals that the BTZ BH space–time serves as a solution within the framework of Ricci-inverse (RI) gravity, particularly within Class-I models defined by f(R,A)=(R+αA). Here, R=gμνRμν and A=gμνAμν denote the Ricci and anti-curvature scalars, respectively, while α represents the coupling parameter. We show that this new modified theory induces modifications to the cosmological constant, demonstrating the influence of the coupling parameter α when analyzed in a vacuum as matter content. Additionally, we study the thermodynamic properties of this BTZ BH solution obtained within the RI-gravity framework and analyze the associated physical quantities. It is evident that the thermodynamic parameters, including BH horizons, Hawking temperature, entropy, free energy, internal energy, and specific heat capacity, undergo alterations due to the coupling constant α. Specifically, when α=0, our findings align with the outcomes documented in existing literature obtained in the general relativity (GR) context using the BTZ BH solution.

Near-horizon geometries and black hole thermodynamics in higher-derivative AdS5 supergravity

Higher-derivative corrections in the AdS/CFT correspondence allow us to capture finer details of the dual CFT and to explore the holographic dictionary beyond the infinite N and strong coupling limits. Following an effective field theory approach, we investigate extremal AdS black hole solutions in five-dimensional supergravity with higher-derivative corrections. We provide a general analysis of near-horizon geometries of rotating extremal black holes and show how to obtain their corresponding charges and chemical potentials. We discuss the near-horizon solutions of the two-derivative theory, which we write using a novel parametrization that eases our computation of the higher-derivative corrections. The charges and thermodynamic properties of the black hole are computed while clarifying the ambiguities in their definitions. The charges and potentials turn out to satisfy a near-horizon version of the first law of thermodynamics whose interpretation we make clear. In the supersymmetric case, the results are shown to match the field theory prediction as well as previous results obtained from the on-shell action.

Exploring non-perturbative corrections in thermodynamics of static dirty black holes

This research delves into an extensive exploration of the thermodynamic characteristics exhibited by a contaminated black hole subject to a uniform electric field, within the theoretical framework of the Einstein-Nonlinear Electrodynamics (ENE)-dilaton theory. The investigation encompasses a thorough analysis of diverse thermodynamic facets, encompassing heat capacity, Helmholtz free energy, and internal energy. Through this comprehensive examination, valuable insights are provided into the distinctive behavior of the black hole when subjected to the influence of the electric field. Moreover, our study embarks on an exploration of the nuanced interplay between quantum effects and the thermodynamic profile, with a particular focus on scrutinizing the quantum-corrected entropy. This approach allows for a deeper understanding of the intricate relationship between quantum mechanics and the thermodynamic attributes exhibited by the system. By doing so, we aim to illuminate the non-perturbative corrections inherent in this intricate system, thereby contributing to a holistic comprehension of the altered thermodynamics characterizing dirty black holes within the confines of the specified theoretical framework. In essence, this research endeavors to uncover the subtleties of the modified thermodynamic landscape governing black holes tainted by external factors, specifically within the context of the ENE-dilaton theory. The outcomes of this study promise to extend our understanding of the intricate interactions within such complex systems, offering valuable insights into the non-perturbative corrections that manifest in their thermodynamic behavior.

Thermodynamics for regular black holes as intermediate thermodynamic states and quasinormal frequencies

The thermodynamics for regular black holes (RBHs) is considered under the restricted phase space (RPS) formalism. It is shown that the RPS formalism seems to hold for RBHs, however, in order for the extensive thermodynamic parameters to be independent from each other, the RBHs need to be viewed as intermediate thermodynamic states in a larger class of black holes (BHs) which admit both regular and singular states. This idea is checked for several classes of BHs. In particular, for the electrically charged Hayward class BHs, it is shown that the regular states can either be thermodynamically stable or unstable, depending on the amount of charges carried by the BHs. The quasinormal frequencies for the Hayward class BHs are also analyzed, and it turns out that, even for the thermodynamically unstable regular states, the dynamic stability still holds, at least under massless scalar perturbations.

