Hawking Temperature Research Articles

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.

Analogous Hawking Radiation in Dispersive Media

In the framework of the analogous Hawking effect, we significantly improve our previous analysis of the master equation that encompasses very relevant physical systems, like Bose–Einstein condensates (BECs), dielectric media, and water. In particular, we are able to provide two significant improvements to the analysis. As our main result, we provide a complete set of connection formulas for both the subluminal and superluminal cases without resorting to suitable boundary conditions, first introduced by Corley, but simply on the grounds of a rigorous mathematical setting. Moreover, we provide an extension to the four-dimensional case, showing explicitly that, apart from obvious changes, adding transverse dimensions does not substantially modify the Hawking temperature in the dispersive case. Furthermore, an important class of exact solutions of the so-called reduced equation that governs the behavior of non-dispersive modes is also provided.

Thermodynamics and quasinormal modes of the Dymnikova black hole in higher dimensions

In this study, we investigate the thermodynamic properties and quasinormal modes of Dymnikova black holes within the context of higher dimensions in Einstein’s general theory of relativity. We calculate the thermodynamic parameters, including the Hawking temperature and heat capacity, which allowed us to investigate the black hole’s stability. Lastly the quasinormal modes with the WKB formula were calculated.

Quantum-corrected Schwarzschild AdS black hole surrounded by quintessence: Thermodynamics and shadows

In this paper, we study the quantum-corrected Schwarzschild AdS black hole surrounded by quintessence matter in two folds: its thermal quantities and shadows. For this purpose, first, we present a detailed analysis of the influences of the quintessence matter field on Hawking temperature, mass, Gibbs free energy, and specific heat functions. Then, we examine the shadows by following Carter’s approach. We find that the shadow radius value takes smaller values for greater quintessence state parameter values. On the other hand, we see that the shadow radius takes greater values for greater values of the normalization parameter. Finally, in a brief section, we discuss the energy emission rate and show that the Gaussian-type plots’ peak values are also affected by the quintessence matter field parameters.

Analysis of the three possible event horizons of anti-de Sitter space–time in the Klein–Gordon equation

In this paper, we calculate exactly the solution of Klein–Gordon equation in anti-de Sitter space–time. Due to spherical symmetry, the angular wave functions are given by spherical harmonics. The radial wave functions are given by local Heun functions. We analyze the behavior of the radial wave function in regions near three possible event horizon positions [Formula: see text] and investigate the decay rate, Hawking radiation and Hawking temperature for these three cases. Comparing the results, we verify that if the decay rate and Hawking radiation are greater, then the closer the event horizon is to the singularity of the black hole. Finally, we analyze the special case of a small black hole limit.

The Effects of a Minimal Length on the Kerr Metric and the Hawking Temperature

The Effects of a Minimal Length on the Kerr Metric and the Hawking Temperature

Moving mirrors, OTOCs and scrambling

We explore the physics of scrambling in the moving mirror models, in which a two-dimensional CFT is subjected to a time-dependent boundary condition. It is well-known that by choosing an appropriate mirror profile, one can model quantum aspects of black holes in two dimensions, ranging from Hawking radiation in an eternal black hole (for an “escaping mirror”) to the recent realization of Page curve in evaporating black holes (for a “kink mirror”). We explore a class of OTOCs in the presence of such a boundary and explicitly demonstrate the following primary aspects: First, we show that the dynamical CFT data directly affect an OTOC and maximally chaotic scrambling occurs for the escaping mirror for a large-c CFT with identity block dominance. We further show that the exponential growth of OTOC associated with the physics of scrambling yields a power-law growth in the model for evaporating black holes which demonstrates unitary dynamics in terms of a Page curve. We also demonstrate that, by tuning a parameter, one can naturally interpolate between an exponential growth associated with scrambling and a power-law growth in unitary dynamics. Our work explicitly exhibits the role of higher-point functions in CFT dynamics as well as the distinction between scrambling and Page curve. We also discuss several future possibilities based on this class of models.

Non-Markovian dynamics control of an open quantum system in a Schwarzschild space–time

By considering two qubits respectively coupled with two independent reservoirs and ignoring the interaction between them, two different cases are studied in two models: only one qubit accelerates and hovers near the event horizon or both two qubits accelerate and hover near the event horizon. The first model is given by referring to the damping Jaynes–Cummings model with a reservoir described by Lorentzian spectral density. And the second model is a pure dephasing model with a reservoir described by Ohmic spectral density. We investigate the impact of acceleration and Hawking temperature on the non-Markovianity and the quantum speed limit time of a two-qubit open quantum system. Through the numerical calculation, it is found that for these two models, by reducing the acceleration of qubits and the Hawking temperature outside the event horizon, the non-Markovianity of the dynamic process of the quantum system in the Schwarzschild space–time can be enhanced until it approaches the non-Markovianity when both qubits are in the inertial frame. However, we find that in the first model, the evolution speed of quantum state can be accelerated with decreasing acceleration and Hawking temperature. While in the second model, the quantum state evolution speed can be accelerated with increasing acceleration and Hawking temperature. For both models, the evolution speed of the quantum state of the system in the Markovian dynamics can still be accelerated.

