In this study, we develop universal thermodynamic topological classes for the static black holes in the context of the Conformal Killing Gravity. Our findings indicate that the Conformal Killing Gravity significantly reconstructs the thermodynamic properties of both the smallest inner and the largest outer black hole states. Additionally, it considerably alters the thermodynamic stability of black holes across both high-temperature and low-temperature regimes. This analysis shows that different CKG parameter settings will lead to $$W^{0+}$$ $$(\lambda >0)$$ and $$W^{1+}$$ $$(\lambda <0)$$ categories for the charged AdS black hole, the Reissner–Nordstr $$\ddot{o}$$ m black hole in Conformal Killing Gravity is classified into the $$W^{0+}$$ and $$W^{1+}$$ categories. Furthermore, we examine the specific scenario where charge is neglected. The study reveals that within the framework of Conformal Killing Gravity, the Schwarzschild black hole similar to the Schwarzschild-AdS black hole, can be classified into the $$W^{1-}$$ and $$W^{0-}$$ categories. This work provides key insights into the fundamental nature of quantum gravity theory.

China

Hao Chen

Di Wu

Meng-Yao Zhang

Spain

Soroush Zare

Czechia

Hassan Hassanabadi

Bekir Lütfüoğlu

Zheng-Wen Long

Universal thermodynamic topological classes of static black holes in Conformal Killing Gravity

In this study, we investigate a Schwarzschild black hole surrounded by Dehnen-type dark matter. A comprehensive thermodynamic analysis of black holes is conducted, leading to the calculation of black hole remnants. We investigate the trajectory of light, establishing an upper limit for the parameters based on Event Horizon Telescope (EHT) observations of Sgr A*, ensuring that the black hole’s shadow resides within the allowed region. Furthermore, we derive the quasinormal modes (QNMs) for both scalar and electromagnetic perturbations. Utilizing a topological framework, we examine the stability of the photon sphere and classify the topology of the black hole in accordance with its thermodynamic potentials.

Azerbaijan

Farokhnaz Hosseinifar

Russia

Shahin Mamedov

Filip Studnička

Quasinormal modes and topological characteristics of a Schwarzschild black hole surrounded by the Dehnen type dark matter halo

In response to the limitations of the classical Oppenheimer-Snyder model of black holes, we investigate the quantum framework proposed by Lewandowski et al. (2023) [29]. This quantum model incorporates corrections that allow for a detailed analysis of features such as black hole thermodynamics and Hawking radiation. In particular, we focus on the evaporation process and quasi-normal modes, utilizing the Rosen-Morse approximation method. Furthermore, we explore the topology of photon spheres and the thermodynamic topology of the black hole.

Mexico

Shi-Hai Dong

Some new properties of black holes in the quantum Oppenheimer-Snyder model

In various fields of mathematical research, the Brouwer degree is a potent tool for topological analysis. By using the Brouwer degree defined in one-dimensional space, we interpret the equation of state for temperature in black hole thermodynamics, $$T=T(V,x_i)$$ , as a spinodal curve, with its derivative defining a new function . The sign of the slope of indicates the topological charge of the black hole’s critical points, and the total topological charge can be deduced from the asymptotic behavior of the function . We analyze a spherical hairy black hole within the framework of Lovelock gravity, paying particular attention to the topological structure of black hole thermodynamics under Gauss–Bonnet gravity. Here, the sign of the scalar hair parameter influences the topological classification of uncharged black holes. When exploring the thermodynamic topological properties of hairy black holes under cubic Lovelock gravity, we find that the spherical hairy black hole reproduces the thermodynamic topological classification results seen under Gauss–Bonnet gravity.

Hou-You Zhou

Topological classification of critical points for hairy black holes in Lovelock gravity

Motivated by the prediction of a minimal measurable length at Planck scale found in many candidate theories of quantum gravity, we examine the Klein-Gordon equation with a <math><mi>λ</mi><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>4</mn></mrow></msup></math> interaction and a symmetry-breaking term, in the presence of a generalized uncertainty principle associated with a minimal length. This allows us to assess the correction which underlying physical systems of scalar fields would undergo. Further, we solve the Euler-Lagrange equation by applying the Hybrid Analytical and Numerical (or HAN, for short) method, an effective approach for solving a large variety of nonlinear ordinary and partial differential equations.