Thermodynamics of black holes charged with a conformally invariant electrodynamics in (n+1)-dimensional scalar-tensor theory

The Jordan frame (JF) field equations of scalar-tensor (ST) theory are strongly coupled and, the exact solutions cannot be obtained easily. By using the conformal transformation (CT), the ST action has been translated to the Einstein frame (EF) where the theory is known as the Einstein-dilaton (Ed) gravity. Also, an [Formula: see text]-dimensional electromagnetic Lagrangian has been introduced which remains invariant under CT. The Ed-conformal-invariant field equations, which are confronted with the mathematical indeterminacy problem, have been solved by use of a power-law ansatz function. We have introduced two classes of black holes (BHs) which are asymptotically non-flat and non-AdS. The Ed exact solutions can produce BHs with three, two, one and without horizons. By calculating the thermodynamic quantities, and making use of the Smarr mass relation it has been shown that the thermodynamical first law is valid in the EF. Thermal stability of Ed BHs has been analyzed by considering specific heats, thermodynamic Ricci scalars and Gibbs free energies, separately. Then using the inverse CTs, the ST exact solutions have been obtained which show two classes of horizonless, one-horizon, two-horizon and three-horizon BHs. We found that CTs preserve thermodynamic quantities and, thermodynamic properties of the ST BHs are just like those of Ed ones.

Recovery of consistency in thermodynamics of regular black holes in Einstein's gravity coupled with nonlinear electrodynamics

As one of candidate theories in the construction of regular black holes, Einstein's gravity coupled with nonlinear electrodynamics has been a topic of great concerns. Owing to the coupling between Einstein's gravity and nonlinear electromagnetic fields, we need to reconsider the first law of thermodynamics, which will lead to a new thermodynamic phase space. In such a phase space, the equation of state accurately describes the complete phase transition process of regular black holes. The Maxwell equal area law strictly holds when the phase transition occurs, and the entropy obeys the Bekenstein-Hawking area formula, which is compatible with the situation in Einstein's gravity.

Modified Friedmann equations and fractal Black Hole thermodynamics

The general relativity unification and quantum theory is a significant open problem in theoretical physics. This problem arises from the fact that these two fundamental theories, which describe gravity and the behavior of particles at the microscopic level, respectively, are currently incompatible. The unification of these theories is crucial for a complete comprehension of the fundamental forces and the nature of the universe. In this regard, the quantum properties of a Black Hole result in fundamental importance. By analyzing such properties in quantum field theory, in the first step, the gravity enters as a classical background. In semi-classical approximation, Black Holes will emit Hawking radiation with an almost thermal spectrum, while Black Hole’s entropy is proportional to the Black Hole’s horizon. Besides, Hawking’s temperature and Black Hole entropy should follow the first law of Black Hole thermodynamics. Also, Jacobson [Thermodynamics of spacetime: The Einstein equation of state, Phys. Rev. Lett. 75 (1995) 1260, doi:10.1103/PhysRevLett.75.1260] showed shown that there is a connection between Black Hole thermodynamics and Einstein’s equation that opens the root of a potential thermodynamic nature of gravity. This issue opened a new impressive research framework in which the Einstein field equation can be expressed as a form of the first law of thermodynamics and vice versa. In this study, it is assumed that the universe has a fractal structure. Accordingly, modified Friedmann’s equations and the Black Holes thermodynamics in a fractal universe have been examined. The fractal framework shows what features and changes occur in the description of the universe, particularly in studying the thermodynamics of a Black Hole. However, the paper strategy is organized as follows: in the beginning, we consider the first thermodynamic law in a fractal universe. Then, we investigate the Friedmann equation of the fractal universe in the form of the entropy balance, this means [Formula: see text], where [Formula: see text] and [Formula: see text] are the thermal energy and horizon temperature. We consider the entropy [Formula: see text] have two terms; (1) obeys the usual area law and (2) the entropy production term due to the non-equilibrium thermodynamics of a fractal universe. Therefore, in a fractal universe, a term with non-equilibrium thermodynamics of spacetime may be needed. Also, we study the generalized second law of thermodynamics in a fractal universe. When the temperature of the apparent horizon and the temperature of the matter fields inside the horizon are equal, i.e. [Formula: see text], the second law of generalized thermodynamics can be obtained according to the state parameter range equation, which is consistent with the recent observations. Finally, in Sec. 6, based on the mathematical calculations, we study the various cosmological parameters such as the Hubble parameter, scale factor, deceleration parameter and equation of state parameter.

Quantum thermodynamics of the charged AdS black hole with nonlinear electrodynamics field

In this paper, we investigate the thermodynamic properties of an AdS-charged black hole coupled with a nonlinear electrodynamic field, taking into account the effects of thermal fluctuations. Our analysis focuses on how thermal fluctuations impact the entropy of the black hole. It is known that at the quantum level, thermal fluctuations bring about changes in the entropy of a black hole in both exponential and logarithmic ways. We present the logarithmic and exponentially corrected thermodynamic characteristics of the black hole, such as Helmholtz free energy, pressure, enthalpy, Gibbs free energy, and specific heat. A comparative analysis of equilibrium states with corrected thermodynamic potentials is conducted to observe the significant influence of the black hole under consideration. Additionally, we examine a second-order phase transition in the case of non-perturbed correction.

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.