The goal of our work is to analyze the thermodynamic topology of accelerated charged anti-de Sitter black holes with a generalized Barrow modification of the entropy. Using Duan’s $$\phi $$ -mapping theory and generalized Gibbs free energy, we analyze the topological classes of black holes. These tools enable us to calculate integer values that represent the topological features of the black hole. We examine the system within three distinct thermodynamic frameworks: the canonical, mixed canonical, and grand canonical ensembles. In the canonical ensemble, the system maintains fixed electric and magnetic charges. In the mixed canonical ensemble, the electric and magnetic potentials are kept constant. In contrast, the grand canonical ensemble maintains fixed electric and magnetic potentials but allows for charge exchange with the surroundings. These distinct ensembles provide a platform to study how black holes respond to various physical conditions. Specifically, we examine the charged and uncharged topological characteristics related to thermodynamic stability criteria. By applying these analytical methods, we aim to uncover new insights into the thermodynamic and topological properties of black holes. Additionally, we examine the geodesic deviation in an accelerated charged black hole, focusing on the influence of electric and magnetic charges on the courses of nearby geodesics. The complex effects of space-time curvature in this situation are reflected in the tendency of angular geodesics to converge as one advances away from the black hole, in contrast to radial geodesics. This study provides a deeper understanding of how black holes depend on gravitational frameworks and thermodynamic conditions, offering a fresh perspective on their nature and expanding our knowledge in this field.

China

Muhammad Yasir

Pakistan

Tehreem Aslam

Shahid Qaisar

Wei Liu

Azerbaijan

Faisal Javed

Saudi Arabia

Mansoor Alshehri

Thermodynamic topology and geodesics analysis of accelerated charged-AdS black hole with Barrow entropy corrections

Throughout the cosmic evolution of the Universe, when the temperature of a boson gas drops below a certain threshold, the Bose–Einstein condensation phenomenon may occur. In this scenario, the dark matter, viewed as a non-relativistic Newtonian gravitational condensate, is described by the Gross–Pitaevskii–Poisson system. Our research explores the evolution dynamics of the Bose–Einstein condensation of bosonic dark matter, considering it as an approximate first-order phase transition within a quantum gravitational-corrected cosmological setting referred to as Barrow entropy-based cosmology, which reflects the fractal nature of horizon geometry. We assess the quantities that characterize the dynamics of the Universe, such as temperature, energy density, scale factor, redshift, Hubble parameter, and deceleration parameter, before, during, and after the Bose–Einstein condensation phase crossover. Moreover, we specifically focus on the period of co-existence of $\textit{normal}$ and condensate phases of dark matter. We analyze the temporal behavior of an important parameter known as the $\textit{condensate dark matter fraction}$ throughout the condensation process and determine the duration of dark matter condensation. Our findings indicate that incorporating Bose–Einstein condensate dark matter within the framework of Barrow-modified cosmology significantly impacts the cosmic evolution of the Universe compared to the standard cosmological model. For a typical value of the Barrow exponent $$\delta = -1.3$$ , our model can account for an accelerated Universe without including a dark energy component and also addresses the age problem of our Universe. The negative value of $$\delta $$ speculates a spongy or porous structure for the cosmological horizon geometry at the Planck scale.

India

Subhra Mondal

Amitava Choudhuri

On the dynamics of cosmological phase transition during Bose–Einstein condensation of dark matter in Barrow entropy-based cosmology

In this work, we study the Barrow Holographic Dark Energy (BHDE) model (Phys Rev D 102:123525, 2020), which is based on Barrow’s modification of entropy. We show that this model is a special case of the more general Nojiri–Odintsov HDE (NO-HDE) framework (Eur Phys J C 77:528, 2017). In the same way, the Granda–Oliveros (GO) cutoff also appears as a particular case of the NO cutoff. After this, we reconstruct the dynamics of BHDE using a k-essence scalar field, which provides a field theory picture of its evolution. The results show how the Barrow deformation parameter and the infrared cutoff affect the kinetic term and the behaviour of the scalar field. Further, we test the thermodynamic consistency of the model by checking the generalized second law on cosmological horizons. Overall, the study confirms that both BHDE and the GO cutoff can be understood as limits of the NO-HDE framework, and that they are consistent with scalar field theory and the principles of thermodynamics. Also we confront the reconstructed BHDE–k-essence model with late-time cosmological data from cosmic chronometers and baryon acoustic oscillations. The features derived in the study the models under as viable models to explain the late-time cosmic acceleration.

