Horizon Thermodynamics Research Articles

Thermodynamics of a newly constructed black hole coupled with nonlinear electrodynamics and cloud of strings

This paper finds an exact singular black hole solution in the presence of nonlinear electrodynamics as the source of matter field surrounded by a cloud of strings in 4DAdS spacetime. Here, the presence of the cloud of string, the usual Bardeen solution, becomes singular. The obtained black hole solution interpolates with the AdS Letelier black hole in the absence of both the deviation parameter and magnetic charge and interpolates with the AdS Bardeen black hole in the absence of the deviation parameter and a cloud of strings parameter. We analyse the horizon structure and thermodynamics properties, including the stability of the resulting black hole, numerically and graphically. Thermodynamical quantities associated with the black hole get modified due to the nonlinear electrodynamics and cloud of strings. Moreover, we study the effect of a cloud of strings parameter, magnetic charge and deviation parameter on critical points and phase transition of the obtained black hole where the cosmological constant is treated as the thermodynamics pressure. The critical radius increases with increasing deviation parameter values and magnetic charge values. In contrast, the critical pressure and temperature decrease with increasing deviation parameters and magnetic charge values.

Different Aspects of Entropic Cosmology

We provide a short review of the recent developments in entropic cosmology based on two thermodynamic laws of the apparent horizon, namely the first and the second laws of thermodynamics. The first law essentially provides the change in entropy of the apparent horizon during the cosmic evolution of the universe; in particular, it is expressed by TdS=−d(ρV)+WdV (where W is the work density and other quantities have their usual meanings). In this way, the first law actually links various theories of gravity with the entropy of the apparent horizon. This leads to a natural question—“What is the form of the horizon entropy corresponding to a general modified theory of gravity?”. The second law of horizon thermodynamics states that the change in total entropy (the sum of horizon entropy + matter fields’ entropy) with respect to cosmic time must be positive, where the matter fields behave like an open system characterised by a non-zero chemical potential. The second law of horizon thermodynamics importantly provides model-independent constraints on entropic parameters. Finally, we discuss the standpoint of entropic cosmology on inflation (or bounce), reheating and primordial gravitational waves from the perspective of a generalised entropy function.

Emergence of cosmic space and horizon thermodynamics from Kaniadakis entropy

Abstract Utilizing Kaniadakis entropy associated with the apparent horizon of the Friedmann-Robertson-Walker (FRW) Universe and applying the emergence of cosmic space paradigm, we deduce the modified Friedmann equation for a non-flat (n+1)-dimensional universe. Employing the first law of thermodynamics, we arrive at the same modified Friedmann equation, showing the connection between emergence of cosmic space and first law of thermodynamics. We also establish the condition to satisfy the Generalized second law of thermodynamics within the Kaniadakis framework. Our study illuminates the intricate connection between the law of emergence and horizon thermodynamics, offering a deeper insight through the lens of Kaniadakis entropy.

Insights on Granda–Oliveros holographic dark energy: possibility of negative dark energy at z≳2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z\\gtrsim 2$$\\end{document}

In holographic dark energy (HDE) models, infrared cut-offs with derivatives of the Hubble parameter, such as the Granda–Oliveros cut-off, offer a coherent explanation for late-time acceleration while ensuring causal consistency. We show that such HDE will inevitably mimic the dominant energy forms unless we forcefully calibrate the free parameters. This feature reveals the dependency between the model’s ability to explain the late-time acceleration and the integration constant, highlighting that one cannot arbitrarily set this constant to zero. We see that the origins of HDE and the Friedmann equations from the first law of horizon thermodynamics offer a natural explanation for this behaviour. Thus, the holographic principle naturally extends to all energy components, diverging from the prevalent notion in HDE models. The model also allows dark energy to transit from an early negative energy to a present positive value, with a singular dark energy equation of state parameter, which can relax the tension in the BAO Lyman-α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} observations. Furthermore, we present observational constraints utilizing Pantheon+,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^+,$$\\end{document} OHD, CMB Shift parameter, QSO and BAO data, indicating the presence of early negative energy as an unavoidable consequence. Upon using the SH0ES prior, we see that the model accounts for the Hubble parameter at the cost of affecting the matter density while simultaneously relaxing the tensions in BAO Lyman-α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} observations and the age estimations. This study also underscores notable features stemming from the comprehensive utilization of the covariance matrix within cosmic chronometers, BAO and CMB distance prior and clarifies the implications of negative dark energy density derived from the high redshift Pantheon+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^+$$\\end{document} sample. Additionally, we provide a brief overview of the theoretical framework surrounding linear perturbation within the wGOHDE model.

