Black Hole Entropy Research Articles

Accretion mechanism for regular black holes with asymptotically Minkowski Cores and improved Schwarzschild black holes

In this paper, we investigate the fascinating implications of the accretion process for two different kinds of black holes. A detailed analysis of the moving fluid in this accretion process is provided. The radial velocity u(r), the energy density ρ(r), speed of sound a2s and the mass accretion rate Ṁ of the regular black holes and improved Schwarzschild black hole are explored. Interestingly, we consider the most generic black hole space–times with isotropic fluid for this accretion process. The required and necessary physical behaviors around the black holes, such as the radial velocity, the energy density of the moving fluid within the scope of dust, stiff fluid and quintessence, are achieved. Our findings suggest that critical parameters like l in regular black holes, Γ in improved Schwarzschild black holes and the state parameter k are responsible for the accretion mechanism.

Atom falling into a quantum corrected charged black hole and HBAR entropy

Atom falling into a quantum corrected charged black hole and HBAR entropy

Extremal black hole decay in de Sitter space

The decay of extremal charged black holes has been a useful guidance to derive consistency conditions in quantum gravity. In de Sitter space it has been argued that requiring (extremal) charged Nariai black holes to decay without forming a big crunch singularity yields the Festina Lente (FL) bound: particles with mass ms and charge q should satisfy ms2≫MpHq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {m}_s^2\\gg {M}_p Hq $$\\end{document}, where Mp is the Planck mass and H the Hubble parameter. Using a tunneling approach we show that the decay probability of charged black holes in de Sitter space in the s-wave sector is P ∼ exp(∆Sb), where ∆Sb is the change in the black hole entropy. We find that the FL bound corresponds to ∆Sb ≤ – 1 in the Nariai and probe limit. However, taking into account backreaction we identify unsuppressed decay channels, which might be subdominant, that violate this bound but nonetheless do not result in a big crunch for every observer.

Phase transition and central charge criticality of RN AdS black hole immersed in perfect fluid dark matter

This paper delves into the thermodynamic properties of RN AdS black hole immersed in perfect fluid dark matter. We vary the Newton’s gravitational constant, cosmological constant and the perfect fluid dark matter parameter in the bulk. When studying the first law of thermodynamics for black holes, the boundary conformal field theory introduces the central charge, leading to modifications in the thermodynamic volume and chemical potential of black hole. Our analysis shows that the black hole’s free energy is affected by changes in both the central charge and the parameter of perfect fluid dark matter. The F−T curve shows a swallowtail behavior when central charge is above a critical value, which means the occurrence of first-order phase transition from a small black hole to a large black hole. Additionally, we analyzed the heat capacity as a function of temperature for different PFDM parameter values to study the stability of the black hole.

Entropy of dynamical black holes

We propose a new formula for the entropy of a dynamical black hole—valid to leading order for perturbations off of a stationary black hole background—in an arbitrary classical diffeomorphism covariant Lagrangian theory of gravity in n dimensions. In stationary eras, this formula agrees with the usual Noether charge formula, but in nonstationary eras, we obtain a nontrivial correction term. In particular, in general relativity, our formula for the entropy of a dynamical black hole differs from the standard Bekenstein-Hawking formula A/4 by a term involving the integral of the expansion of the null generators of the horizon. We show that, to leading perturbative order, our dynamical entropy in general relativity is equal to 1/4 of the area of the apparent horizon. Our formula for entropy in a general theory of gravity is obtained from the requirement that a “local physical process version” of the first law of black hole thermodynamics hold for perturbations of a stationary black hole. It follows immediately that for first order perturbations sourced by external matter that satisfies the null energy condition, our entropy obeys the second law of black hole thermodynamics. For vacuum perturbations, the leading-order change in entropy occurs at second order in perturbation theory, and the second law is obeyed at leading order if and only if the modified canonical energy flux is positive (as is the case in general relativity but presumably would not hold in more general theories of gravity). Our formula for the entropy of a dynamical black hole differs from a formula proposed independently by Dong and by Wall. We obtain the general relationship between their formula and ours. We then consider the generalized second law in semiclassical gravity for first order perturbations of a stationary black hole. We show that the validity of the quantum null energy condition (QNEC) on a Killing horizon is equivalent to the generalized second law using our notion of black hole entropy but using a modified notion of von Neumann entropy for matter. On the other hand, the generalized second law for the Dong-Wall entropy is equivalent to an integrated version of QNEC, using the unmodified von Neumann entropy for the entropy of matter. Published by the American Physical Society 2024