Kazakhstan

Guldana Bekova

Aziza Altaibayeva

Ulbossyn Ualikhanova

Surajit Chattopadhyay

Cosmology of barrow holographic dark energy with generalized infrared cutoffs and validity of the generalized second law of thermodynamics

This research examines the dynamics and thermodynamics of a non-rotating Frolov black hole (BH) surrounded by a quintessence field, described by the parameters <math altimg='si12.svg'><mi>Q</mi></math> (charge), <math altimg='si13.svg'><mi>&#945;</mi></math> (Hubble length) and <math altimg='si14.svg'><mi>&#946;</mi></math> (quintessence coupling). In addition, the space-time structure, analyzed through the lapse function <math altimg='si1.svg'><mrow><mi>h</mi><mo>(</mo><mi>r</mi><mo>)</mo></mrow></math>, reveals that increasing <math altimg='si12.svg'><mi>Q</mi></math>, <math altimg='si13.svg'><mi>&#945;</mi></math>, or radial distance <math altimg='si15.svg'><mi>r</mi></math> enhances <math altimg='si1.svg'><mrow><mi>h</mi><mo>(</mo><mi>r</mi><mo>)</mo></mrow></math>, while <math altimg='si14.svg'><mi>&#946;</mi></math> exerts a negligible influence on the horizon radii. The particle dynamics near the BH is governed by an effective potential <math altimg='si16.svg'><msub><mi>V</mi><mrow><mrow><mi mathvariant='normal'>e</mi></mrow><mi>f</mi><mi>f</mi></mrow></msub></math>, angular momentum <math altimg='si17.svg'><mi mathvariant='script'>L</mi></math>, and a specific energy <math altimg='si18.svg'><mi mathvariant='script'>E</mi></math>, which delineates stable and unstable orbits. The innermost stable circular orbits (ISCOs) contract with increasing <math altimg='si12.svg'><mi>Q</mi></math> and <math altimg='si13.svg'><mi>&#945;</mi></math>, but expand with <math altimg='si14.svg'><mi>&#946;</mi></math>, reflecting competing gravitational and quintessence-driven effects. Harmonic oscillations display unique radial, latitudinal, and orbital frequencies, which are redshift for observers at a distance, whereas periastron precession decreases for greater <math altimg='si12.svg'><mi>Q</mi></math> and <math altimg='si13.svg'><mi>&#945;</mi></math>. From a thermodynamic perspective, the BH shows positive mass and temperature throughout various parameter ranges, indicating global stability. Heat capacity anomalies and the swallowtail patterns of Gibbs free energy indicate phase transitions, with transitions from stable to unstable relying on <math altimg='si13.svg'><mi>&#945;</mi></math>, <math altimg='si12.svg'><mi>Q</mi></math>, and <math altimg='si14.svg'><mi>&#946;</mi></math>. Energy emission rates decrease as the parameters increase.

Oman

S.K. Maurya

Allah Ditta

Algeria

Abdelmalek Bouzenada

Asifa Ashraf

Akram Ali

Uzbekistan

Farruh Atamurotov

Barrow entropy effects on thermodynamics and QPOs of a quintessence surrounded Frolov black hole model

