The exploration of black holes in the presence of dark photon fields offers a compelling pathway to investigate hidden sector interactions and their gravitational impacts. We analyze static, spherically symmetric black hole solutions within dark photon models featuring Yukawa-type interactions and higher-order magnetic dipole corrections. These modifications are introduced via a generalized energy-momentum tensor sourced by the dark photon field, resulting in a nontrivial deformation of the spacetime geometry. We investigate the dynamics of massless and massive particles, emphasizing the influence of dark sector parameters on effective potentials, photon spheres, and circular geodesics. Notably, the innermost stable circular orbit radius, particle energy, and angular momentum exhibit sensitive dependence on <math altimg='si33.svg'><msub><mi>m</mi><msup><mi>A</mi><mo>&#8242;</mo></msup></msub></math> and <math altimg='si7.svg'><msub><mi>g</mi><mi>D</mi></msub></math>, suggesting observable deviations in accretion disk behavior and gravitational wave emissions. Through numerical analysis, we compute the shadow radius <math altimg='si34.svg'><msub><mi>R</mi><mi>s</mi></msub></math> and demonstrate that dark photon corrections either compress or enlarge the black hole shadow, depending on the interplay between Yukawa screening and gauge coupling. The geodetic precession frequency <math altimg='si35.svg'><msub><mstyle mathvariant='normal'><mi>&#920;</mi></mstyle><mtext>GPF</mtext></msub></math> is also shown to vary significantly from classical expectations, pointing to dark-sector-induced frame-dragging effects. Additionally, we explore the superradiance phenomenon by solving the Klein-Gordon equation for charged scalar perturbations in the modified background. Our results identify conditions for wave amplification and highlight how dark photon interactions can enhance or suppress the superradiant scattering regime. Overall, this study presents a unified framework that connects dark photon physics with black hole thermodynamics, geodesic motion, optical properties, and stability.

Pakistan

Azerbaijan

Shahid Chaudhary

United Kingdom

Muhammad Danish Sultan

Thailand

Talha Anwar

Saudi Arabia

Atif Mossad Ali

Uzbekistan

Farruh Atamurotov

Muhammad Hadi

M.A. Sayed

Ali M. Mubaraki

Superradiance, geodesics and shadows of black holes in dark photon with higher-order correction

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

China

Asifa Ashraf

Akram Ali

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

In this paper, we examined the motion of a spinning particle around a Reissner-Nordström-like black hole. Initially, we analyze the dynamics of the spinning test particles using the Mathisson–Papapetrou–Dixon equation. Subsequently, we derive the effective potential and examine it for the parameter of the Reissner-Nordström-like black hole. We then examine the impact of the particle’s spin on the innermost stable circular orbits (ISCO), specific angular momentum, and energy at ISCO for different parameters of hairy black holes. Furthermore, we determine the critical values of the particle’s spin <math altimg='si6.svg'><mi>s</mi></math>, above which time-like particles become non-physical and space-like. Furthermore, we plot and discuss the variation of the critical spin values for different values of <math altimg='si2.svg'><mi>l</mi></math> and charge <math altimg='si3.svg'><mi>Q</mi></math>. Additionally, particle trajectories near a Reissner-Nordstr&#246;m-like (RN-like) black hole are examined for different spacetime and particle parameters. In conclusion, we analyze the center-of-mass of two spinning particles colliding near the boundary of the hairy black hole.

Gulnisa Abdukayumova

Ahmadjon Abdujabbarov

Phongpichit Channuie

G. Mustafa

Dynamics of spinning particles around the Reissner-Nordstrom-like black hole

We investigate a novel realization of warm inflation driven by the Standard Model (SM) Higgs field within the Palatini formulation of gravity, supplemented by an $$R^2$$ curvature correction. By incorporating dissipative dynamics and a thermal radiation bath, our model eliminates the need for a separate reheating phase and naturally flattens the inflationary potential. We derive the slow-roll dynamics in the strong dissipation regime, compute the resulting inflationary observables, and demonstrate compatibility with the latest CMB constraints from Planck, BICEP/Keck, and BAO data. Specifically, we show that the scalar spectral index $$n_s$$ lies in the range 0.963–0.965, and the tensor-to-scalar ratio $\textit{r}$ is strongly suppressed, $$r \sim \mathscr {O}(10^{-3}$$ – $$10^{-2})$$ , for Higgs quartic couplings $$\lambda \sim 10^{-9}$$ . These predictions remain robust under two distinct growing-mode functions. Furthermore, we show that the model is consistent with the refined de Sitter swampland conjecture due to entropy production during inflation. This work represents the first comprehensive study of warm minimal Higgs inflation in Palatini $$R^2$$ gravity, unifying quantum gravity criteria, thermal field dynamics, and observational consistency within a single inflationary framework.

