Search Results (75)

We investigate the statistical entropy of black holes within the framework of the generalized uncertainty principle (GUP) by employing effective metrics that incorporate leading-order and all-order quantum gravitational corrections. We construct three distinct effective metrics induced by the GUP, which are derived from the GUP-corrected temperature, entropy, and all-order GUP corrections, and analyze their impact on black hole entropy using ’t Hooft’s brick wall method. Our results show that, despite the differences in the effective metrics and the corresponding ultraviolet cutoffs, the statistical entropy consistently satisfies the Bekenstein–Hawking area law when expressed in terms of an invariant (coordinate-independent) distance near the horizon. Furthermore, we demonstrate that the GUP naturally regularizes the ultraviolet divergence in the density of states, eliminating the need for artificial cutoffs and yielding finite entropy even when counting quantum states only in the vicinity of the event horizon. These findings highlight the universality and robustness of the area law under GUP modifications and provide new insights into the interplay between quantum gravity effects and black hole thermodynamics. Full article

We investigate the evolution of future trapping horizons through the dynamics of the Misner–Sharp mass using ingoing Eddington–Finkelstein coordinates. Our analysis shows that an integral formulation of Hayward’s first law governs much of the evolution of general spherically symmetric spacetimes. To account for the accretion backreaction, we consider a near-horizon approximation, which yields first-order corrections of a Vaidya-dark energy form. We further propose a systematic perturbative scheme to study these effects for an arbitrary background. As an application, we analyze an accreting Reissner–Nordström black hole and demonstrate the horizon shifts produced. Finally, we compute accretion-induced corrections to an extremal configuration. It is shown that momentum influx and energy density produce distinct effects: the former forces the splitting of the extremal horizon, while the latter induces significant displacements in its position, computed up to first-order perturbative corrections. These results highlight how different components of the stress–energy tensor significantly affect horizon geometry, with potential implications for broader areas of research, including black-hole thermodynamics. Full article

Sadi Carnot’s seminal work laid the foundation for exploring the effects of thermodynamics across diverse domains of physics, stretching from quantum to cosmological scales. Here, we build on the principles of the original Carnot heat engine, and apply it in the context of a particular toy model black brane. This theoretical construct of an effectively two-dimensional, stable, and stationary gravitational object in four-dimensional spacetime derives from a hypothetical flat planet collapsed under the influence of gravity. By constructing a thermodynamic cycle involving three such black branes, we explore the possibility of energy extraction or mining, driven by the temperature gradients and gravitational potential differences characteristic of curved spacetime. Analytic solutions obtainable within this toy model illuminate key aspects of black hole thermodynamics in general, particularly for spacetimes that are not asymptotically flat. Central to these findings is the relation between gravitationally induced temperature ratios and entropy changes, which collectively offer a novel perspective on obtainable energy transfer processes around gravitational structures. This analysis highlights potential implications for understanding energy dynamics in gravitational systems in general, including for black hole evaporation and experimentally implemented black hole analogues. The presented findings not only emphasise the universality of the thermodynamic principles first uncovered by Carnot, but also suggest future research directions in gravitational thermodynamics. Full article

This paper assesses the thermodynamic stability of clay minerals in the upper organo-mineral horizon of podzolic soil, as well as in the rhizosphere of Norway spruce (Picea abies (L.) H. Karst.) and Norway maple (Acer platanoides L.). Moreover, it determines the impact of soil organic matter on the thermodynamic stability of clay minerals. Calculations of ΔG_f and the saturation index (SI) for clay minerals in laboratory experiments simulating soil conditions without soil moisture outflow allowed us to find out that the thermodynamic stability of clay minerals decreased in the series kaolinite > illite > vermiculite > chlorite. In the rhizosphere of spruce, kaolinite, vermiculite and illite have the lowest, and in the soil under maple-the highest thermodynamic stability, which is associated with differences in the properties of soil organic matter of rhizospheres of different tree species. Laboratory experiments on the sorption of soil humic acid (HA) on clay minerals demonstrated that sorbed HA decreased the thermodynamic stability of biotite and increased the thermodynamic stability of kaolinite and muscovite. Thermodynamic stability of clay minerals decreased with increased proportion of sorbed thermolabile organic matter. Full article

Cutting out an infinite tube around $r=0$ formally removes the Schwarzschild singularity, but without a physical mechanism, this procedure seems ad hoc and artificial. In this paper, we provide justification for such a mechanism by means of non-locality. Motivated by the Gauss law, we define a suitable radius variable as the inverse of a regular non-local potential, and use this variable to model a non-singular black hole. The resulting geometry has a de Sitter core, and for generic values of the regulator, there is no inner horizon, saving this model from potential issues via mass inflation. An outer horizon only exists for masses above a critical threshold, thereby reproducing the conjectured “mass gap” for black holes in non-local theories. The geometry’s density and pressure terms decrease exponentially, thereby rendering it an almost-exact vacuum solution of the Einstein equations outside of astrophysical black holes. Its thermodynamic properties resemble those of the Hayward black hole, with the notable exception that for critical mass, the horizon radius is zero. Full article

