In this paper, we investigate the gravitational lensing properties of magnetically charged black holes within the framework of nonlinear electrodynamics. We derive the deflection angle and examine the influence of the nonlinear electrodynamics parameter $$\xi $$ on light bending. We initially employ a geometric approach based on the Gauss–Bonnet theorem to analyze the gravitational deflection of null and timelike particles. This method encapsulates the global characteristics of the lensing effect in an elegant manner. In the subsequent part of the work, we explore the impact of nonlinear electromagnetic corrections on the black hole shadow. Using numerical techniques, we study the behavior of the photon sphere and demonstrate that a reduction in the photon sphere radius leads to a correspondingly smaller shadow. We compare these results with those for the Schwarzschild and Reissner–Nordström black holes, highlighting the distinctive features introduced by nonlinear electrodynamics. Furthermore, we examine the strong deflection limit for light trajectories near these black holes, focusing on the roles of both the magnetic charge $$Q$$ and the nonlinear parameter $$\xi $$ . Our analysis reveals that the combined effects of $$Q$$ and $$\xi $$ enhance the strong deflection angle, resulting in a more pronounced lensing effect than that predicted by the classical Reissner–Nordström solution. These findings suggest that the nonlinear interactions may provide a potential observational signature for identifying NED black holes.

Pakistan

Italy

Hira Waseem

Philippines

Nikko Lobos

Türkiye

Ali Övgün

Reggie Pantig

Analyzing deflection angles and photon sphere dynamics of magnetically charged black holes in nonlinear electrodynamic

In this paper, we investigate the properties of relativistic stars made of isotropic matter within the framework of the minimal Standard Model Extension, where a Bumblebee field (BF) coupled to spacetime induces spontaneous Lorentz symmetry breaking. We adopt analytic equations-of-state describing either condensate dark stars or strange quark stars. We solve the structure equations numerically, and we compute the mass-to-radius relationships. The influence of the Bumblebee parameter <bold>l</bold> is examined in detail, and an upper bound is obtained using the massive pulsar (PSR) J0740+6620 and the strangely light High Energy Stereoscopic System (HESS) J1731-347 compact object.

Chile

Grigoris Panotopoulos

Strange quark stars and condensate dark stars in Bumblebee gravity

Motivated by the work of Cardoso et al. (2022) <cross-ref refid='br0150' id='crf0030'>[15]</cross-ref> on black holes in galaxies, we derive a new black hole solution surrounded by a Dekel-Zhao (DZ) dark matter profile. The derived metric, influenced by DZ profile parameters, exhibits two distinct regimes: for <math altimg='si1.svg'><mi>r</mi><mo>&#8810;</mo><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> ( <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> is a characteristic radius), exponential corrections dominate, producing significant deviations from the Schwarzschild solution near dense cores, while for <math altimg='si3.svg'><mi>r</mi><mo>&#8811;</mo><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math>, these corrections vanish, restoring the Schwarzschild metric at large distances. These findings ensure consistency with general relativity in vacuum. The black hole shadow and deflection angle are analyzed, demonstrating that the shadow radius increases with black hole mass ( <math altimg='si4.svg'><msub><mrow><mi>M</mi></mrow><mrow><mi mathvariant='normal'>BH</mi></mrow></msub></math>), while higher central densities ( <math altimg='si5.svg'><msub><mrow><mi>&#961;</mi></mrow><mrow><mi mathvariant='normal'>ch</mi></mrow></msub></math>) result in smaller shadows, reflecting the environmental impact of dense dark matter halos. Photon dynamics reveal how DZ profiles modify critical impact parameters and effective potentials, with gravitational lensing effects highly sensitive to the characteristic radius ( <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math>). Smaller <math altimg='si2.svg'><msub><mrow><mi>r</mi></mrow><mrow><mi mathvariant='normal'>c</mi></mrow></msub></math> values lead to larger deflection angles due to stronger gravitational effects near compact cores. This work highlights the significance dark matter profiles in shaping black hole observables, providing a theoretical foundation for future observational studies and advancing the understanding of dark matter-black hole interactions in astrophysical and cosmological contexts.