Jureeporn Yuennan

Kazakhstan

Ratbay Myrzakulov

India

P. Sahoo

Minimal warm higgs inflation in palatini $$R^{2}$$ gravity

Recently, a study on shadow of quantum corrected Schwarzschild black hole in loop quantum gravity appeared in (Ye et al. in Phys Lett B 851:138566, 2024, ) assuming a fixed value of Barbero–Immirzi parameter $$\gamma $$ . Following this approach, we considered its rotating counterpart being a quantum corrected Kerr black hole in effective loop quantum gravity and studied its deviation from Kerr black hole for a fixed value of $$\gamma $$ . We proposed and proved a theorem describing the location of unstable circular null orbits for all such Kerr-like metrics. The deviation between the shadows of the Kerr and quantum corrected Kerr black holes has also been studied, and the spin parameter is constrained by comparison with the EHT results for M87* and Sgr A* to precisely probe the quantity of deviation due to quantum correction. Lastly, we immersed the quantum corrected Kerr black hole in an inhomogeneous plasma and studied its impact on the shadow size. We found that the unstable null orbits for the quantum corrected Kerr black hole are always smaller than the unstable null orbits for Kerr black hole. The effect of Barbero–Immirzi parameter allows the quantum corrected Kerr black hole to mimic Sgr A* with a higher probability than the Kerr black hole. However, the quantum corrected Kerr black hole does not mimic M87*. The plasma reduces the size of the shadow of quantum corrected black hole, and the plasma parameter in the case II is more sensitive than that in case I.

Muhammad Raza

M. Zubair

Influence of quantum correction on Kerr black hole in effective loop quantum gravity via shadows and EHT results

In this study, we explore metric-Palatini gravity extended by the antisymmetric component of the affine curvature. This gravitational theory results in general relativity plus a geometric Proca field. Building on our previous work, where we constructed its static spherically symmetric solutions in the Anti-de Sitter (AdS) background (Eur. Phys. J. C 83(4):318, 2023), we conduct a comprehensive analysis of the system’s thermodynamics. We examine the thermodynamic properties of the Einstein-Geometric Proca AdS compact objects, focusing on the Hawking temperature, enthalpy, heat capacity, entropy, and Gibbs free energy. Particular attention is given to the dependence of the Hawking temperature, enthalpy, and heat capacity on the uniform potential $$q_1$$ and the electromagnetic-type charge $$q_2$$ . Through numerical analysis, we compute the entropy and Gibbs free energy and investigate how these quantities vary with the model parameters.

Asalkhon Alimova

Türkiye

Elham Ghorani

Israel

Beyhan Puliçe

Thermodynamics of Einstein-Geometric Proca AdS compact objects

In this paper, we investigate the thermodynamical and optical characteristics of a black hole surrounded by massive spin-1 vector fields in the framework of Kaluza–Klein gravity. Motivated by the natural emergence of massive vector fields through the dimensional reduction of higher-dimensional gravity, we explore their role in modifying the near-horizon physics and observable signatures of black holes. These vector fields, akin to dark photons, introduce Yukawa-like corrections to the gravitational potential and mimic dark matter effects without invoking exotic particles. Our thermodynamic analysis, extended via logarithmic-corrected Barrow entropy, reveals that these fields significantly alter black hole temperature, specific heat, and Gibbs free energy. Notably, phase transitions are identified and confirmed using thermodynamic geometry tools, including Quevedo and HPEM metrics, highlighting the presence of stable remnants under quantum gravity corrections. Furthermore, we examine accretion disk structures and black hole shadow images through ray-tracing techniques under both static and infalling spherical accretion models. The direct and secondary images of the disk, as well as photon ring features, exhibit distinct deformations based on $$\gamma $$ and $$\lambda $$ . These modifications affect observable properties such as shadow size, intensity profiles, and lensing behavior, suggesting potential avenues for empirical testing via black hole imaging. Our findings underscore the rich phenomenology induced by massive vector fields in KK gravity, providing a unified perspective on black hole thermodynamics, dynamical stability, and observational signatures.

Ali Koam

Ali Ahmad

Ibtisam Masmali

Probing Kaluza–Klein black holes with massive vector fields via thermodynamics, shadows, and accretion disks

