In this study, we investigate the gravitational lensing effects of deformed Horava-Lifshitz black holes, considering both strong and weak-field limit approximations and incorporating the impact of rainbow functions. Initially, we numerically compute the coefficients of the deflection angle, <math altimg='si1.svg'><mover accent='true'><mrow><mi>a</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></math>, <math altimg='si2.svg'><mover accent='true'><mrow><mi>b</mi></mrow><mrow><mo stretchy='false'>&#175;</mo></mrow></mover></math>, and <math altimg='si3.svg'><msub><mrow><mi>u</mi></mrow><mrow><mi>p</mi><mi>s</mi></mrow></msub><mo stretchy='false'>/</mo><msub><mrow><mi>R</mi></mrow><mrow><mi>s</mi></mrow></msub></math>, and plot the deflection angle <math altimg='si132.svg'><msub><mrow><mi>&#945;</mi></mrow><mrow><mi>d</mi></mrow></msub></math> as a function of the impact parameter <italic>u</italic>. We then proceed to calculate observable quantities, including the angular deflection <math altimg='si5.svg'><msub><mrow><mi>&#952;</mi></mrow><mrow><mo>&#8734;</mo></mrow></msub></math>, the total deflection area <italic>S</italic>, and the radius of the multiple gravitational arcs, <math altimg='si6.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi>m</mi><mi>g</mi><mi>a</mi></mrow></msub></math>, for supermassive black holes such as <math altimg='si7.svg'><mi>M</mi><msup><mrow><mn>87</mn></mrow><mrow><mo>&#8270;</mo></mrow></msup></math>, <math altimg='si8.svg'><mi>S</mi><mi>g</mi><mi>r</mi><msup><mrow><mi>A</mi></mrow><mrow><mo>&#8270;</mo></mrow></msup></math>, and <math altimg='si9.svg'><mi>N</mi><mi>G</mi><mi>C</mi><mn>4649</mn></math>. Additionally, we examine the Einstein ring, <math altimg='si10.svg'><msubsup><mrow><mi>&#952;</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>E</mi></mrow></msubsup></math>, for a range of supermassive black holes. Using the Gauss-Bonnet theorem, we derive the deflection angle in the weak-field limit for deformed Horava-Lifshitz black holes while considering rainbow functions. The results are compared with those for a Schwarzschild black hole, where <math altimg='si11.svg'><mi>&#945;</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0</mn></math> and <math altimg='si12.svg'><mi>g</mi><mo>,</mo><mi>h</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1</mn></math>.

India

Aniruddha Ghosh

Ujjal Debnath

Gravitational lensing by deformed Horava-Lifshitz black hole in rainbow gravity

In this work, we have studied the mass accretion mechanism of a 4-dimensional black hole in the Bumblebee gravity framework. We work with three well-known red-shift parameterizations of dark energy EoS, namely, Linear, Chevallier–Polarski–Lindler (CPL), and Jassal–Bagla–Padmanabhan (JBP) parameterization. First, we discussed the fundamentals of Bumblebee gravity theory, specifically the basic field equations, and then went on to discuss the three dark energy models and their respective equations of state, energy density equations, and associated Hubble parameter equations. Next, the free parameters for the Bumblebee theory of gravity are constrained using the MCMC analysis. After determining the necessary parameters, we initiated the mass accretion procedure. We derived the mass equation for the models using the redshift function and then graphically depicted how the black hole’s mass changed with redshift. The accretion of all the dark energy candidates discussed above led us to the final conclusion that the mass of a 4-dimensional Bumblebee Black Hole will progressively rise in accordance with the universe’s evolution.