Minimally deformed regular Hayward black hole solutions in Rastall theory

Abstract We profit from the minimal geometric deformation technique of
gravitational decoupling and extend the regular Hayward black hole,
to derive new black hole solutions in the context of Rastall theory.
The field equations with an extended matter source are decoupled
into two subsystems. The first of these are specified by the metric
components of the regular Hayward black hole while the second set
which contains the effects of the added source is solved by
utilizing a constraint imposed via a linear equation of state. By a
linear combination of the solutions of these two subsystems, we
obtain two cases of the extended solutions. For specified values of
the Rastall and decoupling parameters, we investigate some
physical/thermodynamical properties of the obtained models. It turns
out that only the first model preserves asymptotic flatness. It is
found that the first and second models are described by exotic and
ordinary matter, respectively. Finally, we obtain an acceptable
behavior of the Hawking temperature and thermodynamic stability for
both models.

Study of first-order quantum corrections of thermodynamics to a Dyonic black hole solution surrounded by a perfect fluid

In this work, we review the metric for a dyonic global monopole with a perfect fluid. To calculate the standard temperature of a Dyonic black hole surrounded by a perfect fluid, we analyze the graphical interpretation of the Hawking temperature concerning the horizon under the effects of the black hole's surrounding field and electric-magnetic charges. For this purpose, we follow the semi-classical method, the Wentzel-Kramers-Brillouin (WKB) approximation, and the Lagrangian equation in the presence of quantum gravity as seen in the generalized uncertainty principle (GUP). We calculate the improved temperature of a Dyonic black hole using a bosonic tunneling strategy based on the Hamilton-Jacobi technique. We observe that the physical state of the Dyonic black hole is surrounded by a perfect fluid under the effects of the black hole solution and the gravity parameter. Further, we examine the improved entropy to study the influences of quantum gravity and black hole geometry on entropy. We explore the graphical behavior of entropy based on the black hole's horizon structure and analyze the influence of perfect fluid parameters, electric charge, magnetic charge, and quantum gravity on entropy. Finally, we investigate the unstable and stable conditions of a black hole via graphical results.

Barrow’s nonlinear charged anti-de Sitter black hole and stability

AbstractAs we know, the horizon area of a black hole will increase when it absorbs matter. Based on Barrow’s concept of a fractal black hole horizon, it has been proposed (Phys Lett B 831:137181, 2022) that for a spherically fractal structure, the minimum increase in the horizon area is the area of the smallest bubble sphere. The corresponding black hole entropy is of a logarithmic form, which is similar to that of Boltzmann entropy under a certain condition. Based on this, we re-derive the entropy of Barrow’s Einstein–power-Yang–Mills (EPYM) anti-de Sitter (AdS) black hole, and calculate its temperature and heat capacity. There exists an interesting phenomenon wherein the ratio between Barrow’s temperature and the Hawking temperature of the EPYM AdS black hole is fully consistent with that of other Schwarzschild-like black holes. The Barrow and Hawking temperatures within a certain range of $$\Lambda $$ Λ are found to increase monotonically, and the corresponding heat capacities are all positive, which means that these black holes are thermodynamically stable. In addition, for Barrow’s EPYM AdS black hole, its heat capacity has a Schottky anomaly-like behavior, which may reflect the existence of a discrete energy level and microscopic degrees of freedom.

Exact solutions for analog Hawking effect in dielectric media

In the framework of the analog Hawking radiation for dielectric media, we analyze a toy model and also the 2D reduction of the Hopfield model for a specific monotone and realistic profile for the refractive index. We are able to provide exact solutions, which do not require any weak dispersion approximation. The theory of Fuchsian ordinary differential equations is the basic tool for recovering exact solutions, which are rigorously identified and involve the so-called generalized hypergeometric functions F34(α1,α2,α3,α4;β1,β2,β3;z). A complete set of connection formulas are available, both for the subcritical case and for the transcritical one, and also the Stokes phenomenon occurring in the problem is fully discussed. From the physical point of view, we focus on the problem of thermality. Under suitable conditions, the Hawking temperature is deduced, and we show that it is in full agreement with the expression deduced in other frameworks under various approximations. Published by the American Physical Society 2024

