arXiv subjects

Saeed Noori Gashti

Publications and source records attributed to Saeed Noori Gashti.

At least 37 records · Page 2Linked to original sources

arXiv2025

Thermodynamics and Joule-Thomson Expansion for Schwarzschild-AdS Black Holes with Cloud of Strings and Quintessential-like Fluid

In this study, we explore the thermodynamic properties of a Schwarzschild black hole (BH) embedded in an anti-de Sitter (AdS) background, which is further coupled with a cloud of strings and surrounded by a quintessence-like fluid. Beginning with the formulation of BH mass in terms of the event horizon radius, we incorporate the concept of pressure as related to the AdS curvature radius within the framework of extended phase space thermodynamics. Using this setup, we derive key thermodynamic quantities, including the Gibbs free energy and internal energy, to characterize the energetic behavior of the black hole system. To assess the stability of the black hole, we compute the specific heat capacity and analyze how it is influenced by external parameters, such as the string cloud and the quintessence-like fluid. These geometric and matter fields are shown to significantly modify the thermal response of the BH. Furthermore, we examine the inversion temperature associated with the black hole and highlight its distinction from the standard Hawking temperature, providing deeper insight into the phase structure. Additionally, we investigate the Joule-Thomson expansion process and demonstrate how the aforementioned parameters affect this thermodynamic phenomenon, showing important aspects of BH cooling and heating behavior in an extended thermodynamic context.

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arXiv2025

Schwarzschild-AdS Black Holes with Cloud of Strings and Quintessence: Geodesics, Thermodynamic Topology, and Quasinormal Modes

In this study, we explore a Schwarzschild-anti de-Sitter black hole (BH) coupled with a cloud of strings (CoS) possessing both electric- and magnetic-like components of the string bivector, embedded in a Kiselev-type quintessence fluid (QF). We analyze the dynamics of photons and test particles, focusing on trajectories, photon spheres, BH shadows, and innermost stable circular orbits (ISCO), highlighting how CoS and QF parameters affect these features. We then examine the thermodynamic topology of the system by analyzing vector field zeros, showing that varying CoS leads to distinct topological configurations with total charges of either $0$ or $+1$, corresponding to known classes like RN and AdS-RN. Additionally, we study scalar field dynamics via the massless Klein-Gordon equation, reformulated into a Schr$\ddot{o}$dinger-like form to derive the effective potential. We compute the quasinormal modes (QNMs) of scalar perturbations, showing how CoS and QF influence oscillation frequencies and damping rates, with implications for gravitational confinement and thermalization in the AdS/CFT context.

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arXiv2025

Probing the Weak Gravity Conjecture: Novel Aschenbach Signatures in Superextremal Non-Linear Charged AdS Black Holes

This study investigates the nonlinear charged Anti-de Sitter (AdS) black hole solution within the framework of massive gravity, motivated by recent advancements linking the Weak Gravity Conjecture (WGC) to phenomena such as Weak Cosmic Censorship Conjecture (WCCC) and photon sphere dynamics. Building on these foundations, we focus on the Aschenbach effect-a relativistic phenomenon intricately tied to the geometry of photon spheres and known to occur in some special sub-extremal non rotating black holes. Our primary objective is to determine whether this effect persists not only up to the extremal limit but also beyond, into the superextremal regime, thus probing the stability and validity of black hole characteristics in these extreme conditions. By analyzing the nonlinear charged AdS black hole solutions in massive gravity, we demonstrate that the Aschenbach effect remains a robust feature across both extremal and superextremal configurations. This extension suggests that key relativistic signatures and the underlying spacetime structures associated with high-spin black holes continue to hold beyond classical boundaries. Our results provide new insights into the behavior of ultra-compact objects and highlight promising directions for exploring the limits of general relativity, as well as potential generalizations of the WGC and WCC in strong gravitational fields.