Second law of horizon thermodynamics during cosmic evolution

Second law of horizon thermodynamics during cosmic evolution

Emergence of cosmic space and the maximization of horizon entropy

The spatial expansion of the universe can be described as the emergence of space with the progress of cosmic time, through a simple equation, ΔV=ΔtNsurf−Nbulk. This law of emergence suggested by Padmanabhan in the context of general relativity for a flat universe has been generalized by Sheykhi to Gauss Bonnet and Lovelock gravity for a universe with any spatial curvature. We investigate whether this generalized holographic equipartition effectively implies the maximization of horizon entropy. First, we obtain the constraints imposed by the maximization of horizon entropy in Einstein, Gauss Bonnet and Lovelock gravities for a universe with any spatial curvature. We then analyze the consistency of the law of emergence in Ahmad Sheykhi (2013), with these constraints obtained. Interestingly, both the law of emergence and the horizon entropy maximization demands an asymptotically de Sitter universe with ω≥−1. More specifically, when the degrees of freedom in the bulk (Nbulk) becomes equal to the degrees of freedom on the boundary surface (Nsurf), the universe attains a state of maximum horizon entropy. Thus, the law of emergence can be viewed as a tendency for maximizing the horizon entropy, even in a non flat universe. Our results points at the deep connection between the law of emergence and horizon thermodynamics, beyond Einstein gravity irrespective of the spatial curvature.

Entropic Inflation in Presence of Scalar Field

In spirit of the recently proposed four-parameter generalized entropy of apparent horizon, we investigate inflationary cosmology where the matter field inside of the horizon is dominated by a scalar field with a power law potential (i.e., the form of ϕn where ϕ is the scalar field under consideration). Actually without any matter inside of the horizon, the entropic cosmology leads to a de-Sitter spacetime, or equivalently, an eternal inflation with no exit. Thus in order to achieve a viable inflation, we consider a minimally coupled scalar field inside the horizon, and moreover, with the simplest quadratic potential. It is well known that the ϕ2 potential in standard scalar field cosmology is ruled out from inflationary perspective as it is not consistent with the recent Planck 2018 data; (here it may be mentioned that in the realm of “apparent horizon thermodynamics”, the standard scalar field cosmology is analogous to the case where the entropy of the apparent horizon is given by the Bekenstein–Hawking entropy). However, the story becomes different if the horizon entropy is of generalized entropic form, in which case, the effective energy density coming from the horizon entropy plays a significant role during the evolution of the universe. In particular, it turns out that in the context of generalized entropic cosmology, the ϕ2 potential indeed leads to a viable inflation (according to the Planck data) with a graceful exit, and thus the potential can be made back in the scene.

Horizon thermodynamics and cosmological equations: a holographic-like connection between thermostatistical quantities on a cosmological horizon and in the bulk