Reggie C. Pantig

Black hole in the Dekel-Zhao dark matter profile

In this work, we analyze various phenomena influenced by the gravitational field in a bumblebee gravity solution, with a particular emphasis on a traversable wormhole for massless particle modes. Specifically, we calculate the index of refraction, group velocity, time delay, modified distances, and interparticle potential, demonstrating the possibility of photon-photon interactions due to the wormhole geometry. For the latter aspect, we also extend the analysis to massive particle modes, resulting in a “combination” of modified Yukawa- and Coulomb-like potentials. These calculations are shown to be dependent on the wormhole’s parameters, particularly the wormhole throat. In addition to these analyses, the Hawking temperature is derived using the trapping horizon method, yielding negative values. Furthermore, we derive the thermodynamic properties of photon-like modes by incorporating the modified dispersion relation arising from the wormhole geometry, focusing on non-interacting particle modes. Remarkably, all calculations are conducted in a fully framework.

Brazil

A. Filho

J. Reis

Modified particle dynamics and thermodynamics in a traversable wormhole in bumblebee gravity

In recent times, the study of the Casimir effect in quantum field theory has garnered increasing attention because of its potential to be an ideal source of exotic matter needed for stabilizing traversable wormholes. It has been confirmed through experimental evidence that this phenomenon involves fluctuations in the vacuum field, leading to a negative energy density. Motivated by the above, we have investigated Casimir wormholes with corrections from the Generalized Uncertainty Principle (GUP) within the framework of matter-coupled teleparallel gravity. Our analysis includes three well-known GUP models: the Kempf, Mangano, and Mann (KMM) model, the Detournay, Gabriel, and Spindel (DGS) model, and a third model called Model II. For a broader analysis, we have considered two well-known model functions for the teleparallel theory: a linear  $$f(T,\mathcal {T})=\alpha T+\beta \mathcal {T}$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>T</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> <mo>=</mo> <mi>α</mi> <mi>T</mi> <mo>+</mo> <mi>β</mi> <mi>T</mi> </mrow> </math>   and a quadratic model  $$f(T,\mathcal {T})=\eta T^2+\chi \mathcal {T}$$  <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>T</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>η</mi> <msup> <mi>T</mi> <mn>2</mn> </msup> <mo>+</mo> <mi>χ</mi> <mi>T</mi> </mrow> </math>  . The shape function solutions corresponding to both models are examined in the absence of tidal forces in spacetime. We also demonstrate the crucial role played by the parameters of the  $$f(T,\mathcal {T})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>T</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> </math>   models in the violation of the energy conditions. With the increasing interest in detecting gravitational waves from astrophysical objects, we have thoroughly discussed the perturbation of the wormhole solutions in the scalar, electromagnetic, axial gravitational, and Dirac field backgrounds. We employ the 3rd order WKB expansion to find the complex frequencies associated with the quasinormal modes of energy dissipation. Additionally, we also calculate the active mass and total gravitational energy for the wormhole geometry. The amount of exotic matter involved in sustaining these wormholes is also found in this paper. Furthermore, the physical stability of such Casimir wormholes is examined using the Tolman–Oppenheimer–Volkoff equation.

India

Mohammed Rizwan

Zinnat Hassan

P. Sahoo

Influence of GUP corrected Casimir energy on zero tidal force wormholes in modified teleparallel gravity with matter coupling

We consider black holes with quintessence matter and cloud of strings to study shadow, optical appearance and stability by using the extended generalized uncertainty principle. We first evaluate the relations for modified Hawking temperature, heat capacity, equation of state and remnant mass for the considered model and then plot these relations in order to analyze the quantum correction effects on the stability of the black holes. In the visual plot of specific heat, we observe critical regions where the black hole transitions from being thermodynamically stable to unstable and vice versa. Moreover, we also observe that the regions of stability and instability are not uniform across, suggesting that extended generalized uncertainty principle plays a vital role in thermodynamic properties. We also investigate the silhouette and optical properties of the Lovelock black hole, particularly analyzing illumination with two theoretical models of static accretion. We observe that different values of Lovelock coupling constants significantly influence the size of image and intensities of the black hole.