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arXiv2025

Cosmic-Quantum Connections: Assessing the Viability of Weak Gravity and Weak Cosmic Censorship Conjectures in Kerr-Newman-Kiselev-Letelier Black Hole

This paper addresses a potential validation of the weak gravity conjecture (WGC) with the weak cosmic censorship conjecture (WCCC), as a significant challenge in quantum gravity. We explore the viability of the WGC and WCCC in the context of the Kerr-Newman-Kiselev-Letelier (KNKL) black hole. Although these conjectures appear unrelated, but surprising connection between these conjectures, It establishes a bridge between the quantum and the cosmic. By imposing specific constraints on the black hole's parameters, we demonstrate that the WGC and WCCC can be compatible in certain regions. We examine the properties of the KNKL black hole for $q/m > (Q/M )_{ext}$, where $(Q/M )_{ext}$ is the charge-to-mass ratio of a large extremal black hole. We present figures to test the validity of both conjectures simultaneously. Without the spin parameter $a$, the cloud of string parameter $b$, quintessence parameter $γ$, and equation of state parameter $ω$, the black hole either has two event horizons if $Q^2/M^2 \leq 1$ or none event horizon if $Q^2/M^2 > 1$ which leads to a naked singularity that contradicts the WCCC. However, when $a$, $b$, $γ$, and $ω$ are present, the black hole has event horizons in some regions in the $Q^2/M^2 > 1$ that ensure the singularity is covered and both the WGC and WCCC are fulfilled. Actually, we face this issue in the extremality state of the black hole viz these conjectures remain viable, with the black hole maintaining an event horizon. We conclude that certain regions of $a$, $b$, $γ$, and $ω$ parameters can make the WGC and WCCC compatible, indicating their agreement when these parameters are present.

hep-th↗

arXiv2025

Van der Waals Black Holes: Universality, Quantum Corrections, and Topological Classifications

In this paper, we investigate the universal extremality relation and thermodynamic topology of Van der Waals (VdW) black holes-solutions of Einstein's equations whose thermodynamic behavior closely resembles that of Van der Waals fluids. In the classical case, the black hole entropy obeys the Bekenstein-Hawking area law and satisfies the standard universality relation. We then incorporate quantum corrections using three distinct frameworks: the Generalized Uncertainty Principle (GUP), the Extended Uncertainty Principle (EUP), and Rainbow Gravity. While these corrections modify the entropy law, we find that a generalized form of the universal extremality relation still holds. Next, we explore the thermodynamic topology of VdW black holes, focusing on the distribution of topological charges. Our analysis reveals that variations in the black hole and model parameters lead to significant changes in topological classifications and stability, as quantified by winding numbers. In the GUP-corrected case, topological charge distributions exhibit robustness against parameter variations, suggesting classification stability. For EUP-corrected black holes, we identify two distinct topological classes, with some configurations displaying three non-zero topological charges and others maintaining a total charge of zero, despite changes in individual charge counts. The Rainbow Gravity-corrected scenario shows similar consistency in topological behavior.

gr-qc↗

arXiv2025

Black Holes in Lorentz-Violating Gravity: Thermodynamics, Geometry, and Particle Dynamics

We investigate the thermodynamics, topology, and geometry of black holes in Lorentz-violating gravity. Modifications in the theory by perturbative parameter lead to coupled changes in horizon structure and thermodynamic behaviour, allowing us to derive generalized universal relations and explore implications for the Weak Gravity Conjecture. The thermodynamic topology reveals distinct topological charges, with photon spheres identified as robust topological defects. Our analysis shows that the Ruppeiner curvature remains universally negative across thermodynamic ensembles, indicating dominant attractive interactions among microstructures. This ensemble-independent behaviour highlights a fundamental thermodynamic universality in Lorentz-violating settings. Together, these results provide a consistent and rich framework for understanding black hole microphysics and gravitational consistency in modified theories. We further study the motion of timelike test particles in these black hole spacetimes by analyzing the effective potential shaped by the Lorentz-violating couplings. The resulting dynamics reveal the existence of bound orbits and stable circular trajectories, with the location of the innermost stable circular orbit and turning points significantly influenced by the parameters $\ell_{1,2}$, and the cosmological constant. Numerical simulations of trajectories in the $x-y,\,x-z$, and 3D planes show precessing, bounded, and plunging orbits, depending on the particle's specific energy and angular momentum. These results highlight how Lorentz-violating effects alter the structure of geodesic motion and provide potential observational signatures in the dynamics of massive particles near black holes.