Hawking Temperature Modification and the Physical Dynamics of Black Holes: A Study of the Influence of Internal and Cosmological Variables

<p>The main objective of the study is to develop a model that modifies the traditional Hawking temperature by considering the influence of internal variables such as radius, mass, electric charge, angular momentum, and cosmological constant. The research method involves mathematical analysis and computational modeling based on the modified Hawking temperature equation. The results show that the modified Hawking temperature produces non-linear corrections that show the interaction between black holes and the quantum structure of spacetime. graphical representations visualize the variation of Hawking temperature with changes in area, electric charge, angular momentum, and cosmological parameters. The implications of the research extend to the understanding of the thermal properties of black holes in the context of gravitational and quantum theories. The research identifies gaps in the knowledge of the effects of cosmological parameters on black hole thermodynamics and introduces Hawking temperature modifications that have not been mapped in detail before. The study concludes that the Hawking temperature modification provides a strong foundation for further research in black hole physics, particularly in the effect of physical and cosmological parameters on the thermal properties of black holes.</p>

Black hole thermodynamics in generalized Proca theories

Black hole thermodynamics in generalized Proca theories

Holographic thermodynamics of a charged AdS black holes with global monopole

Abstract By regarding the Newton constant GN and cosmological constant Λ as variables, we in this paper study the thermodynamics and phase transition of Reissner-Nordström anti-de Sitter (RN-AdS) black hole with global monopole in the framework of AdS/CFT correspondence. It is found that there are interesting critical phenomena and phase behaviors 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 increases with the global monopole increases. In (Q, V, C) ensemble, the range of unstable region increases with the increase of global monopole. In (Φ, V, C) ensemble, when Φ<Φc, the free energy appears two branches, the upper and lower branches correspond to low entropy 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 positively 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 monopole 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.

Boltzmannian state counting for black hole entropy in causal set theory

This paper presents the first numerical study of black hole thermodynamics in causal set theory, focusing on the entropy of a Schwarzschild black hole as embodied in the distribution of proposed horizon molecules. To simulate causal sets we created a highly parallelized computational framework in ++ which allowed for the generation of causal sets with over a million points, the largest causal sets in a nonconformally flat spacetime to date. Our results confirm that the horizon molecules model is consistent with the Bekenstein-Hawking formula up to a dimensionless constant that can be interpreted as the fundamental discreteness scale in the order of a Planck length. Furthermore, the molecules are found to straddle the horizon of the black hole to within a few Planck lengths, indicating that entropy lives on the surface of the black hole. Finally, possible implications for the information paradox are drawn. In particular, we show how the horizon molecules model could yield a finite black hole temperature cutoff or even prevent full black hole evaporation. Published by the American Physical Society 2024

Klein-Gordon and Schrödinger solutions in Lovelock quantum gravity

This study investigates the application of wave functions to explore various solutions of the Klein-Gordon and Schrödinger equations within the framework of Lovelock gravity. We also present the derived Smarr formula from the topological density. The Klein-Gordon solution leads to the Wheeler-de Witt Hamiltonian and quasinormal modes, and we demonstrate the connection between the potential and the black hole temperature within the Schwarzschild limit. Additionally, we discuss different solutions of the Schrödinger equation, with one solution highlighting the influence of the Airy solution on the wave function's evolution over time.