Shahid Chaudhary

United Kingdom

Muhammad Danish Sultan

China

Adnan Malik

Atiq ur Rehman

Saudi Arabia

Ayman A. Ghfar

Images and stability of black hole with cloud of strings and quintessence in EGUP framework

Recent observations of black hole shadows have revolutionized our ability to probe gravity in extreme environments. This manuscript presents a novel analytic method to calculate, in leading-order terms, the key parameters of photon sphere and shadow radius. This method offers advantages for complex metrics where traditional approaches are cumbersome. We further explore the impact of black hole mass on the photon sphere radius, providing insights into black hole interactions with their surroundings. Our findings contribute significantly to black hole physics and gravity under extreme conditions. By leveraging future advancements in observations, such as the next-generation Event Horizon Telescope (ngEHT), this work paves the way for even more precise tests of gravity near black holes.

Russia

Vitalii Vertogradov

General approach on shadow radius and photon spheres in asymptotically flat spacetimes and the impact of mass-dependent variations

In this work, we investigate wormhole solutions through the utilization of gravitational decoupling, employing the Minimal Geometric Deformation (MGD) procedure within the framework of Trace-Free Gravity. We base our investigation on static and spherically symmetric Morris-Thorne traversable wormholes, considering both constant and variable equation of state parameters. We derive the field equations and extract the shape function for each scenario. Moreover, we explore the gravitational decoupling technique and examine various forms of energy density for both a smeared and particle-like gravitational source, encompassing the realm of noncommutative geometry and a statically charged fluid. We also examinethe wormhole geometry through the utilization of embedding diagrams. Through our analysis, we uncover a violation of the Null Energy Condition (NEC). To conclude, we employ the Gauss-Bonnet theorem to determine the weak deflection angle for the wormhole configurations.

Thailand

Piyachat Panyasiripan

Narakorn Kaewkhao

Phongpichit Channuie

Traversable wormholes in minimally geometrical deformed trace-free gravity using gravitational decoupling

In this paper we investigate new dyonic black holes of massive gravity sourced by generalized quasitopological electromagnetism in arbitrary dimensions. We begin by deriving the exact solution to the field equations defining these black holes and look at how graviton’s mass, dimensionality parameter, and quasitopological electromagnetic field affect the horizon structure of anti-de Sitter dyonic black holes. We also explore the asymptotic behaviour of the curvature invariants at both the origin and infinity to analyze the geometric structure of the resultant black holes. We also compute the conserved and thermodynamic quantities of these dyonic black holes with the help of established techniques and known formulas. After investigating the relevancy of first law, we look at how various parameters influence the local thermodynamic stability of resultant black hole solution. We also examine how thermal fluctuations affect the local stability of dyonic black holes in massive gravity. Finally, we study the shadow cast of the black hole.

Askar Ali

Topological dyonic black holes of massive gravity with generalized quasitopological electromagnetism

In this paper, we obtain a new spherically symmetric black hole surrounded by the pseudo-isothermal dark matter halo. Furthermore, to explore the effects of the pseudo-isothermal halo profile on a rotating black hole at the M87 galactic center, we derive a rotating black hole solution encompassed by the pseudo-isothermal halo by using the Newman-Janis method. Our investigation focuses on the impact of the pseudo-isothermal halo on the black hole event horizon, time-like and null orbits, as well as the black hole shadow. We find that as the spin parameter a increases, the interval between the inner event horizon and the outer event horizon of the rotating black hole surrounded by the pseudo-isothermal halo in M87 diminishes. This leads to the formation of an extreme black hole. The presence of dark matter, however, has minimal effect on the event horizon. Moreover, in the M87 as the spin parameter a increases, the black hole shadow deviates increasingly from a standard circle, with larger spin parameters causing more pronounced distortion relative to the standard circle. Surprisingly, we observe that the dark matter density has very little influence on the shadow of the black hole surrounded by the pseudo-isothermal halo in the M87. This study contributes to a deeper understanding of black hole structures and the role of dark matter in the universe.