Iran

Narges Heidari

Canada

Marc de Montigny

Ali Ahmadi Azar

Malaysia

Thambiayya Sathiyaraj

Solutions of the nonlinear Klein-Gordon equation and the generalized uncertainty principle with the hybrid analytical and numerical method

In the present study, we investigate the topological properties of black holes in terms of Rényi statistics as an extension of the Gibbs-Boltzmann (GB) statistics, aiming to characterize the non-Boltzmannian thermodynamic topology of Kerr-Sen and dyonic Kerr-Sen black holes. Through this research, we discover that the topological number derived via Rényi statistics differs from that obtained through GB statistics. Interestingly, although the nonextensive parameter λ changes the topological number, the topological classification of the Kerr-Sen and dyonic Kerr-Sen black holes remains consistent under both GB and Rényi statistics. In addition, the topological numbers associated with these two types of black holes without cosmological constant using Rényi entropy processes are the same as the AdS cases of them by considering the GB entropy, as further evidenced by such a study found here. This indicates the cosmological constant has some potential connections with the nonextensive parameter from the perspective of thermodynamic topology.

Hui Yang

Thermodynamic topology of Kerr-Sen black holes via Rényi statistics

We are interested in a fermion-antifermion pair in magnetized <math><mn>2</mn><mo>+</mo><mn>1</mn></math> dimensional optical background with constant negative curvature. One implements this background for obtaining the optical metric of the BTZ black hole similar to the hyperbolic wormhole. To analyze the evolution of the considered system, we start with constructing the corresponding form of a one-time fully-covariant many-body Dirac equation derived from quantum electrodynamics. The associated equation leads <math><mn>4</mn><mo>×</mo><mn>4</mn></math> dimensional matrix equation resulting in a set of coupled equations consisting of four first-order equations since the two-body equation possesses spin algebra constructed through the Kronecker product of the generalized Dirac matrices. Also, we show a nonperturbative wave equation for the considered system. Accordingly, we seek analytical solutions to the wave equation. We obtain that relativistic energy of the system depends on the parameters of the background as well as the magnetic field. Also, we adapt the results to a Weyl pair. Our results imply that the lifetime of such a pair can be actively tuned, in principle.

Türkiye

Abdullah Guvendi

Fermion-antifermion pair in magnetized optical wormhole background

The classification of critical points of charged topological black holes (TBHs) in anti-de Sitter spacetime (AdS) under the Power Maxwell Invariant (PMI)-massive gravity is accomplished within the framework of black hole chemistry (BHC). Considering the grand canonical ensemble (GCE), we show that  $$d=4$$  <math> <mrow> <mi>d</mi> <mo>=</mo> <mn>4</mn> </mrow> </math>   black hole have only one topological class, whereas  $$d\ge 5$$  <math> <mrow> <mi>d</mi> <mo>≥</mo> <mn>5</mn> </mrow> </math>   black holes belong to two different topology classes. Furthermore, the conventional critical point characterized by negative topological charge coincides with the maximum extreme point of temperature; and the novel critical point featuring opposite topological charge corresponds to the minimum extreme point of temperature. With increasing pressure, new phases emerge at the novel critical point while disappear from the conventional one. Moreover, a atypical van der Waals (vdW) behavior is found in  $$d\ge 6$$  <math> <mrow> <mi>d</mi> <mo>≥</mo> <mn>6</mn> </mrow> </math>   dimensions, and the anomaly disappears at the traditional critical point. In the limit of nonlinearity parameter  $$s\rightarrow 1$$  <math> <mrow> <mi>s</mi> <mo>→</mo> <mn>1</mn> </mrow> </math>  , different topology classes are only obtained in the GCE and they may not exist within the canonical ensemble. With the absence of electric potential  $$\Phi $$  <math> <mi>Φ</mi> </math>  , the neutral TBHs share the same topological classification results as the charged TBHs in the GCE of Maxwell-massive gravity.

Topology of nonlinearly charged black hole chemistry via massive gravity

In this paper, we investigate the quantum correction on thermodynamics of the Reissner-Nordström black hole in the presence of the quintessence matter associated with dark energy. To this end, the modified Hawking temperature, heat capacity, and entropy functions of the black hole are derived. Investigation reveals that the modified uncertainty principles and normalization factor α restrict the lower bound value of horizon radius to affect the Hawking temperature and the parameter <math><msub><mrow><mi>η</mi></mrow><mrow><mn>0</mn></mrow></msub></math> has a non-negligible effect on the heat capacity threshold. Furthermore, the correction of entropy does not depend on the quintessence matter. It is also examined the equation of state associated with the pressure and the volume in this framework. In addition, we employ graphical methods to compare and discuss the findings within the generalized uncertainty principle (GUP) and extended uncertainty principle (EUP).

Bekir Can Lütfüoğlu

Thermodynamics of the Reissner-Nordström black hole with quintessence matter on the EGUP framework

In this paper, by studying the COW experiment and the Einstein Bohr’s photon box, we investigate the associated modified phase shift and Hawking temperature. Next, we comment on the effective Newton constant suggested by the doubly special relativity based on the generalized uncertainty principle.