Thermodynamics of Magnetic Black Holes with Nonlinear Electrodynamics in Extended Phase Space

We study Einstein’s gravity in AdS space coupled to nonlinear electrodynamics. Thermodynamics in extended phase space of magnetically charged black holes is investigated. We compute the metric and mass functions and their asymptotics, showing that black holes may have one or two horizons. The metric function is regular, f(0)=1, and corrections to the Reissner–Nordström solution are in the order of O(r−3) when the Schwarzschild mass is zero. We prove that the first law of black hole thermodynamics and the generalized Smarr relation hold. The magnetic potential and vacuum polarization conjugated to coupling are computed and depicted. We calculate the Gibbs free energy and the heat capacity showing that first-order and second-order phase transitions take place.

Black hole zeroth law of the Einstein-complex scalar-Gauss-Bonnet gravity

The zeroth law of black hole mechanics asserts that the stationary black hole has a constant surface gravity on the event horizon. This study investigates the zeroth law within the Einstein-Scalar-Gauss-Bonnet gravity, particularly involving a complex scalar field (ECSGB). Assuming that the Lie derivative of the complex scalar field is proportional to itself other than stationary, and that ECSGB gravity converges to the Einstein's gravity analyticaly as the coupling constant approaches zero, as well as the minimally coupled matter fields satisfy the dominant energy condition, we demonstrate that the surface gravity remains constant over the entire event horizon without reliance on additional symmetries.

Logarithmic Corrections to Kerr Thermodynamics.

Recent work has shown that loop corrections from massless particles generate 3/2logT_{Hawking} corrections to black hole entropy which dominate the thermodynamics of cold near-extreme charged black holes. Here we adapt this analysis to near-extreme Kerr black holes. Like AdS_{2}×S^{2}, the near-horizon extreme Kerr (NHEK) metric has a family of normalizable zero modes corresponding to reparametrizations of boundary time. The path integral over these zero modes leads to an infrared divergence in the one-loop approximation to the Euclidean NHEK partition function. We regulate this divergence by retaining the leading finite temperature correction in the NHEK scaling limit. This "not-NHEK" geometry lifts the eigenvalues of the zero modes, rendering the path integral infrared finite. The quantum-corrected near-extremal entropy exhibits 3/2logT_{Hawking} behavior characteristic of the Schwarzian model and predicts a lifting of the ground state degeneracy for the extremal Kerr black hole.

Higher-curvature gravity in AdS3 , holographic c -theorems, and black hole microstates

We construct higher-derivative gravity theories in three dimensions that admit holographic c-theorems and exhibit a unique maximally symmetric vacuum, at arbitrary order n in the curvature. We show that these theories exhibit special properties, the most salient ones being the decoupling of ghost modes around anti–de Sitter (AdS) space, the enhancement of symmetries at linearized level, and the existence of a one-parameter generalization of the Bañados-Teitelboim-Zanelli (BTZ) black hole that, while being asymptotically AdS, is not of constant curvature but rather exhibits a curvature singularity. For such black holes, we provide a holographic derivation of their thermodynamics. This gives a microscopic picture of black hole thermodynamics for nonsupersymmetric solutions, of nonconstant curvature in higher-derivative theories of arbitrary order in the curvature. Published by the American Physical Society 2024

Particle motion, shadows and thermodynamics of regular black hole in pure gravity

This paper investigates the thermodynamic behaviors and optical properties of regular black holes within pure gravity theories, notable for their absence of singularities. Using both analytical and numerical methods, we analyze the thermodynamics to identify stability and phase transitions, and explore the particle dynamics behavior of regular black holes. We analyze the particle dynamics properties by investigating the effective potential, energy density, angular momentum, ISCO, photon, and shadow radius. We analyze the thermal features by exploring the mass, temperature, specific heat, and Gibbs free energy. Our findings demonstrate that regular black holes exhibit distinct behaviors from traditional singular black holes, providing valuable insights into black hole physics and general relativity. This study suggests new directions for future research in fundamental gravitational theories.