In this work, we explore the Barrow Agegraphic Dark Energy (BADE) and New Barrow Agegraphic Dark Energy (NBADE) models within the framework of a fractal universe, incorporating Barrow entropy and the holographic principle with a time scale as the infrared (IR) cut-off. By analyzing both conformal time and the universe's age as IR cutoffs, we investigate the cosmological implications of these dark energy models and examine the evolution of a universe filled with the proposed dark energy components alongside pressureless matter. Using BAO and <math altimg='si1.svg'><mi>P</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi>h</mi><mi>e</mi><mi>o</mi><msup><mrow><mi>n</mi></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>+</mo></mrow></msup></math> datasets, we constrain the model parameters and plot the Hubble parameter and distance modulus for both datasets. The results align well with current observations and demonstrate excellent agreement with the &#923;CDM model. Additionally, we extract various cosmological parameters and assess the stability of the BADE and NBADE models through squared sound speed analysis. We study the <math altimg='si2.svg'><msub><mrow><mi>&#969;</mi></mrow><mrow><mi>d</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>&#8722;</mo><msubsup><mrow><mi>&#969;</mi></mrow><mrow><mi>d</mi></mrow><mrow><mo>&#8242;</mo></mrow></msubsup></math> analysis of the BADE and NBADE models and the statefinder diagnostic for both models in the <math altimg='si3.svg'><mi>q</mi><mo linebreak='goodbreak' linebreakstyle='after'>&#8722;</mo><mtext mathvariant='bold'>S</mtext></math> and <math altimg='si4.svg'><mi>q</mi><mo linebreak='goodbreak' linebreakstyle='after'>&#8722;</mo><mi>r</mi></math> planes. Also, we studied the energy conditions, evaluated our models through the framework of thermodynamics, and analyzed their thermal stability. Furthermore, in a dedicated section, we investigate the impact of introducing an interaction term between dark energy and dark matter on the classical and thermal stability of the models, as well as its role in alleviating the Hubble tension. Then, we correspond each model with quintessence, tachyon, DBI-essence, and k-essence scalar field models of DE in FRW space-time to reconstruct potentials and the dynamics for these scalar fields. Finally, we test the swampland conjecture for each reconstructed model, providing insights into their theoretical consistency within string theory. We also examine the inflationary behavior of the models by analyzing the evolution of the slow-roll parameters <italic>&#1013;</italic> and <italic>&#951;</italic>.

Anamika Kotal

Alok Sardar

Arijit Malakar

Ujjal Debnath

Parameter estimation of Barrow Agegraphic and New Barrow Agegraphic Dark Energy models in fractal universe: Correspondence with scalar field models

In this study, we are interested in exploring the impact of Barrow entropy on Joule-Thomson expansion of Rastal charged-AdS black hole and then we explore the particle dynamics. We examine the manner in which the characteristics of inversion curves and the Joule-Thomson coefficient behave under different physical conditions. We find that for smaller black holes, the Joule-Thomson coefficients are positive, shifting to negative values as charge grows, and that the coefficients increase as the Rastall parameter becomes positive. The inversion temperature likewise rises with increasing Rastall parameter. The behavior of inversion temperature and Joule-Thomson coefficient decreases as the Barrow entropy parameter approaches 1. The intricate link between the black hole mass and charge is revealed by the isenthalpic curves, which show bigger peaks for larger masses and a drop with decreasing mass values and a negative larger Rastall parameter. It is found that the Barrow entropy parameter greatly affects the heating and cooling regions of Rastal charged-AdS black hole. Further, we investigate that the larger Rastall parameter yields greater positive potential values, and the effective potential also shows a declining tendency as mass increases. We also study test particle dynamics around the charged-AdS black holes, seeing a change in the innermost stable circular orbit radius as charge increases and a clear periodic pattern when particles interact with the gravitational field's fixed points. This study advances the comprehension of black hole phenomena within modified gravity theories and establishes a basis for further investigating their complex behaviors in astrophysical settings.

M. Zeeshan Gul

Kuwait

Orhan Donmez

Tayyab Naseer

Mansoor H. Alshehri

Joule-Thomson expansion with Barrow entropy and particle dynamics of charged Rastall-AdS black hole

The goal of our work is to explore the topology classifications of black holes in Massive gravity. We use Duan's <italic>&#981;</italic>-mapping theory to study the topology classes. This tool helps us to compute the integer numbers to characterize the topological features of the black hole. Our analysis is carried out across two different thermodynamic ensembles. These statistical ensembles are the canonical ensemble and the mixed canonical ensemble. Every ensemble corresponds to a different thermodynamic condition, allowing us to investigate how the black holes respond to other physical conditions. Thus, employing these analytical techniques, it is expected that further insights into topological and thermodynamic aspects of black holes in these modified gravity frameworks can be explored. This work helps to shed light on black hole dependencies on gravitational theories and conditions in thermal processes and thus expands the knowledge, proposing a new essence of black holes.