Anuka Basak

Accretion of dark energy onto black hole in Bumblebee field

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

Anamika Kotal

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

This research focuses on examining a non-flat Friedmann–Robertson–Walker (FRW) cosmological model of the universe incorporating both dark matter and dark energy. Two intriguing dark energy models, Barrow agegraphic dark energy (BADE) and new Barrow agegraphic dark energy (NBADE), which were introduced in accordance with the holographic principle incorporating Barrow entropy, have been selected to play the role of dark energy. Using datasets from cosmic chronometers and baryon acoustic oscillations, we utilized the Markov Chain Monte Carlo (MCMC) technique to constrain the parameters of our model. This enables us to make several possible comparisons between these novel models of dark energy and the $$\Lambda $$ CDM models. Here, we explore cosmological parameters, including the equation of state(EoS) parameter, jerk parameter, deceleration parameter, and cosmological planes such as the $$q-r$$ plane, $$\omega _d - \omega '_d$$ for different values of the model parameters by considering both the presence and absence of mutual interactions of the dark sector of the universe. In addition, we examined the thermal stability and the Swampland criteria of our constructed models. Additionally, we analyze the energy conditions and find that NEC and DEC are fulfilled, but SEC is broken, indicating model stability and supporting the current acceleration of the universe. In order to give a more precise explanation of the origin of cosmic structures, we lastly conduct a linear perturbation analysis to examine the growth in matter density perturbations.

Sayani Maity

Anirudh Pradhan

Parameter constraints and cosmographic analysis of Barrow agegraphic and new Barrow agegraphic dark energy models

We propose a novel dynamical dark energy model within the frameworks of Einstein gravity and Horava–Lifshitz gravity, utilizing the DCMPM parametrization of the dark energy equation of state to derive the Hubble parameter. We keep $$ r_d $$ as a free parameter, and use different cosmological datasets such as cosmic chronometer measurements, Type Ia Supernovae observations, and Baryon Acoustic Oscillation data from DESI Y1 and SDSS-IV to extract the posterior distributions of each model parameters. Furthermore, we investigate the evolution of the Universe using various cosmographic parameters and conduct diagnostic analyses, including the statefinder and $$ O_m $$ diagnostics. Using various statistical metrics, we compare both models against the standard $$\Lambda $$ CDM model and find that all are well-supported by current data. Notably, the DCMPM parameterization within Einstein gravity emerges as a promising extension to the standard $$\Lambda $$ CDM framework.

Romania

Himanshu Chaudhary

Niyaz Molla

Azerbaijan

S. Pacif

China

G. Mustafa

Estimation of $$ H_0 $$ and $$ r_d $$ in the $$\omega (z)$$ parameterization within Einstein and Horava–Lifshitz gravity using DESI-Y1 and SDSS-IV

We study the structure and basic physical properties of non-rotating dark energy stars in Hořava–Lifshitz (HL) gravity. The interior of proposed stellar structure is made of isotropic matter obeys extended Chaplygin gas EoS. The structure equations representing the state of hydrostatic equilibrium i.e., generalize TOV equation in HL gravity is numerically solved by using chosen realistic EoS. Next, we investigate the deviation of physical features of dark energy stars in HL gravity as compared with general relativity (GR). Such investigation is depicted by varying a parameter $$\omega $$ , whereas for $$\omega \rightarrow \infty $$ HL coincide with GR. As a result, we find that necessary features of our stellar structure are significantly affected by $$\omega $$ in HL gravity specifically on the estimation of the maximum mass and corresponding predicted radius of the star. In conclusion, we can predict the existence of heavier massive dark energy stars in the context of HL gravity as compared with GR with not collapsing into a black hole. Moreover, we investigate the stability of our proposed stellar system. By integrating the modified perturbations equations in support of suitable boundary conditions at the center and the surface of the stellar object, we evaluate the frequencies and eigenfunctions corresponding to six lowest excited modes. Finally, we find that physically viable and stable dark energy stars can be successfully discussed in HL gravity by this study.

Krishna Das

Study of stable dark energy stars in Hořava–Lifshitz gravity

In the astrophysical universe, the falling matter accretion around the black hole is becoming an engrossing chapter. Our present manuscript reveals the matter accretion onto the acoustic-charged black hole in the background of Gross–Pitaevskii theory. This type of black hole is popular to several researchers. Following Hamiltonian dynamics, we go through the accretion process to face the cosmological mechanism. Depending on the tuning parameter $$\xi $$ of this black hole, we formulate sonic points to have a physical analysis of the speed of sound at sonic points. Undergoing the isothermal test fluids, we generate field equations at sonic points for our proposed model. Then we observe the accretion flow of the distinctive fluids around the acoustic-charged black hole with the variation of the tuning parameter. The most fascinating part of this work is to look for an analysis of the rate of flow of mass accretion of the different kinds of fluid onto our proposed black hole at sonic points with a graphical analysis. By investigating the accretion rate of these fluids, we seek stable and reliable results to check the compactness with the observational data.

