Search Results (26)

We investigated the thermodynamic topology of quantum-corrected AdS-Reissner-Nordström black holes in Kiselev spacetime using non-extensive entropy formulation derived from Loop Quantum Gravity (LQG). Through systematic analysis, we examined how the Tsallis parameter $\lambda$ influences topological charge classification with respect to various equation of state parameters. Our findings revealed a consistent pattern of topological transitions: for $\lambda =0.1$, the system exhibited a single topological charge $(\omega =-1)$ with total charge $W=-1$, as $\lambda$ increased to 0.8, the system transitioned to a configuration with two topological charges $(\omega =+1,-1)$ and total charge $W=0$. When $\lambda =1$, corresponding to the Bekenstein–Hawking entropy limit, the system displayed a single topological charge $(\omega =+1)$ with $W=+1$, signifying thermodynamic stability. The persistence of this pattern across different fluid compositions—from exotic negative pressure environments to radiation—demonstrates the universal nature of quantum gravitational effects on black hole topology. Full article

Within the novel context of primary scalar hair black holes, this article explores the fascinating subject of black hole thermal stability. Thermodynamic stability is the main subject of our investigation, which involves measuring the bound points, divergence points, black hole mass, thermal temperature, and specific heat capacity. In addition, we determine the scalar curvatures of thermodynamic geometries like Ruppeiner, Weinhold, Hendi-Panahiyah-Eslam-Momennia, and geometrothermodynamics formulations inside the framework of primary scalar hair black holes and delve into their complexities. Improving our knowledge of fundamental scalar hair black holes, this study sheds light on the intricate thermal geometric properties of these objects. 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 investigate a spherically symmetric exact solution of Einstein’s gravity with cosmological constant in (2 + 1) dimensions, non-minimally coupled to a scalar field. The solution describes the gravitational field of a black hole, which is free of curvature singularities in the entire spacetime. We use the formalism of geometrothermodynamics to investigate the geometric properties of the corresponding space of equilibrium states and find their interpretation from the point of view of thermodynamics. It turns out that, as a result of the presence of thermodynamic interaction, the space of equilibrium states is curved with two possible configurations, which depend on the value of a coupling constant. In the first case, the equilibrium space is completely regular, corresponding to a stable thermodynamic system. The second case is characterized by the presence of two curvature singularities, which are shown to correspond to locations where the system undergoes two different phase transitions, one due to the breakdown of the thermodynamic stability condition and the second one due to the presence of a divergence at the level of the response functions. Full article

Both classical and quantum arguments suggest that if Barrow entropy is correct, its index $\delta$ must be energy-dependent, which would affect the very early universe. Based on thermodynamic stability that sufficiently large black holes should not fragment, we argue that Barrow entropy correction must be small, except possibly at the Planckian regime. Furthermore, the fact that a solar mass black hole does not fragment implies an upper bound $\delta \lesssim O\left({10}^{-3}\right)$, which surprisingly lies in the same range as the bound obtained from some cosmological considerations assuming fixed $\delta$. This indicates that allowing $\delta$ to run does not raise its allowed value. We briefly comment on the case of Kaniadakis entropy. Full article

We studied Einstein’s gravity with negative cosmological constant coupled to nonlinear electrodynamics proposed earlier. The metric and mass functions and corrections to the Reissner–Nordström solution are obtained. Black hole solutions can have one or two horizons. Thermodynamics and phase transitions of magnetically charged black holes in Anti-de Sitter spacetime are investigated. The first law of black hole thermodynamics is formulated and the generalized Smarr relation is proofed. By calculating the Gibbs free energy and heat capacity we study the black hole stability. Zero-order (reentrant), first-order, and second-order phase transitions are analyzed. The Joule–Thomson expansion is considered, showing the cooling and heating phase transitions. It was shown that the principles of causality and unitarity are satisfied in the model under consideration. Full article