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arXiv2025

Thermodynamic Curvature and Topological Insights of Hayward Black Holes with String Fluids

In this paper, we study the influence of string fluids on the extended thermodynamic structure and microscopic interactions of Hayward black holes by employing thermodynamic geometry as an empirical tool. Using the novel equation of state obtained for regular black holes surrounded by string fluids, we analyze the extended phase space with enthalpy as the central thermodynamic potential. By examining the behavior of the normalized Ruppeiner curvature scalar $R_N$ in the temperature-volume $(T,V)$ plane, we analyzed the influence of the string fluid parameters on the microstructure of the black hole. Our analysis reveals that the presence of string fluids significantly modifies the dominant microscopic interactions, transitioning from attractive to repulsive regimes depending on the charge and volume of the black hole. We see that the thermodynamic curvature effectively detects critical points and phase transitions, reflecting the nature of repulsive or attractive interactions among black hole microstructures. We further investigate thermodynamic topology to provide a novel classification scheme for stability and phase behavior, delineating local stable and unstable regions in parameter space. We investigate the thermodynamic topology of Hayward-AdS black holes surrounded by string fluids, showing that the number and type of topological charges depend on the parameters $ε$ and $b$, revealing phase transitions and stability characteristics encoded in the global topological charge $W$. This integrated study of the thermodynamic geometry and topology structure enhances the understanding of Hayward black holes surrounded by string fluids, showing overall thermodynamic stability and configuration with significant implications for holographic duality and potential astrophysical observations.

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arXiv2025

Overcoming Barriers: Kramers' Escape Rate Analysis of Metastable Dynamics in First-Order Multi-Phase Transitions

The expanding application of classical thermodynamic methods to black hole physics has yielded significant advances in characterizing phase transition behavior. Among these approaches, thermodynamic analysis -- particularly kinetic formulations like the Kramers' escape rate -- provides a robust framework for probing black hole phase transitions with minimal relativistic constraints. This study investigates the kinetics and dynamic evolution of first-order phase transitions in black holes exhibiting multiple critical points, employing a particle-based escape rate model. The distinct free energy landscapes inherent to multi-critical systems, which can simultaneously support multiple local minima under specific thermodynamic conditions (temperature and pressure) within a given reference frame, raise fundamental questions regarding transition pathways. We rigorously assess whether the Kramers' escape rate retains its predictive validity in these complex multi-minima systems, as established for conventional single-minimum configurations. Furthermore, we examine whether transitions proceed via a sequential, stepwise mechanism between adjacent minima, or if pathways exist that bypass intermediate states through direct descent to the global minimum. Our analysis of black holes undergoing multiphase transitions reveals both parallels and significant deviations from single-transition models. Crucially, we demonstrate that the Kramers' escape rate remains a quantitatively reliable indicator of first-order phase transitions in black holes, even within multi-critical frameworks. This approach offers deeper insights into the governing energetic landscapes and kinetic processes underlying these phenomena.