Bander Almutairi

Thermodynamic topology of black hole in Massive gravity with generalized Barrow modification of entropy

This paper mainly aims to solve the anti-deSitter Black Holes (AdS BH) under the Barrow entropy under polytropic gas fluid, especially the Chaplygin gas. First, we develop this last polytropic model in detail to then obtain the possible solutions and thermodynamic conditions on the energy momentum and the Barrow entropy for spacetimes of spatial dimension $$D>3$$ . Then, we focus on thermodynamic solutions and the different impacts on the Barrow entropy of the black hole, the temperature profile, the mass, and the various physical quantities involved. Afterwards, we focus on the specific cases of the solutions of dimensions $$D=4$$ and 5 to concretely test the models, especially from the point of view of the thermodynamic topology. Finally, we generalize everything by elaborating and testing the stability of the models to arrive at the thermal geometry of the AdS BH.

Yassine Sekhmani

Bidyut Hazarika

P. Phukon

Canada

Alexandre Landry

S. Maurya

J. Rayimbaev

The $\textit{D}$-dimensional charged AdS black holes solutions in polytropic dark energy from Barrow entropy

We present a comprehensive investigation exploring the theoretical framework of Einstein–Aether gravity theory when combined with two modified cosmological paradigms: the Barrow Agegraphic Dark Energy (BADE) and its newer variant, the New Barrow Agegraphic Dark Energy (NBADE). Our study focuses on reconstructing the functional form of the Einstein–Aether Lagrangian component $\textit{F}$($\textit{K}$) from these phenomenological dark energy models. Model parameters are constrained using a Markov Chain Monte Carlo (MCMC) approach based on multiple datasets, including cosmic chronometers (CC), Baryon Acoustic Oscillations (BAO), and the Pantheon+SH0ES compilation. Using best-fit parameters, we analyze various cosmological diagnostics: Hubble and deceleration parameter evolution, dark energy equation of state ( $$\omega _{DE}$$ ), density parameter trajectories, $$\omega _{DE}'$$ – $$\omega _{DE}$$ phase space behavior, statefinder diagnostics $$(r,s^*)$$ and ($\textit{r}$, $\textit{q}$), and Om(z) trajectories. Both models exhibit late-time acceleration, with the dark energy sector showing a quintessence-like nature in the current epoch and evolving toward a phantom regime in the future. Stability analysis based on the squared sound speed ( $$v_s^2$$ ) highlights partial epoch-dependent stability. While our results demonstrate reasonable agreement with observational data and reveal physically plausible dynamics, the models do not yet offer a fundamentally superior alternative to other dark energy reconstructions. Nonetheless, their behavior under modified entropy assumptions and their flexibility in dynamical diagnostics provide a useful framework for probing non-standard extensions of Einstein–Aether gravity and dark energy phenomenology.

Banadipa Chakraborty

Tamal Mukhopadhyay

Reconstructions of Einstein–Aether gravity from Barrow agegraphic and new Barrow agegraphic dark energy models: examinations and observational limits

In this study, we investigate the brane inflation scenario by modifying the field equations of motion based on Barrow’s entropy proposal, while also considering the constant-roll condition. We address the $$\eta $$ -problem by fixing the constant-roll parameter at $$\sigma = 0.018$$ , consistent with observational constraints on the spectral index $$n_s$$ and the scalar-to-tensor ratio $\textit{r}$. The fixed value of the constant-roll parameter ensures that the $$\eta $$ -problem is addressed while satisfying the slow-roll condition. A correlation is found between the parameter of the D-brane KKLT potential and the parameter present in Barrow entropy. Another parameter of the D-brane KKLT potential is determined using the COBE formalism, which describes the energy scale of inflation. The quintessential behavior of the D-brane KKLT potential is examined within a scaling regime. The parameters established during the slow-rolling phase significantly influence the emergence of the quintessence phase. This scenario demonstrates the presence of a quintessence-type fluid following the slow-rolling phase, as approximated by the effective equation of state (EoS) parameter derived from the scaling solutions of the model. The early inflation of the universe is shown to emerge from two phases via the D-brane KKLT potential.

Türkiye

A. Keskin

Levent Canpolat

K. Kurt

Slow-rolling and quintessence inflation with the D-brane KKLT potential in Barrow entropy