Prigogine’s Second Law and Determination of the EUP and GUP Parameters in Small Black Hole Thermodynamics

In 1974, Stephen Hawking made the groundbreaking discovery that black holes emit thermal radiation, characterized by a specific temperature now known as the Hawking temperature. While his original derivation is intricate, retrieving the exact expressions for black hole temperature and entropy in a simpler, more intuitive way without losing the core physical principles behind Hawking’s assumptions is possible. This is obtained by employing the Heisenberg Uncertainty Principle, which is known to be connected to thenvacuum fluctuation. This exercise allows us to easily perform more complex calculations involving the effects of quantum gravity. This work aims to answer the following question: Is it possible to reconcile Prigogine’s second law of thermodynamics for open systems and the second law of black hole dynamics with Hawking radiation? Due to quantum gravity effects, the Heisenberg Uncertainty Principle has been extended to the Generalized Uncertainty Principle (GUP) and successively to the Extended Uncertainty Principle (EUP). The expression for the EUP parameter is obtained by conjecturing that Prigogine’s second law of thermodynamics and the second law of black holes are not violated by the Hawking thermal radiation mechanism. The modified expression for the entropy of a Schwarzschild black hole is also derived.

Thermalization and hotspot formation around small primordial black holes

We quantitatively analyze a basic question: what is the stationary solution of the background plasma temperature profile around a black hole (BH)? One may naively expect that the temperature profile continuously decreases from the Hawking temperature at the surface of the BH towards an outer region. We show analytically and numerically that this is not the case because local thermal equilibrium cannot be maintained near the surface of the BH and also because the high-energy particles emitted from Hawking radiation cannot be instantaneously thermalized into the background plasma. The temperature profile has a plateau within a finite distance from the BH, and even the overall amplitude of background temperature at a distance far away from the BH is significantly suppressed compared with the naive expectation. The main reason for these counterintuitive results comes from the fact that the size of the BH is too small that particles of Hawking radiation goes far away within the typical time scale of interactions.

A Quantization for the Toy Model of Black Hole and a Suggestion to the Unification Theory

In my previous paper about the correlations between quantum mechanics and the four different natural forces, I suggested that there may be a fifth force or even the existence of a new particle. However, it remains a mystery to physicists, even after nearly a hundred years, that they cannot unify these four natural forces. This may be because there are indeed too many variables for them to consider. Also, there is a possibility that quantum mechanics may coexist with quantum field theory. In the present paper, this author proposes that there may be a misconception in the computational equation for relative time or gaps in the system for measuring time between quantum mechanics and general relativity. Hence, one may still not be able to unify these natural forces. This author suggests that we may need to rewrite parts of quantum mechanics – the Schrödinger equation – or even the general relativity equation. Additionally, this author proposes that there may be a bridge equation converting between quantum mechanics and general relativity. Moreover, this author has employed the non-trivial zeta zeros to simulate the black hole or the so-called black hole toy model. In practice, there may be an electromagnetic field surrounding the boundary of the black hole, as well as the existence of a continuum along the boundary contour. This author hopes that, in such a case, we may decode those high-frequency electromagnetic waves into useful information and take a further step toward verifying Stephen Hawking’s famous theory on black hole radiation and information entropy. In fact, this author has used the HKLam statistical model theory to express the electromagnetic field energy-stress tensor (with the possibility of quantization) to analogically establish a quantized model for the Einstein Gravitational Field Equation. Hence, the problem of quantum gravity may then be solved. Last but not least, this author also expects that humanity may finally find a way to unify quantum mechanics and general relativity through modifications to the current quantum gravity theory, such as my proposed bridge-converting equation, etc.

Probing the thermodynamics of charged Gauss Bonnet AdS black holes with the Lyapunov exponent

In this paper, we investigate the thermodynamic properties of the charged AdS Gauss–Bonnet black holes and their associations with the Lyapunov exponent. The chaotic features of the black holes and the isobaric heat capacity characterized by the Lyapunov exponent are studied to reveal the thermodynamic stability of the black hole phases. By considering both the timelike and null geodesics, we find that the relationship between the Lyapunov exponent and the Hawking temperature can accurately represent the features of the Small/Large phase transition and even the triple point. We also reveal the properties of the difference in the Lyapunov exponent as an order parameter. It is demonstrated that there is a negative correlation between the Lyapunov exponent and the size of the black hole shadow, which can be used to bridge the thermodynamic properties and the shadow of black holes.