The first part of this work provides a review of recent research on generalised entropies and their origin, as well as its application to black hole thermodynamics. To start, it is shown that the Hawking temperature and the Bekenstein–Hawking entropy are, respectively, the only possible thermodynamical temperature and entropy of the Schwarzschild black hole. Moreover, it is investigated if the other known generalised entropies, which include Rényi’s entropy, Tsallis entropy, and the four- and five-parameter generalised entropies, could correctly yield the Hawking temperature and the ADM mass. The possibility that generalised entropies could describe hairy black hole thermodynamics is also considered, both for the Reissner–Nordström black hole and for Einstein’s gravity coupled with two scalar fields. Two possibilities are investigated, namely, the case when the ADM mass does not yield the Bekenstein–Hawking entropy, and the case in which the effective mass expressing the energy inside the horizon does not yield the Hawking temperature. For the model with two scalar fields, the radii of the photon sphere and of the black hole shadow are calculated, which gives constraints on the BH parameters. These constraints are seen to be consistent, provided that the black hole is of the Schwarzschild type. Subsequently, the origin of the generalised entropies is investigated, by using their microscopic particle descriptions in the frameworks of a microcanonical ensemble and canonical ensemble, respectively. Finally, the McLaughlin expansion for the generalised entropies is used to derive, in each case, the microscopic interpretation of the generalised entropies, via the canonical and the grand canonical ensembles. Full article

We obtain exact black hole solutions to Einstein gravity coupled with a nonlinear electrodynamics field, in the presence of a cloud of strings and quintessence, as sources. The solutions have four parameters, namely m, k, a, and $\alpha$, corresponding to the physical mass of the black hole, the nonlinear charge of a self-gravitating magnetic field, the cloud of strings, and the intensity of the quintessential fluid. The consequences of these sources on the regularity or singularity of the solutions, on their horizons, as well as on the energy conditions, are discussed. We study some aspects concerning the thermodynamics of the black hole, by taking into account the mass, Hawking temperature, and heat capacity and show how these quantities depend on the presence of the cloud of strings and quintessence, in the scenario considered. Full article

The thermodynamics of black holes (BHs) and their corrections have become a hot topic in the study of gravitational physics, with significant progress made in recent decades. In this paper, we study the thermodynamics and corrections of spherically symmetric BHs in models $f\left(R\right)=R+\alpha R^2$ and $f\left(R\right)=R+2\gamma \sqrt{R+8\Lambda }$ under the $f\left(R\right)$ theory, which includes the electrodynamic field and the cosmological constant. Considering thermal fluctuations around equilibrium states, we find that, for both f(R) models, the corrected entropy is meaningful in the case of a negative cosmological constant (anti-de Sitter–RN spacetime) with $\Lambda =-1$. It is shown that when the BHs’ horizon radius is small, thermal fluctuations have a more significant effect on the corrected entropy. Using the corrected entropy, we derive expressions for the relevant corrected thermodynamic quantities (such as Helmholtz free energy, internal energy, Gibbs free energy, and specific heat) and calculate the effects of the correction terms. The results indicate that the corrections to Helmholtz free energy and Gibbs free energy, caused by thermal fluctuations, are remarkable for small BHs. In addition, we explore the stability of BHs using specific heat. The study reveals that the corrected BH thermodynamics exhibit locally stable for both models, and corrected systems undergo a Hawking–Page phase transition. Considering the requirement on the non-negative volume of BHs, we also investigate the constraint on the EH radius of BHs. Full article

We present a comparative analysis of the plethora of nonextensive and/or nonadditive entropies which go beyond the standard Boltzmann–Gibbs formulation. After defining the basic notions of additivity, extensivity, and composability, we discuss the properties of these entropies and their mutual relations, if they exist. The results are presented in two informative tables that are of strong interest to the gravity and cosmology community in the context of the recently intensively explored horizon entropies for black hole and cosmological models. Gravitational systems admit long-range interactions, which usually lead to a break of the standard additivity rule for thermodynamic systems composed of subsystems in Boltzmann–Gibbs thermodynamics. The features of additivity, extensivity, and composability are listed systematically. A brief discussion on the validity of the notion of equilibrium temperature for nonextensive systems is also presented. Full article

We review constructions of three-dimensional ‘quantum’ black holes. Such spacetimes arise via holographic braneworlds and are exact solutions to an induced higher-derivative theory of gravity consistently coupled to a large-c quantum field theory with an ultraviolet cutoff, accounting for all orders of semi-classical backreaction. Notably, such quantum-corrected black holes are much larger than the Planck length. We describe the geometry and horizon thermodynamics of a host of asymptotically (anti-) de Sitter and flat quantum black holes. A summary of higher-dimensional extensions is given. We survey multiple applications of quantum black holes and braneworld holography. Full article

