In this work, the Schwarzschild black hole immersed in a Dehnen-type dark matter halo is considered for analyzing its various properties such as thermodynamics (through various entropies), shadow and optical appearance. For this purpose, we analytically describe the thermodynamic characteristics of BHs, like heat capacity and Helmholtz and Gibbs free energy, to study the local and global stability of such BHs by utilizing different entropy models. We also investigate the sparsity of Hawking radiations and found that the halo core radius and density are key factors determining the sparsity of this black hole. Astrophysical BHs are believed to be surrounded by luminous accretion disks. By considering the geometrically and optically thin accretion flow around the Schwarzschild black hole immersed in a Dehnen-type dark matter halo, we investigate the shadow and optical appearance of such a black hole. We show that in addition to the structure of the space-time geometry, the black hole’s image depends on the location of the accretion disk. By analyzing three specific radii, we determine the impact of direct emissions, photon rings, and lensing rings on the total intensity. The results indicate that direct emissions dominate the intensity while lensing and photon rings contribute minimally.

China

Pakistan

Shamaila Rani

Abdul Jawad

Iran

Malihe Heydari-Fard

Japan

Usman Zafar

Thermodynamic and shadow analysis of Dehnen type dark matter Halo corrected Schwarzschild black hole surrounded by thin disk

In this work, we investigate the cosmic analysis in detail by assuming squared speed of sound parameterizations in the framework of Brans-Dicke theory. For this purpose, we extract various cosmological parameters such as Hubble, deceleration, equation of state, <italic>Om</italic> diagnostic and jerk. We also explore the viability of the universe through the <math altimg='si1.svg'><mi>&#969;</mi><mo linebreak='goodbreak' linebreakstyle='after'>&#8722;</mo><msup><mrow><mi>&#969;</mi></mrow><mrow><mo>&#8242;</mo></mrow></msup></math> plane and the statefinder plane. We present the analytical and graphical solutions for all of the above-mentioned parameters. From the graphical analysis, it is noted that the deceleration parameter demonstrates the deceleration to acceleration expansions of the universe. In most cases, the <italic>Om</italic> diagnostic shows a quintessence-like era, the jerk parameter and statefinder parameter show the &#923;CDM limit and the <math altimg='si1.svg'><mi>&#969;</mi><mo linebreak='goodbreak' linebreakstyle='after'>&#8722;</mo><msup><mrow><mi>&#969;</mi></mrow><mrow><mo>&#8242;</mo></mrow></msup></math> plane indicates a freezing region of the universe. Our investigation reveals that the squared speed of sound demonstrates stable behavior across all considered parameterizations. To analyze the thermodynamic properties of the proposed models, we examine the validity of the generalized second law of thermodynamics with generalized six parameters entropy as horizon entropy. We found the validity of this law for all squared speed of sound parameterizations.

Nadeem Azhar

Saudi Arabia

Mohammad Mahtab Alam

Uzbekistan

Azerbaijan

Sanjar Shaymatov

 Sania

Physical insights of squared speed of sound parameterized Brans-Dicke gravity through cosmic parameters and thermodynamics

In this work, we investigate the thermodynamic properties of Bardeen black hole which is coupled with cloud of strings and minimally coupled to nonlinear electrodynamics. The modified entropy in the form of Sharma–Mittal entropy is used to discuss these properties which include mass, temperature, pressure, Gibbs free energy and trace of Hessian matrix. We obtain stable behavior along with physical solution for some specific values of parameters a and q. Furthermore, our work provides a thermodynamic metric using the Hessian matrix of black hole mass, changing the conformal connection between Quevedo and Ruppeiner’s geometries. Investigating the first principle of thermodynamics for regular black holes, such as the Bardeen AdS black hole, exposes significant behavior changes during phase transitions in an extended phase space.

Hussnain Raza

Maham Muzaffar

Hifza Riaz

Thermodynamic properties and geometries of bardeen black hole surrounded by string clouds

In this paper, we study the viability and stability of anisotropic compact stars in the context of  $$f({\mathcal {Q}})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>Q</mi> <mo>)</mo> </mrow> </math>   theory, where  $${\mathcal {Q}}$$  <math> <mi>Q</mi> </math>   is non-metricity scalar. We use Finch–Skea solutions to investigate the physical properties of compact stars. To determine the values of unknown constants, we match internal spacetime with the exterior region at the boundary surface. Furthermore, we study the various physical quantities, including effective matter variables, energy conditions and equation of state parameters inside the considered compact stars. The equilibrium and stability states of the proposed compact stars are examined through the Tolman–Oppenheimer–Volkoff equation, causality condition, Herrera cracking approach and adiabatic index, respectively. It is found that viable and stable compact stars exist in  $$f({\mathcal {Q}})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>Q</mi> <mo>)</mo> </mrow> </math>   theory as all the necessary conditions are satisfied.

Muhammad Gul

Muhammad Adeel

Viable and stable compact stars in  $$f({\mathcal {Q}})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>Q</mi> <mo>)</mo> </mrow> </math>   theory

This paper delves the thermodynamics of 5-dimensional Schwarzschild  $$AdS_5 \times S^5$$  <math> <mrow> <mi>A</mi> <mi>d</mi> <msub> <mi>S</mi> <mn>5</mn> </msub> <mo>×</mo> <msup> <mi>S</mi> <mn>5</mn> </msup> </mrow> </math>   black hole by considering the recently proposed effective models of exponential entropies. The conventional understanding of cosmological constant  $$\Lambda $$  <math> <mi>Λ</mi> </math>   as thermodynamic pressure with volume being its counterpart cannot be directly applied in the framework of the AdS/CFT correspondence. In order to resolve this issue, we establish a connection between the cosmological constant  $$\Lambda $$  <math> <mi>Λ</mi> </math>   in the boundary gauge theory and number of colors N while chemical potential is considered as thermodynamic conjugate. In this study, we replace the geometric parameters L and r of the AdS black hole with two thermodynamic parameters  $$N^2$$  <math> <msup> <mi>N</mi> <mn>2</mn> </msup> </math>   and S in the micro-canonical ensemble. Additionally, we explore the various thermodynamic geometry models such as Ruppeiner, Quevedo and Weinhold to derive the associated scalar curvatures for the 5-D Schwarzschild AdS BH. We analyze that these geometries exhibit microscopic attraction/repulsion forces on the particles of black hole.