Horizon thermodynamics is expected to be related to the effective energy based on the energy density calculated from the Friedmann equation for a Friedmann–Robertson–Walker (FRW) universe. In the present study, the effective energy and thermostatistical quantities on a cosmological horizon are examined to clarify the holographic-like connection between them, with a focus on a de Sitter universe. To this end, the Helmholtz free energy on the horizon is derived from horizon thermodynamics. The free energy is found to be equivalent to the effective energy calculated from the Friedmann equation. This consistency is interpreted as a kind of holographic-like connection. To examine this connection, Padmanabhan’s holographic equipartition law, which is related to the origin of spacetime dynamics, is applied to a de Sitter universe. It is found that the law should lead to a holographic-like connection. The holographic-like connection is considered to be a bridge between thermostatistical quantities on the horizon and in the bulk. For example, cosmological equations for a flat FRW universe can be derived from horizon thermodynamics by accepting the connection as a viable scenario. In addition, a thermal entropy equivalent to the Bekenstein–Hawking entropy is obtained from the Friedmann equation using the concept of a canonical ensemble in statistical physics. The present study should provide new insight into the discussion of horizon thermodynamics and cosmological equations.

Entropy product function and central charges in NUT geometry

We define an entropy product function (EPF) for Taub–Newman–Unti–Tamburino (TNUT) black hole (BH) following the prescription suggested by Wu et al. [Phys. Rev. D 100, 101501(R) (2019)]. The prescription argues that a generic four-dimensional TNUT space–time might be expressed in terms of three or four different types of thermodynamic hairs. They can be defined as the Komar mass ([Formula: see text]), the angular momentum ([Formula: see text]), the gravitomagnetic charge ([Formula: see text]), the dual (magnetic) mass [Formula: see text]. Taking this prescription and using the EPF, we derive the central charges of dual conformal field theory (CFT) via Cardy’s formula. Remarkably, we find that for TNUT BH there exists a relation between the central charges and EPF as [Formula: see text], where [Formula: see text] is EPF and [Formula: see text] is one of the integer-valued charges i.e. the NUT charges ([Formula: see text]) or any new conserved charges ([Formula: see text]). We reverify these results by calculating the exact values of different thermodynamic parameters. We define the EPF [Formula: see text] from the first law of thermodynamics of both horizons. Moreover, we write the first laws of both the horizons for left-moving and right-moving sectors. Introducing the Bézout’s identity, we show that for TNUT BH one can generate more holographic descriptions described by a pair of integers [Formula: see text]. More holographic pictures have a great significance towards understanding the holographic nature of quantum gravity. Furthermore, using the EPF we derive the central charges for Reissner–Nordström–NUT (RNNUT) BH, Kerr–Taub–NUT (KNUT) BH and Kerr–Newman–NUT (KNNUT) BH. Finally we prove that they are equal in both sectors provided that the EPF is mass-independent (or universal).

Zooming in on the horizon when in its Meissner state

When approaching extremality, rotating black holes tend to expel the magnetic field in which they are immersed. This phenomenon, being reminiscent of the Meissner-Ochsenfeld effect in superconductors, is known as the black hole Meissner effect, and here we study it in the backreacting regime and from the near horizon perspective. By resorting to methods recently developed in the literature, which allow to compute conserved charges in the near horizon region, regardless the details of the asymptotia at large distance, we investigate the properties of the black hole horizon when in its Meissner state. We show that, when in such state, the horizon exhibits two sets of supertranslation symmetries as well as a symmetry generated by the local conformal group. The supertranslations are generated by two infinite sets of currents, one of which comes from local dilations of the advanced null coordinate at the horizon, and the other from local gauge transformations that preserve the electromagnetic field configuration at the horizon. We show that the evaluation of the conserved charges associated to these symmetries correctly reproduce the physical charges of the magnetized black holes and their thermodynamics. This represents a concrete application of the techniques developed in [1–3] and it extends the results of [4] to arbitrary values of the black hole charges. In addition, we elaborate on the charges computation at the horizon: we show the equivalence between the horizon charges and the evaluation of the corresponding Komar integrals. Besides, we show the validity of the Gauss phenomenon by explicitly relating near horizon charges with fluxes and charges computed by other techniques. All this provides a method to derive the thermodynamics of magnetized horizons in a quite succinct way, including the case of horizons exhibiting the Meissner effect.