Iyer-Wald ambiguities and gauge covariance of Entropy current in Higher derivative theories of gravity

In [1, 2] [arXiv:2105.06455, arXiv:2206.04538], the authors have been able to argue for an ultra-local version of the second law of black hole mechanics, for arbitrary diffeomorphism invariant theories of gravity non-minimally coupled to matter fields, by constructing an entropy current on the dynamical horizon with manifestly positive divergence. This has been achieved by working in the horizon-adapted coordinate system. In this work, we show that the local entropy production through the divergence of the entropy current is covariant under affine reparametrizations that leave the gauge of horizon-adapted coordinates invariant. We explicitly derive a formula for how the entropy current transforms under such coordinate transformations. This extends the analysis of [3] [arXiv:2204.08447] for arbitrary diffeomorphism invariant theories of gravity non-minimally coupled to matter fields. We also study the Iyer-Wald ambiguities of the covariant phase formalism that generically plague the components of the entropy current.

Topological classes of thermodynamics of the static multi-charge AdS black holes in gauged supergravities: novel temperature-dependent thermodynamic topological phase transition

In this paper, we investigate, in the framework of the topological approach to black hole thermodynamics, using the generalized off-shell Helmholtz free energy, the topological numbers of the static multi-charge AdS black holes in four- and five-dimensional gauged supergravities. We find that the topological number of the static-charged AdS black holes in four-dimensional Kaluza-Klein (K-K) gauged supergravity theory is W = 0, while that of the static-charged AdS black holes in four-dimensional gauged –iX0X1-supergravity and STU gauged supergravity theories, and five-dimensional Einstein-Maxwell-dilaton-axion (EMDA) gauged supergravity and STU gauged supergravity, and five-dimensional static-charged AdS Horowitz-Sen black hole are both W = 1. Furthermore, we observe a novel temperature-dependent thermodynamic topological phase transition that can happen in the four-dimensional static-charged AdS black hole in EMDA gauged supergravity theory, the four-dimensional static-charged AdS Horowitz-Sen black hole, and the five-dimensional static-charged AdS black hole in K-K gauged supergravity theory. We believe that the novel temperature-dependent thermodynamic topological phase transition could help us better understand black hole thermodynamics and, further, shed new light on the fundamental nature of gauged supergravity theories.

Thermodynamics of black holes with probe D-branes

Understanding how the thermodynamic properties of a black hole are modified when probed by D-branes is an important problem in AdS/CFT. This work focuses on a recently proposed black hole/D3-brane system in AdS5×S5, which is dual to four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM in the presence of a two-dimensional surface defect. The Laplace transform that extracts the asymptotic growth of states in this defect CFT naturally defines a thermodynamic approach in the gravitational side of the duality for which charges and entropy are real. Studying the superconformal defect index in a large-charge expansion for all values of N, we compute the leading correction to the entropy of the combined system, which matches precisely with its gravity counterpart.

Covariant phase space analysis of Lanczos-Lovelock gravity with boundaries

This work introduces a novel prescription for the expression of the thermodynamic potentials associated with the couplings of a Lanczos-Lovelock theory. These potentials emerge in theories with multiple couplings, where the ratio between them provide intrinsic length scales that break scale invariance. Our prescription, derived from the covariant phase space formalism, differs from previous approaches by enabling the construction of finite potentials without reference to any background. To do so, we consistently work with finite-size systems with Dirichlet boundary conditions and rigorously take into account boundary and corner terms: including these terms is found to be crucial for relaxing the integrability conditions for phase space quantities that were required in previous works. We apply this prescription to the first law of (extended) thermodynamics for stationary black holes, and derive a version of the Smarr formula that holds for static black holes with arbitrary asymptotic behaviour.

Minimal black holes and species thermodynamics

The species scale provides a lower bound on the shortest possible length that can be probed in gravitational effective theories. It may be defined by the size of the minimal black hole in the theory and, as such, it has recently been given an interpretation along the lines of the celebrated black hole thermodynamics. In this work, we extend this interpretation to the case of charged species. We provide working definitions of minimal black holes for the case of uncharged and charged species constituents. Then, examining the modifications in the thermodynamic properties of near-extremal charged species compared to the uncharged case, we uncover interesting implications for the cosmology of an expanding universe, particularly within the context of the Dark Dimensions Scenario. Finally, we explore possible microscopic constructions in non-supersymmetric string theories in which towers of charged near-extremal species may arise.