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arXiv2025

Assessing WGC Compatibility in ModMax Black Holes via Photon Spheres Analysis and WCCC Validation

It seems that the regime of Hawking radiation and evaporation ultimately drives charged black holes toward super-extremality of the charge parameter and the dominance of extremal conditions. This progression, in turn, lays the groundwork for satisfying the necessary conditions for the Weak Gravity Conjecture (WGC). Preliminary studies indicate that black holes such as the Reissner-Nordstr$ö$m (RN) model, in their initial form, lack the capacity to sustain super-extremality of the charge parameter. If such conditions arise, these black holes transition into naked singularities-a scenario that is highly undesirable due to the loss of causality and the breakdown of space-time geometry. This raises whether the inability to sustain super-extremality is an inherent property of the model or a consequence of the approximations and precision limitations employed in its construction. To address this, we turned to the ModMax model, which represents an extension of the RN model. Our analysis revealed that the ModMax model not only accommodates super-extremality of the charge parameter but also, under certain conditions, emerges as a promising candidate for investigating the WGC. Furthermore, we independently observed how the inclusion of the de Sitter radius ($\ell$) in the AdS model and $f(R)$ gravitational corrections-both of which enhance and complicate the model-can have a direct impact on the range of super-extremal charge tolerance which, in turn, provides the realization of the conditions necessary for the WGC.

hep-th↗

arXiv2025

Reconciling the Weak Gravity and Weak Cosmic Censorship Conjectures in Einstein-Euler-Heisenberg-AdS Black Holes

The potential conflict between the Weak Gravity Conjecture (WGC) and the Weak Cosmic Censorship Conjecture (WCCC) poses a significant challenge in general relativity. The WCCC serves as a fundamental assumption ensuring the coherence of gravitational theory. This study investigates the reconciliation of the WGC and the WCCC by examining Einstein-Euler-Heisenberg-AdS black holes in four-dimensional spacetime. By imposing specific constraints on the metric parameters, we demonstrate that the WGC and the WCCC can coexist harmoniously. Detailed analyses of Einstein-Euler-Heisenberg-AdS black holes for $ Q > M $ validate the simultaneous fulfillment of the two conjectures, particularly in scenarios where $ q^2/m^2 \geq \left(Q^2 / M^2\right)_{\text{e}} $. The electromagnetic self-interaction parameter $ μ$ plays a crucial role in achieving this compatibility. Our findings establish that Einstein-Euler-Heisenberg-AdS black holes provide a robust framework for harmonizing the WGC and the WCCC. In particular, for exceedingly small values of ($μ$)-or, equivalently, when the condition ($μ\ll \ell$) is satisfied-the structure of our black hole transitions in a way that distinctly reveals its compatibility with the WGC. This study also explores the compatibility of the WGC and the WCCC with photon spheres. It examines parameter spaces that satisfy both conjectures, ensuring event horizons and photon spheres while maintaining black hole properties. Key results demonstrate that small $ μ$ values preserve WCCC adherence and validate WGC through photon sphere characteristics.

gr-qc↗

arXiv2025

Cooling and heating regions of Joule-Thomson expansion for AdS black holes: Einstein-Maxwell-Power-Yang-Mills and Kerr Sen black holes

In this paper, we study the Joule-Thomson Expansion (JTE) process for two types of black holes: AdS-Einstein-Maxwell-Power-Yang-Mills (AEMPYM) and AdS-Kerr-Sen (AKS). Our study focuses on understanding how various parameters influence the Joule-Thomson Coefficient (JTC), the inversion curve, and the ratio of minimum inversion temperature to critical temperature. For the AKS black hole, we observe that the isenthalpic curves can exhibit either cooling or heating behavior. This behavior is determined by the inversion curve, which is affected by the black hole's mass and specific parameters such as $b$ (parameter signifies the ionic charge of the black hole) and $a$ (rotation parameter). In the case of the AEMPYM black hole, our findings reveal that the ratio of minimum inversion temperature to critical temperature approaches a specific value as Maxwell's charge increases. This ratio remains constant for certain parameter values, while it varies for others. Specifically, when the parameter $q$ (real positive parameter of AEMPYM black hole) is greater than 1, the ratio is almost equal to 1/2 as Maxwell's charge (C) increases. When q equals 1/2, the ratio is exactly 1/2 for all values of (C). For values of (q) between 1/2 and 1, the ratio is close to 1/2, and for values of (q) between 0 and 1/2, the ratio decreases, moving away from 1/2. For the AKS black hole, we find that specific parameter values, such as (a = 0.00951) and (b = 0.00475 ), yield a ratio of minimum inversion temperature to a critical temperature that is approximately 1/2. This consistency across different parameter values highlights the robustness of our findings. Finally, we compare our results with those reported in the existing literature, providing a comprehensive summary in detailed tables.