This paper presents optical and astrophysical aspects of charged dilatonic black holes within the framework of dilaton-massive gravity, a promising extension of General Relativity motivated by low-energy string theory. By incorporating a nonminimally coupled scalar dilaton field and massive graviton terms into the Einstein-Maxwell action, we study static, spherically symmetric black hole solutions characterized by the parameters <math altimg='si1.svg'><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub></math>, <math altimg='si2.svg'><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub></math>, and <math altimg='si3.svg'><msub><mrow><mi>m</mi></mrow><mrow><mn>0</mn></mrow></msub></math>, which control the strength of scalar-gravity and massive gravity couplings. We use Gauss-Bonnet theorem to compute the weak deflection angle of light around the black hole. The results reveal that the coupling parameter <math altimg='si1.svg'><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub></math> intensifies light bending, while more negative values of <math altimg='si2.svg'><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub></math> and higher graviton masses <math altimg='si3.svg'><msub><mrow><mi>m</mi></mrow><mrow><mn>0</mn></mrow></msub></math> suppress it. Extending this analysis to realistic astrophysical settings, we introduce a cold, non-magnetized plasma environment and derive the plasma-corrected deflection angle. The presence of plasma leads to chromatic dispersion, increasing the bending of light at lower frequencies, and amplifying the influence of dilaton-massive gravity on lensing observables. Next, we examine the black hole's shadow by numerically solving for the photon sphere and evaluating the shadow radius. Our findings demonstrate that larger values of <math altimg='si1.svg'><msub><mrow><mi>c</mi></mrow><mrow><mn>1</mn></mrow></msub></math> and <math altimg='si3.svg'><msub><mrow><mi>m</mi></mrow><mrow><mn>0</mn></mrow></msub></math> decrease the shadow size due to increased spacetime curvature, whereas increasing <math altimg='si2.svg'><msub><mrow><mi>c</mi></mrow><mrow><mn>2</mn></mrow></msub></math> expands it by lowering the gravitational potential. These effects are visualized through shadow images in celestial coordinates, clearly illustrating how modified gravity alters the observable structure of black holes.

M.M. Alam

Gravitational lensing and shadows of dilatonic black holes in dilaton-massive gravity

We investigate the dynamics of spinning test particles orbiting static black holes in effective quantum gravity (EQG) using the Mathisson–Papapetrou–Dixon (MPD) formalism with two distinct models. The purpose of using two models is to compare qualitatively different realizations of EQG corrections and assess their impact on spin-gravity coupling and orbital behavior. Through analysis of the effective potential, we demonstrate how $$\zeta $$ and particle spin $\textit{s}$ jointly influence orbital stability, revealing that (i) in Model-1, increasing $$\zeta $$ elevates the potential barrier while spin effects become dominant near the horizon, (ii) Model-2 shows weaker dependence on $$\zeta $$ except for high-spin configurations. The innermost stable circular orbits (ISCOs) exhibit characteristic scaling $$r_{\text {ISCO}}(\zeta ,s)$$ , with quantum corrections that increase the radius of the ISCO by up to 27% relative to Schwarzschild for $$\zeta =4$$ in Model-1. We derive critical spin values $$s_{\text {max}}$$ beyond which particle trajectories become spacelike, finding $$s_{\text {max}}$$ decreases monotonically with $$\zeta $$ in Model-2 but shows non-monotonic behaviour in Model-1. The particle collision energetics are analyzed, showing that the center-of-mass energies $$E_{\text {cm}}$$ can be enhanced by spin-parameter tuning, reaching $$E_{\text {cm}}/2m \sim 8$$ for $$(\zeta ,s_1,s_2)=(4,-0.5,0.5)$$ near the horizon. Trajectory simulations reveal that quantum corrections in Model-1 induce precession effects absent in Model-2, suggesting observational signatures to distinguish EQG models. Our results establish the combined influence of quantum spacetime structure and spin-curvature coupling on the test particle dynamics, with implications for EQG phenomenology and gravitational wave astronomy.

Dilmurod Umarov

South Africa

Sushant Ghosh

Dynamics of spinning particles around static black holes in effective quantum gravity

We investigate the motion of neutral test particles around a non-rotating regular black hole within the framework of asymptotically safe gravity, analyzing the impact of the black hole’s parameters on particle motion. This black hole solution is characterized by an additional parameter, $$\eta $$ , which differentiates it from the standard Schwarzschild black hole solution. We obtain analytical formulations for the energy and angular momentum of equatorial circular orbits as functions of the black hole parameter. The stability of these circular orbits is examined by the effective potential. Additionally, we present a graphical study of the innermost stable equatorial circular orbits as functions of the black hole parameter and investigate the effective force exerted on circular orbits. We also derive the frequencies of radial and latitudinal harmonic oscillations as functions of the model parameters and discuss the key features of quasi-periodic oscillations of test particles near stable circular orbits in the black hole’s equatorial plane. The phenomenon of periastron precession is also considered. Additionally, we explore particle collisions near the black hole and demonstrate that such collisions can produce high energy near the event horizon. Our findings indicate that the black hole parameter significantly influences the motion of test particles around a regular black hole in the context of asymptotically safe gravity. We examine the shadow of black hole and using observational data from the Event Horizon Telescope (EHT) collaboration for Sgr A* and M87*, we have determined the range of $$\eta $$ parameter that corresponds to the observations.

Awad Ibraheem

Gunel Bahaddinova

Testing regular black holes in the framework of asymptotically safe gravity using particle dynamics, QPOs, and shadow constraints