Physically accessible and inaccessible quantum correlations of Dirac fields in Schwarzschild spacetime

In this study, we investigate the influence of Hawking decoherence on the quantum correlations of Dirac fields between Alice and Bob. Initially, they share a Gisin state near the Schwarzschild black hole (SBH) in an asymptotically flat region. Then, Alice remains stationary in this region, while Bob hovers near the event horizon (EH) of the SBH. We expect that Bob, using his excited detector, will detect a thermal Fermi-Dirac particle distribution. We assess the quantum correlations in the evolved Gisin state using quantum consonance and uncertainty-induced non-locality across physically accessible, physically inaccessible, and spacetime regions. Our investigation examines how these measures vary with Hawking temperature, Dirac particle frequency, and the parameters of the initial Gisin state. Additionally, we analyze the distribution of these quantum correlation measures across all possible regions, noting a redistribution towards the physically inaccessible region. Our findings demonstrate that Hawking decoherence reduces the quantum correlations of Dirac fields in the physically accessible region, with the extent of reduction depending on the initial state parameters. Moreover, as Hawking decoherence intensifies in the physically inaccessible and spacetime regions, the quantum correlations of Dirac fields reemerge and ultimately converge to specific values at infinite Hawking temperature. These results contribute to our understanding of quantum correlation dynamics within the framework of relativistic quantum information (RQI).

Entropy correction of Kerr–Newman-AdS black hole in Rastall gravity under Lorentz symmetry violation

The tunneling of scalar particles and fermions across the event horizon of KN-AdS black hole surrounded by perfect fluid in Rastall theory are investigated in the frame dragging coordinate systems by applying modified Klein–Gordon equation and modified Dirac equation under the influence of Lorentz symmetry violation in curved spacetime. The Hawking temperature and the heat capacity of the black hole are modified due to the influence of Lorentz symmetry violation. The Hawking temperature and the Bekenstein–Hawking entropy of the black hole beyond the semiclassical approximation are also derived by taking the effects of Planck constant [Formula: see text]. The modified Hawking temperature and entropy correction of the black hole are dependent on the Lorentz violation parameter [Formula: see text], the ether-like vectors [Formula: see text] and Planck constant [Formula: see text].

Distribution of distance-based quantum resources outside a radiating Schwarzschild black hole

Abstract This study aims to investigate the distribution of distance-based quantum resources for fermionic fields in curved Schwarzschild spacetime (SST), as well as for bosonic fields in both flat Minkowski and curved SSTs. To achieve this, we will examine the quantum resources between an observer falling into a Schwarzschild black hole (SBH) and their stationary partner, who shares a Gisin state. Additionally, we will explore the quantum resources that arise when two uniformly accelerated detectors interact with bosonic fields in the Minkowski vacuum. Furthermore, we will investigate the interactions between these detectors and bosonic fields in the Hartle–Hawking and Boulware vacuums outside the SBH. At an infinite Hawking temperature, the quantum resources for the fermionic fields degrade; the rate of degradation is dependent on the distance between the observer and the event horizon, the fermionic frequency mode, and the Gisin state parameters. In the case of the bosonic fields, our results show that entanglement decreases monotonically, either towards zero or a constant value. Moreover, with increasing Unruh temperature, coherence and discord undergo sudden death followed by a sudden birth, and entanglement cannot be revived for a given initial state. Based on our findings, it appears that the Fermi–Dirac and Bose–Einstein statistics represent the primary differences in quantum resource distribution between the fermionic and bosonic cases. These findings may be essential for enhancing our understanding of the distribution of quantum resources in relativistic frameworks.

Minimally deformed regular Bardeen black hole solutions in Rastall theory

In this study, we utilize the minimal geometric deformation technique of gravitational decoupling to extend the regular Bardeen black hole, leading to the derivation of new black hole solutions within the framework of Rastall theory. By decoupling the field equations associated with an extended matter source into two subsystems, we address the first subsystem using the metric components of the regular Bardeen black hole. The second subsystem, incorporating the effects of the additional source, is solved through a constraint imposed by a linear equation of state. By linearly combining the solutions of these subsystems, we obtain two extended models. We then explore the distinct physical properties of these models for specific values of the Rastall and decoupling parameters. Our investigations encompass effective thermodynamic variables such as density and anisotropic pressure, asymptotic flatness, energy conditions, and thermodynamic properties including Hawking temperature, entropy, and specific heat. The results reveal that both models violate asymptotic flatness of the resulting spacetimes. The violation of energy conditions indicate the presence of exotic matter, for both models. Nonetheless, the energy density, radial pressure, as well as the Hawking temperature exhibit acceptable behavior, while the specific heat and Hessian matrix suggest thermodynamic stability.