hep-th↗

arXiv2025

Thermodynamic topology of Black Holes in $F(R)$-Euler-Heisenberg gravity's Rainbow

The topology of black hole thermodynamics is a fascinating area of study that explores the connections between thermodynamic properties and topological features of black holes. We successfully derive the field equations for $F(R)$-Euler-Heisenberg theory, providing a framework for studying the interplay between modified gravity and non-linear electromagnetic effects. We obtain an analytical solution for a static, spherically symmetric, energy-dependent black hole with constant scalar curvature. Also, our analysis of black holes in F(R)-Euler-Heisenberg gravity's Rainbow reveals significant insights into their topological properties. We identified the total topological charges by examining the normalized field lines along various free parameters. Our findings indicate that the parameters $( R_0 )$ and $( f_ε = g_ε )$ influence the topological charges. These results are comprehensively summarized in Table I. In examining the photon sphere within this model, the sign of the parameter $ R_0 $ plays a crucial role in determining whether the model adopts a dS or AdS configuration. An interesting characteristic of this model is that, in its AdS form, it avoids the formation of naked singularity regions, which sets it apart from many other models. Typically, varying parameter values in other models can result in the division of space into regions of black holes and naked singularities. However, this model consistently retains its black hole behavior by featuring an unstable photon sphere, regardless of parameter values within the acceptable range. In its dS form, the behavior of the model's photon sphere remains consistent with other dS models and does not exhibit unique differences.

gr-qc↗

arXiv2025

Thermodynamic Topology of Kiselev-AdS Black Holes within f (R, T) gravity

In this paper, we investigate the topological charge and the conditions for the existence of the photon sphere (PS) in Kiselev-AdS black holes within $f(R, T)$ gravity. We employ two different methods based on Duan's topological current $ϕ$-mapping theory viz analize of temperature and the generalized Helmholtz free energy methods to study the topological classes of our black hole. By considering the mentioned black hole, we discuss the critical and zero points (topological charges and topological numbers) for different parameters. Our findings reveal that the Kiselev parameter $ω$ and the $f(R, T)$ gravity parameter $γ$ influence the number of topological charges of black holes, leading to novel insights into topological classifications. We observe that for given values of the free parameters, there exist total topological charges ($Q_{total} = -1$) for T-method and total topological numbers ($W = +1$) for the generalized Helmholtz free energy method. Our research findings elucidate that, in contrast to the scenario where $ω= 1/3$, in other cases, increasing the parameter $γ$ increases the number of total topological charges for the black hole. Interestingly, for the phantom field ($ω= -4/3$), we observed that decreasing the parameter $γ$ increases the number of topological charges. Additionally, we study the results for the photon sphere. The studied models clearly reveal that the simultaneous presence of $γ$ and $ω$ effectively expands the permissible range for $γ$. In other words, the model can exhibit black hole behavior over a larger domain. Additionally, it is evident that with the stepwise reduction of $ω$, the region covered by singularity also diminishes and becomes more restricted. However, An interesting point about all three ranges is the elimination of the forbidden region in this model.