From the emergence of cosmic space to horizon thermodynamics in Barrow entropy-based Cosmology

Padmanabhan's paradigm states that the spatial expansion of our Universe can be understood as the consequence of the emergence of space with the progress of cosmic time. Based on this argument, here we extract the first Friedmann equation for a curved (n+1)-dimensional Friedmann-Robertson-Walker Universe and analyze the consistency of Padmanabhan's proposal with horizon entropy maximization in the framework of Barrow entropy. The latter is a one-parameter deformation of Bekenstein-Hawking entropy induced by quantum-gravitational effects. We show that the viability of Padmanabhan's paradigm and its relationship with horizon thermodynamics are well supported in Barrow model, providing preliminary indications on how the emergent gravity perspective should appear in a quantum gravity-like scenario.

Holographic dark energy from the laws of thermodynamics with Rényi entropy

This article investigates the relationship between the holographic principle and the laws of thermodynamics in explaining the late-time acceleration of the universe. First, we explore the possibilities of generating the standard holographic dark energy (SHDE) from the laws of horizon thermodynamics. Except for entropies that follow an exponent stretched area law, unless we redefine the horizon temperature, we found it challenging to construct a one-to-one correspondence between the dark energies defined by the holographic principle and the laws of thermodynamics. Secondly, in SHDE models, unless we invoke some phenomenological interactions, it is impossible to explain the late-time cosmic acceleration with the Hubble horizon as the IR cutoff. On the other hand, it is possible to induce dark energy as an integration constant using the laws of thermodynamics on the Hubble horizon. These motivated us to explore a feasible way to invoke the holographic principle from the laws of horizon thermodynamics. We show that the additional terms that appear in the modified Friedmann equations on using entropies other than the Bekenstein–Hawking entropy in the first law of thermodynamics can behave like a dynamic holographic dark energy (HDE). We study the features of such an HDE with Rényi entropy as the choice without considering any non-standard interactions. Interestingly, the resulting form of dark energy reduces to the standard cosmological constant when Rényi entropy reduces to the Bekenstein–Hawking entropy. By examining different parameters, we affirm the validity of our approach to dark energy, which respects both holographic principle and thermodynamics.

New Entropies, Black Holes, and Holographic Dark Energy

The Bekenstein-Hawking entropy is a cornerstone of horizon thermodynamics but quantum effects correct it, while inequivalent entropies arise also in non-extensive thermodynamics. Reviewing our previous work, we advocate for a new entropy construct that comprises recent and older proposals and satisfies four minimal key properties. The new proposal is then applied to black holes and to holographic dark energy and shown to have the potential to cause early universe inflation or to alleviate the current Hubble tension. We then analyze black hole temperatures and masses consistent with alternative entropies.

Geometry and thermodynamics of coherent quantum black holes

In this paper, we present a quantum description of black holes given by coherent states of gravitons sourced by a matter core. The expected behavior in the weak-field region outside the horizon is recovered, with arbitrarily good approximation, but the classical central singularity is not resolved because the coherent states may not contain modes of arbitrarily short wavelength and the matter core must therefore have finite size. Ensuing quantum corrections both in the interior and exterior is also estimated by assuming that the mean-field approximation holds everywhere. These deviations from the classical black hole geometry can be viewed as quantum hair and will lead to a quantum corrected horizon radius and thermodynamics.

Thermodynamics of Einstein-Aether black holes

We analyze several spherically symmetric exterior vacuum solutions allowed by the Einstein-Aether (EA) theory with a non-static aether and study the thermodynamics of their Killing and universal horizons. We show that there are five classes of solutions corresponding to different values of a combination of the free parameters, c_{2}, c_{13}=c_1+c_3 and c_{14}=c_1+c_4, which are: (A) c_2 ne 0 and c_{13} ne 0 and c_{14}=0, (B) c_2 ne 0 and c_{13} = 0 and c_{14} = 0, (C) c_2 = 0 and c_{13} ne 0 and c_{14} = 0, (D) c_2 = 0, c_{13} = 0 and c_{14} ne 0, and (E) c_2 = - c_{13} ne 0 and c_{14} ne 0. We present explicit analytical solutions for these five cases. All these cases have singularities at r=0 and are asymptotically flat spacetimes and possess both Killing and universal horizons with the universal horizons always being inside the Killing horizons. Finally, we compute the surface gravity, the temperature, the entropy and the first law of thermodynamics for the universal horizons.