Puja Mukherjee

Pameli Saha

Study of mass accretion of fluids flow near the horizon of charged acoustic black hole

In this study, we perform the significant effect of energy-dependent rainbow function on the properties of strange stars, proposed compact stars made up of strange quark matter. We assume the interior fluid of the star is in non-interacting and isotropic mode satisfying non-linear equation of state like color flavor locked state of matter. The new structure equations describe hydrostatic equilibrium state through generalizing the usual TOV equation of Einstein's gravity with involvement of rainbow function. By solving the generalized TOV equation numerically, we perform the behavior of some necessary properties of three considered CFL strange stars in the context of our solutions for physically reasonable by taking five variations of rainbow function including general relativity (GR). Motivated by GW190814 event, we justify the possible existence of compact stars with mass <math altimg='si1.svg'><mo linebreak='badbreak' linebreakstyle='after'>&gt;</mo><mn>2.5</mn><mspace width='0.25em' /><msub><mrow><mi>M</mi></mrow><mrow><mo>&#8857;</mo></mrow></msub></math> by our findings in rainbow gravity (RG). Finally, we get the possible existence of compact stellar objects made by CFL strange matter with the maximum mass that may be placed in the &#8216;mass-gap&#8217; ( <math altimg='si2.svg'><mn>2.5</mn><mspace width='0.25em' /><msub><mrow><mi>M</mi></mrow><mrow><mo>&#8857;</mo></mrow></msub><mtext>&#8211;</mtext><mn>5</mn><mspace width='0.25em' /><msub><mrow><mi>M</mi></mrow><mrow><mo>&#8857;</mo></mrow></msub></math>) region. Also, we perform some other properties like energy density, pressure, stability, etc., for our proposed stellar system in the effect of the rainbow function. In this connection, we illustrate the deviation of our obtained results in RG from GR.

Krishna Pada Das

Effect of rainbow function on the structural properties of color flavor locked strange stars

We extend the black hole solution of Euler-Heisenberg gravitational theory in AdS space-time by introducing quintessence field in it and studied thermodynamics and phase structure using both semi classical analysis and shadow formalism by considering Λ as thermodynamic pressure. We compare the results obtained by these two methods. The N-type change in temperature for <math altimg='si1.svg'><mi>P</mi><mo linebreak='goodbreak' linebreakstyle='after'>&lt;</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub></math> can be seen. The nature of Gibbs free energy ensures the second order phase transition for <math altimg='si1.svg'><mi>P</mi><mo linebreak='goodbreak' linebreakstyle='after'>&lt;</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi></mrow></msub></math>, which agrees with the temperature behaviour and then derived heat capacity, Joule-Thomson coefficient to study local stability and heating (or cooling) effect. Assuming black hole as a thermodynamic engine, we calculate the efficiency of Carnot cycle and Rankin cycle and study the impact of various black hole parameters on them. We also studied Ruppeiner thermodynamic geometry in {S,Q} thermodynamic phase space to study the BH at molecular level.

Debojyoti Mondal

Tanusree Roy

Thermodynamics of Euler-Heisenberg AdS black hole surrounded by quintessence field using shadow

Black holes are the fascinating objects in the universe. They represent extreme deformations in spacetime geometry. Here, we construct <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>P</mi><mo stretchy='false'>)</mo></math> gravity and the first example of static-spherically symmetric black hole solution in <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>P</mi><mo stretchy='false'>)</mo></math> gravity and discuss their thermodynamics. Using the numerical approach and series solution, we discover the solution and demonstrate that it is a generalization of Schwarzschild. The solution is characterized by a single function that satisfies a non-linear fourth-order differential equation. Interestingly, we can analytically calculate the solution's specific heat, Wald entropy, and Hawking temperature as a function of horizon radius. After analyzing the specific heat, we discovered that the black hole is thermodynamically stable over a small horizon radius.