gr-qc↗

arXiv2025

Kramer's Escape Rate and Phase Transition Dynamics in AdS Black Holes

Traditional static methods in phase transition studies, provide good insights into the thermodynamics of black holes. However, they practically lose sight of the dynamic aspects and temporal sequence of events. The Kramer's escape rate, central to our research, offers a somewhat dynamic approach to phase transition. We examine the free energy landscapes for black holes under the influence of 'dark' and 'stringy dark' structures, assessing how additional parameters affect the escape rates and dynamics of the transition during the first-order phase transition from small to large black holes. In our analysis, we consider the escape rate as a function of the black hole radius and study its variations. We will observe that, on one hand, the escape rate well represents our assumption based on the movement from zero, increasing to a maximum point, and then decreasing back to zero as reactive structures become active during the phase transition interval. However, the critical point in this method is the encounter with a specific and distinct point. This is where the diagram of the direct process (escape rate from small to large black holes) intersects with the reverse process (large to small black holes), becoming equally probable (contact point). The point, which seems improbable at the onset of the phase transition or very negligible, gains more significance as the process progresses. This increase indicates the dominance of a region where the escape rate from larger black holes to smaller ones prevails. The predominance of the reverse process, which increases as we approach the end of the process and is necessarily accompanied by a variation in radius, may be considered as a natural reaction of the black hole against the 'phase change' action. A reaction which attempting to prevent any uncontrolled radial growth that could jeopardize the stability of the black hole.

gr-qc↗

arXiv2025

Topological Insights into Black Hole Thermodynamics: Non-Extensive Entropy in CFT framework

In this paper, We conducted an in-depth investigation into the thermodynamic topology of Einstein-Gauss-Bonnet black holes within the framework of Conformal Field Theory (CFT), considering the implications of non-extensive entropy formulations. Our study reveals that the parameter $λ$ (Rényi entropy) plays a crucial role in the phase behavior of black holes. Specifically, when $λ$ is below the critical value (C), it has a negligible impact on the phase behavior. However, when $λ$ exceeds the critical value, it significantly alters the phase transition outcomes. Determining the most physically representative values of $λ$ will require experimental validation, but this parameter flexibility allows researchers to better explain black hole phase transitions under varying physical conditions. Furthermore, the parameters $α$ and $β$ affect the phase structure and topological charge for the Sharma-Mittal entropy. Only in the case of $C>C_c$ and in the condition of $α\approxβ$ will we have a first-order phase transition with topological charge + 1. Additionally, for the loop quantum gravity non-extensive entropy as the parameter $q$ approaches 1, the classification of topological charges changes. We observe configurations with one and three topological charges with respect to critical value $C$, resulting in a total topological charge $W = +1$, and configurations with two topological charges $(ω= +1, -1)$, leading to a total topological charge $W = 0$. These findings provide new insights into the complex phase behavior and topological characteristics of black holes in the context of CFT and non-extensive entropy formulations.

gr-qc↗

arXiv2024

Thermodynamic Topology and Phase Space Analysis of AdS Black Holes Through Non-Extensive Entropy Perspectives

This paper studies the thermodynamic topology through the bulk-boundary and restricted phase space (RPS) frameworks. In bulk-boundary framework, we observe two topological charges $(ω= +1, -1)$ concerning the non-extensive Barrow parameter and with ($δ=0$) in Bekenstein-Hawking entropy. For Renyi entropy, different topological charges are observed depending on the value of the $λ$ with a notable transition from three topological charges $(ω= +1, -1, +1)$ to a single topological charge $(ω= +1)$ as $λ$ increases. Also, by setting $λ$ to zero results in two topological charges $(ω= +1, -1)$. Sharma-Mittal entropy exhibits three distinct ranges of topological charges influenced by the $α$ and $β$ with different classifications viz $β$ exceeds $α$, we will have $(ω= +1, -1, +1)$, $β= α$, we have $(ω= +1, -1)$ and for $α$ exceeds $β$ we face $(ω= -1)$. Also, Kaniadakis entropy shows variations in topological charges viz we observe $(ω= +1, -1)$ for any acceptable value of $K$, except when $K = 0$, where a single topological charge $(ω= -1)$. In the case of Tsallis-Cirto entropy, for small parameter $Δ$ values, we have $(ω= +1)$ and when $Δ$ increases to 0.9, we will have $(ω= +1, -1)$. When we extend our analysis to the RPS framework, we find that the topological charge consistently remains $(ω= +1)$ independent of the specific values of the free parameters for Renyi, Sharma-Mittal, and Tsallis-Cirto. Additionally, for Barrow entropy in RPS, the number of topological charges rises when $δ$ increases from 0 to 0.8. Finally for Kaniadakis entropy, at small values of $K$, we observe $(ω= +1)$. However, as the non-extensive parameter $K$ increases, we encounter different topological charges and classifications with $(ω= +1, -1)$.