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 $TdS=-d\left(\rho V\right)+WdV$ (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. Full article

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, $f\left(0\right)=1$, and corrections to the Reissner–Nordström solution are in the order of $\mathcal{O}\left(r^{-3}\right)$ 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. Full article

We discuss the consequences of the unique symmetry of de Sitter spacetime. This symmetry leads to the specific thermodynamic properties of the de Sitter vacuum, which produces a thermal bath for matter. de Sitter spacetime is invariant under the modified translations, $\mathbf{r}\to \mathbf{r}-e^{Ht}\mathbf{a}$, where H is the Hubble parameter. For $H\to 0$, this symmetry corresponds to the conventional invariance of Minkowski spacetime under translations $\mathbf{r}\to \mathbf{r}-\mathbf{a}$. Due to this symmetry, all the comoving observers at any point of the de Sitter space perceive the de Sitter environment as the thermal bath with temperature $T=H/\pi$, which is twice as large as the Gibbons–Hawking temperature of the cosmological horizon. This temperature does not violate de Sitter symmetry and, thus, does not require the preferred reference frame, as distinct from the thermal state of matter, which violates de Sitter symmetry. This leads to the heat exchange between gravity and matter and to the instability of the de Sitter state towards the creation of matter, its further heating, and finally the decay of the de Sitter state. The temperature $T=H/\pi$ determines different processes in the de Sitter environment that are not possible in the Minkowski vacuum, such as the process of ionization of an atom in the de Sitter environment. This temperature also determines the local entropy of the de Sitter vacuum state, and this allows us to calculate the total entropy of the volume inside the cosmological horizon. The result reproduces the Gibbons–Hawking area law, which is attributed to the cosmological horizon, $S_{\mathrm{hor}}=4\pi KA$, where $K=1/\left(16\pi G\right)$. This supports the holographic properties of the cosmological event horizon. We extend the consideration of the local thermodynamics of the de Sitter state using the $f\left(\mathcal{R}\right)$ gravity. In this thermodynamics, the Ricci scalar curvature $\mathcal{R}$ and the effective gravitational coupling K are thermodynamically conjugate variables. The holographic connection between the bulk entropy of the Hubble volume and the surface entropy of the cosmological horizon remains the same but with the gravitational coupling $K=df/d\mathcal{R}$. Such a connection takes place only in the $3+1$ spacetime, where there is a special symmetry due to which the variables K and $\mathcal{R}$ have the same dimensionality. We also consider the lessons from de Sitter symmetry for the thermodynamics of black and white holes. Full article

A considerable penetration of rooftop PV generation and increasing demand for heating loads will enlarge the peak-to-valley difference, imposing a great challenge to the reliable operation of distribution systems under cold climates. The objective of this paper is to establish a distributionally robust demand response (DR) model for building energy systems for suppressing peak-to-valley load ratios by exploiting cooperative complementarity and flexible transformation characteris-tics of various household appliances. The thermodynamic effect of buildings is modeled for harvesting intermittent renewable energy sources (RESs) on the building roof in the form of thermal energy storages to reduce RES curtailments and eliminate thermal comfort violations in cold weather. Furthermore, the Wasserstein metric is adopted to develop the ambiguity set of the uncertainty probability distributions (PDs) of RESs, and thus, only historical data of RES output is needed rather than prior knowledge about the actual PDs. Finally, a computationally tractable mixed-integer linear programming reformulation is derived for the original distributionally robust optimization (DRO) model. The proposed DRO-based DR strategy was performed on multiple buildings over a 24 h scheduling horizon, and comparative studies have validated the effectiveness of the proposed strategy for building energy systems in reducing the peak/valley ratio and decreasing operation costs. Full article

The region surrounding the Elbrus volcano in the Great Caucasus is a popular tourist destination, home to native people and an area of the richest ore mineral resources. Based on the chemical composition of surface water, mineral, and groundwater in the Elbrus area, as well as statistical and thermodynamic calculations, waters with high concentrations of Mn, Cu, Zn, Mo, Ba, W, Pb, and As were identified, possible mineral phases that may lead to these metal concentrations in water were estimated, and risks to human health were assessed. Two main sources of surface water pollution have been identified: (1) water from tailings that are enriched due to oxidation of sulfide minerals is considered a source of As (181 µg/L) and Mo (2070 µg/L) pollution in the area of the Tyrnyauz W-Mo deposit; and (2) CO₂-rich waters of deep horizons discharge on the earth surface with high concentrations of As (828 µg/L) and W (504 µg/L). It has been shown that compared to all toxic elements studied, only Mo and As have adverse non-carcinogenic effects on adult health. The estimated carcinogenic risk of As in the mine area was 1.7 × 10⁻³ and exceeded the generally accepted range of 10⁻⁴ to 10⁻⁶. In order to minimize the health risks, regular monitoring of water quality is required when mining activities on the Tyrnyauz W-Mo deposit are renewed. Full article