Sadaf Iqbal

Shahid Chaudhary

Analysis of exponential corrected thermodynamic geometries in  $$AdS_5\times S^5$$  <math> <mrow> <mi>A</mi> <mi>d</mi> <msub> <mi>S</mi> <mn>5</mn> </msub> <mo>×</mo> <msup> <mi>S</mi> <mn>5</mn> </msup> </mrow> </math>   black hole

In this paper, we study the effect of Barrow entropy on the thermodynamic properties and geometry of specific black holes along with the nonlinear source. We investigate the mass, temperature, thermodynamic variable, and electric potential of the black hole as well. Furthermore, we examine the behavior of heat capacity to check the stability of a black hole. Geometrothermodynamics allows us to describe interactions between thermodynamics, critical points, and phase transitions by considering the geometric characteristics of the thermodynamic equilibrium space. Our analysis demonstrates that these findings are consistent with the results derived from the classical thermodynamics of black holes.

Mazhar Hussain

Impact of barrow entropy on geometrothermodynamics of specific black holes

In this paper, we analyze the thermodynamics of five-dimensional Schwarzschild AdS black hole in  $$AdS_5 \times S^5$$  <math> <mrow> <mi>A</mi> <mi>d</mi> <msub> <mi>S</mi> <mn>5</mn> </msub> <mo>×</mo> <msup> <mi>S</mi> <mn>5</mn> </msup> </mrow> </math>   spacetime in the presence of Tsallis entropy. Since the cosmological constant  $$\Lambda $$  <math> <mi>Λ</mi> </math>   is considered as thermodynamical pressure with volume as its conjugate, but this explanation cannot be employed in AdS/CFT correspondence. In this study, we associate cosmological constant  $$\Lambda $$  <math> <mi>Λ</mi> </math>   in boundary gauge theory with the number of colors N and chemical potential is taken to be its thermodynamic conjugate. The two geometric parameters in the AdS black hole, r and L are substituted for two thermodynamic parameters in the micro-canonical ensemble, which are considered to be entropy S and  $$N^2$$  <math> <msup> <mi>N</mi> <mn>2</mn> </msup> </math>  . Moreover, we evaluate several thermodynamical geometry formulations, including Weinhold, Ruppeiner, and Quevedo and derive associated scalar curvatures for five-dimensional Schwarzschild AdS black hole. It is suggested that all these geometries show repulsive/attractive forces on the particles at different phases of entropy.

Hooman Moradpour

Aqsa Tanveer

Tsallis entropy inspires geometric thermodynamics of specific black hole

In the framework of dynamical Chern–Simons theory of gravity, we study the recent cosmic expansion with acceleration of the universe. We take interacting scenario of dark energy and dark matter with three cutoffs like Granda–Oliveros, higher order derivative of Hubble parameter and generalized holographic dark energy model. In the flat Friedmann–Robertson–Walker universe, well-known cosmological parameters have been calculated. We study the perturbation of matter density growth, growth factor and growth index behavior for the underlying framework. The cosmological parameters like equation of state parameter, deceleration parameter, and stability of each model are discussed. The outcomes of these models represent the cosmic expansion of the universe with acceleration.

Saba Qummer

Amir Sharif

Study of growth matter index and cosmic implications in dynamical Chern–Simons modified gravity

In the framework of modified Weyl gravity, we observe the equilibrium picture of the thermodynamical laws for flat Friedmann–Robertson–Walker metric with chameleon scalar field and analyze the validity of the generalized second law of thermodynamics and thermal equilibrium condition for Hubble horizon along with Bekenstien–Hawking entropy. Also, we examine the effective equation of state parameter as well as the square speed of sound. By assuming four different choices of deceleration parameter, we investigate the behavior of equation of state parameter as well as the square speed of sound. The validity of generalized second law of thermodynamics and thermal equilibrium condition is also checked by taking the observational values of the model parameters from CC+$$H_o$$ <math><msub><mi>H</mi><mi>o</mi></msub></math>  dataset.

Zoya Khan

Cosmological and thermodynamics analysis in Weyl gravity

In the framework of fractal universe, the unified models of dark energy and dark matter are being presented with the background of homogenous and isotropic FLRW geometry. The aspects of fractal cosmology helps in better understanding of the universe in different dimensions. Relationship between the squared speed of the sound and the equation of state parameter is the key feature of these models. We have used constant as well as variable forms of speed of sound and express it as a function of equation of state parameter. By utilizing the four different forms of speed of sound, we construct the energy densities and pressures for these models and then various cosmological parameters like hubble parameter, EoS parameter, deceleration parameter and Om- diagnostic are investigated. Graphical analysis of these parameters show that in most of the cases EoS parameters and trajectories of Om-diagnostic corresponds to the quintessence like nature of the universe and the deceleration parameters represent accelerated and decelerated phase. In the end, we remark that cosmological analysis of these models indicates that these models correspond to different well known dark energy models.

Sadaf Butt

Khadija Asif

Cosmological aspects of sound speed parameterizations in fractal universe