hep-th↗

arXiv2024

Non-extensive Entropy and Holographic Thermodynamics: Topological Insights

In this paper, we delve into the thermodynamic topology of AdS Einstein-Gauss-Bonnet black holes, employing non-extensive entropy formulations such as Barrow, Rényi, and Sharma-Mittal entropy within two distinct frameworks: bulk boundary and restricted phase space (RPS) thermodynamics. Our findings reveal that in the bulk boundary framework, the topological charges, are influenced by the free parameters and the Barrow non-extensive parameter $(δ)$. So, we faced three topological charges $(ω= +1, -1, +1)$. When the parameter $δ$ increases to 0.9, the classification changes, resulting in two topological charges $(ω= +1, -1)$. When $δ$ is set to zero, the equations reduce to the Bekenstein-Hawking entropy structure, yielding consistent results with three topological charges. Additionally, setting the non-extensive parameter $λ$ in Rényi entropy to zero increases the number of topological charges, but the total topological charge remains (W = +1). The presence of the Rényi non-extensive parameter alters the topological behavior compared to the Bekenstein-Hawking entropy. Sharma-Mittal entropy shows different classifications and the various numbers of topological charges influenced by the non-extensive parameters $α$ and $β$. When $α$ and $β$ have values close to each other, three topological charges with a total topological charge $(W = +1)$ are observed. Varying one parameter while keeping the other constant significantly changes the topological classification and number of topological charges. In contrast, the RPS framework demonstrates remarkable consistency in topological behavior. Under all conditions and for all free parameters, the topological charge remains $(ω= +1)$ with the total topological charge $(W = +1)$. This uniformity persists even when reduced to Bekenstein-Hawking entropy.

hep-th↗

arXiv2024

Topology of Holographic Thermodynamics within Non-extensive Entropy

In this paper, we delve into the thermodynamic topology of AdS Reissner-Nordstr$\ddot{o}$m (R-N) black holes by employing nonextensive entropy frameworks, specifically R$\acute{e}$nyi (with nonextensive parameter $λ$) and Sharma-Mittal entropy (with nonextensive parameter $α, β$). Our investigation spans two frameworks: bulk boundary and restricted phase space (RPS) thermodynamics. In the bulk boundary framework, we face singular zero points revealing topological charges influenced by the free parameter $(λ)$ with a positive topological charge $(ω= +1)$ and the total topological charge $(W = +1)$, indicating the presence of a single stable on-shell black hole. Further analysis shows that when $(λ)$ is set to zero, the equations align with the Bekenstein-Hawking entropy structure, demonstrating different behaviors with multiple topological charges $(ω= +1, -1, +1)$. Notably, increasing the parameter $α$ in Sharma-Mittal entropy results in multiple topological charges $(ω= +1, -1, +1)$ with the total topological charge $(W = +1)$. Conversely, increasing $(β)$ reduces the number of topological charges, maintaining the total topological charge $(W = +1)$. Extending our study to the restricted phase space, we observe consistent topological charges $(ω= +1)$ across all conditions and parameters. This consistency persists even when reducing to Bekenstein-Hawking entropy, suggesting similar behaviors in both non-extended and Hawking entropy states within RPS.

hep-th↗