The many problems faced by the theory of general relativity (GR) have always motivated us to explore the modified theory of GR. Considering the importance of studying the black hole (BH) entropy and its correction in gravity physics, we study the correction of thermodynamic entropy for a kind of spherically symmetric black hole under the generalized Brans–Dicke (GBD) theory of modified gravity. We derive and calculate the entropy and heat capacity. It is found that when the value of event horizon radius $r_{+}$ is small, the effect of the entropy-correction term on the entropy is very obvious, while for larger values $r_{+}$, the contribution of the correction term on entropy can be almost ignored. In addition, we can observe that as the radius of the event horizon increases, the heat capacity of BH in GBD theory will change from a negative value to a positive value, indicating that there is a phase transition in black holes. Given that studying the structure of geodesic lines is important for exploring the physical characteristics of a strong gravitational field, we also investigate the stability of particles’ circular orbits in static spherically symmetric BHs within the framework of GBD theory. Concretely, we analyze the dependence of the innermost stable circular orbit on model parameters. In addition, the geodesic deviation equation is also applied to investigate the stable circular orbit of particles in GBD theory. The conditions for the stability of the BH solution and the limited range of radial coordinates required to achieve stable circular orbit motion are given. Finally, we show the locations of stable circular orbits, and obtain the angular velocity, specific energy, and angular momentum of the particles which move in circular orbits. Full article

In this paper, we investigate the thermal stability and thermodynamic geometries of non-rotating/rotating charged black holes. For these black holes, we apply barrow entropy to determine the physical quantities such as mass and temperature of the system and find their stability through first and second phase transitions of the heat capacity. We analyze the effects of scalar charge Q and hair parameter $\lambda$ on black holes properties by taking both positive and negative values of these parameters. It is noted that heat capacity provide the stable, unstable regions and phase transition points for both black holes. To investigate the thermodynamic geometry of these black holes, various techniques such as Ruppeiner, Weinhold, Quevedo, and HPEM metrics are considered. It is observed that Weinhold, Quevedo, and HPEM give attractive/repulsive behavior of particles in stable/unstable regions of black holes. Full article

We show that the spherically symmetric black hole (BH) solution of a charged (linear case) field equation of Rastall gravitational theory is not affected by the Rastall parameter and this is consistent with the results presented in the literature. However, when we apply the field equation of Rastall’s theory to a special form of nonlinear electrodynamics (NED) source, we derive a novel spherically symmetric BH solution that involves the Rastall parameter. The main source of the appearance of this parameter is the trace part of the NED source, which has a non-vanishing value, unlike the linear charged field equation. We show that the new BH solution is Anti−de-Sitter Reissner−Nordström spacetime in which the Rastall parameter is absorbed into the cosmological constant. This solution coincides with Reissner−Nordström solution in the GR limit, i.e., when Rastall’s parameter is vanishing. To gain more insight into this BH, we study the stability using the deviation of geodesic equations to derive the stability condition. Moreover, we explain the thermodynamic properties of this BH and show that it is stable, unlike the linear charged case that has a second-order phase transition. Finally, we prove the validity of the first law of thermodynamics. Full article

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. Full article

Recently, several methods have been proposed to regularize a $D\to 4$ limit of Einstein–Gauss–Bonnet (EGB), leading to nontrivial gravitational dynamics in $4D$. We present an exact nonsingular black hole solution in the $4D$ EGB gravity coupled to non-linear electrodynamics and analyze their thermodynamic properties to calculate precise expressions for the black hole mass, temperature, and entropy. Because of the magnetic charge, the thermodynamic quantities are corrected, and the Hawking–Page phase transition is achievable with diverges of the heat capacity at a larger critical radius $r=r_{+}^C$ in comparison to the $5D$ counterpart where the temperature is maximum. Thus, we have a black hole with Cauchy and event horizons, and its evaporation leads to a thermodynamically stable extremal black hole remnant with vanishing temperature, and its size is larger than the $5D$ counterpart. The entropy does not satisfy the usual exact horizon Bekenstein–Hawking area law of general relativity with a logarithmic area correction term. Full article