Thermodynamic properties, thermal image and phase transition of Einstein-Gauss-Bonnet black hole coupled with nonlinear electrodynamics

We obtain an exact solution of $AdS$ black hole solution in Einstein-Gauss-Bonnet (EGB) gravity coupled with nonlinear electrodynamics. It interpolates with the $AdS$ regular black hole and $AdS$ EGB black hole in the absence of the Gauss-Bonnet coupling constant and both magnetic monopole charge and deviation parameter, respectively. Based on horizon thermodynamics, we study the thermodynamic properties of the obtained solution (e.g. mass, temperature, entropy, heat capacity and free energy). The Hawking temperature of the nonsingular black hole gets the maximum value at the point where specific heat diverges and the second-order phase transition occurs at the same point. We find that the smaller nonsingular black holes are stable due to positive heat capacity and negative free energy. We explicitly trace the relations between the black hole shadow and the critical behavior of charged EGB $AdS$ regular black hole in the extended phase space.

Alternative entropies and consistent black hole thermodynamics

While the Bekenstein–Hawking entropy is the unique notion of entropy that makes classical black hole thermodynamics consistent, alternative entropy notions (Rényi, Tsallis, and generalized constructs) abound in the literature. We explore conditions under which they are part of a consistent horizon thermodynamics for certain classes of modified gravity black holes. We provide examples in which black hole masses and temperatures going hand-in-hand with these alternative entropies coincide with their usual counterparts associated with the Bekenstein–Hawking entropy.

Near-Horizon Thermodynamics of Hairy Black Holes from Gravitational Decoupling

The horizon structure and thermodynamics of hairy spherically symmetric black holes generated by the gravitational decoupling method are carefully investigated. The temperature and heat capacity of the black hole is determined, as well as how the hairy parameters affect the thermodynamics. This allows for an analysis of thermal stability and the possible existence of a remanent black hole. We also calculate the Hawking radiation corrected by the generalized uncertainty principle. We consider the emission of fermions and apply the tunneling method to the generalized Dirac equation. This shows that, despite the horizon location being the same as the Schwarzschild one for a suitable choice of parameters, the physical phenomena that occur near the horizon of both black holes are qualitatively different.

Emergence of cosmic space and horizon entropy maximization from Tsallis and Cirto entropy

In this note by use of the idea of the emergence of cosmic space suggested by Padmanabhan (Emergence and expansion of cosmic space as due to the quest for holographic equipartition; Res Astro Astrophys 12:891, 2012), we derive the modified Friedmann equation of a Friedmann-Robertson-Walker (FRW) Universe from Tsallis and Cirto entropy in (n+1) dimension with any spatial curvature. We investigate further the consistency of the law of emergence with the maximization of horizon entropy in the context of Tsallis and Cirto horizon entropy. Our results reveal the deep connection between the law of emergence and horizon thermodynamics.

Nonlinearly charged AdS black holes, extended phase space thermodynamics and Joule–Thomson expansion

We study thermodynamics and phase transitions of magnetically charged by nonlinear electrodynamics (NED) Anti-de Sitter (AdS) black holes in an extended phase space. The cosmological constant is treated as a thermodynamic pressure whereas the black hole mass is considered such as the chemical enthalpy. The horizon thermodynamics of black holes shows an analogy with the Van der Walls liquid–gas system. We define a quantities which are conjugated to the parameter of NED and a magnetic charge. It is shown that the first law of thermodynamics and the generalized Smarr relation hold. The critical exponents are the same as in the Van der Waals system. The Joule–Thomson adiabatic expansion of NED-AdS black holes is investigated because of thermodynamic behavior of black holes. The Joule–Thomson coefficient, the inversion and isenthalpic curves are discussed. The minimum of inversion temperature and the corresponding event horizon radius are obtained.