In this paper, we focus on the relation between quasinormal modes (QNMs) and a rotating black hole shadow. As a specific example, we consider the quantum deformed Kerr black hole obtained via Newman–Janis–Azreg-Aïnou algorithm. In particular, using the geometric-optics correspondence between the parameters of a QNMs and the conserved quantities along geodesics, we show that, in the eikonal limit, the real part of QNMs is related to the Keplerian frequency for equatorial orbits. To this end, we explore the typical shadow radius for the viewing angles, ${\theta }_0=\pi /2$, and obtained an interesting relation in the case of viewing angle ${\theta }_0=0$ (or equivalently ${\theta }_0=\pi$). Furthermore we have computed the corresponding equatorial and polar modes and the thermodynamical stability of the quantum deformed Kerr black hole. We also investigate other astrophysical applications such as the quasiperiodic oscillations and the motion of S2 star to constrain the quantum deforming parameter. Full article

We investigate the influence of the first-order correction of entropy caused by thermal quantum fluctuations on the thermodynamics of a logarithmic corrected charged black hole in massive gravity. For this black hole, we explore the thermodynamic quantities, such as entropy, Helmholtz free energy, internal energy, enthalpy, Gibbs free energy and specific heat. We discuss the influence of the topology of the event horizon, dimensions and nonlinearity parameter on the local and global stability of the black hole. As a result, it is found that the holographic dual parameter vanishes. This means that the thermal corrections have no significant role to disturb the holographic duality of the logarithmic charged black hole in massive gravity, although the thermal corrections have a substantial impact on the thermodynamic quantities in the high-energy limit and the stability conditions of black holes. Full article

Among the plethora of available metal(loid) nanomaterials (NMs), those containing selenium are interesting from an applicative perspective, due to their high biocompatibility. Microorganisms capable of coping with toxic Se-oxyanions generate mostly Se nanoparticles (SeNPs), representing an ideal and green alternative over the chemogenic synthesis to obtain thermodynamically stable NMs. However, their structural characterization, in terms of biomolecules and interactions stabilizing the biogenic colloidal solution, is still a black hole that impairs the exploitation of biogenic SeNP full potential. Here, spherical and thermodynamically stable SeNPs were produced by a metal(loid) tolerant Micrococcus sp. Structural characterization obtained by Scanning Electron Microscopy (SEM) revealed that these SeNPs were surrounded by an organic material that contributed the most to their electrosteric stabilization, as indicated by Zeta (ζ) potential measurements. Proteins were strongly adsorbed on the SeNP surface, while lipids, polysaccharides, and nucleic acids more loosely interacted with SeNMs as highlighted by Fourier Transform Infrared Spectroscopy (FTIR) and overall supported by multivariate statistical analysis. Nevertheless, all these contributors were fundamental to maintain SeNPs stable, as, upon washing, the NM-containing extract showed the arising of aggregated SeNPs alongside Se nanorods (SeNRs). Besides, Density Functional Theory (DFT) calculation unveiled how thiol-containing molecules appeared to play a role in SeO₃²⁻ bioreduction, stress oxidative response, and SeNP stabilization. Full article

We explore the quadratic form of the $f\left(R\right)=R+b{R}^2$ gravitational theory to derive rotating N-dimensions black hole solutions with $a_i,i\ge 1$ rotation parameters. Here, R is the Ricci scalar and b is the dimensional parameter. We assumed that the N-dimensional spacetime is static and it has flat horizons with a zero curvature boundary. We investigated the physics of black holes by calculating the relations of physical quantities such as the horizon radius and mass. We also demonstrate that, in the four-dimensional case, the higher-order curvature does not contribute to the black hole, i.e., black hole does not depend on the dimensional parameter b, whereas, in the case of $N>4$, it depends on parameter b, owing to the contribution of the correction $R^2$ term. We analyze the conserved quantities, energy, and angular-momentum, of black hole solutions by applying the relocalization method. Additionally, we calculate the thermodynamic quantities, such as temperature and entropy, and examine the stability of black hole solutions locally and show that they have thermodynamic stability. Moreover, the calculations of entropy put a constraint on the parameter b to be $b<\frac{1}{16\mathrm{\Lambda }}$ to obtain a positive entropy. Full article