In this work, we study gravitational-wave (GW) emission from periodic orbits of test particles, analyze quasi-periodic oscillations (QPOs), and constrain the parameters of the static, spherically symmetric Einstein–nonlinear Maxwell–Yukawa (ENLMY) black hole (BH). Using the Hamiltonian approach, we calculate the equations of motion of the particles. We analyze the effective potential to determine the innermost stable circular orbit (ISCO) and innermost bound circular orbit (IBCO), illustrating how the Yukawa screening parameter <italic>&#945;</italic> and electric charge <italic>Q</italic> affect orbital stability and energy requirements. Periodic orbits are classified by integer triplets and exhibit characteristic zoom-whirl behavior. Based on these orbits, we compute the corresponding GW signals in both the <math altimg='si16.svg'><msub><mi>h</mi><mo>+</mo></msub></math> and <italic>h</italic> <inf>&#8239;&#215;&#8239;</inf> polarizations. Finally, we perform Monte Carlo Markov Chain (MCMC) simulations to constrain the parameters of the ENLMY BH for four microquasars and the galactic center within the relativistic precession model.

Pakistan

Oreeda Shabbir

Uzbekistan

Abubakir Shermatov

Bushra Majeed

China

Tehreem Zahra

Mubasher Jamil

Javlon Rayimbaev

Probing the nature of Einstein-nonlinear Maxwell-Yukawa black hole through gravitational wave forms from periodic orbits and quasiperiodic oscillations

Naked singularities are hypothetical astrophysical entities featuring gravitational singularities without event horizons. In this study, we analyze the shadow properties of Kerr modified gravity (Kerr MOG) naked singularities (KMNSs). We show that the KMNS shadow can appear closed or open, or can even vanish, depending on the dimensionless spin parameter $\textit{a}$, the modified gravity parameter $$\alpha $$ , and the observer’s inclination angle. We identify the critical conditions under which the KMNS shadow develops a gap, a unique feature not present in black hole (BH) shadows. We analyze the properties of a thin accretion disk surrounding a KMNS within the framework of MOG characterized by the parameter $$ \alpha $$ . The study includes a detailed examination of the spacetime geometry and the equations of motion for test particles. In addition, we adopt a simplified model for the disk’s radiative flux, temperature distribution, and spectral luminosity. Our analysis primarily focuses on the flux distribution of the accretion disk around the KMNS with identical mass but varying spin and MOG deformation parameters. This allows us to explore how modifications in rotation and the MOG parameter $$ \alpha $$ influence the radiative properties of the disk. Further, these observational signatures may serve as effective tools for clearly distinguishing KMNSs from standard Kerr naked singularities (KNSs), where the MOG parameter $$ \alpha = 0 $$ .

Saira Yasmin

Azerbaijan

Shadow geometry of Kerr MOG naked singularity and analysis of accretion disk luminosity

In this article, we investigate the orbital dynamics and quasi-periodic oscillations (QPOs) surrounding a static, spherically symmetric geometry of an Einstein–nonlinear Maxwell–-Yukawa (ENLMY) black hole (BH). Using the Hamiltonian formalism, we derive equations of motion and analyze the effective potential. We determine the innermost stable circular orbit (ISCO) and innermost bound circular orbit (IBCO) radii for different values of the Yukawa parameters $$\lambda $$ and $$\delta $$ , and classify periodic orbits via rational frequency analysis, highlighting deviations from Schwarzschild geometry. We also study gravitational wave (GW) emission from periodic orbits and show how Yukawa terms affect GW signals. Fundamental frequencies are computed, and QPOs are analyzed using relativistic precession, warped disk, and tidal disruption models. By increasing $$\lambda $$ , the ENLMY spacetime effectively mimics the behavior of a Schwarzschild spacetime. Constraints on the BH mass and Yukawa parameters are derived using QPO data from stellar-mass (XTE J1550-564, GRO J1655-40, GRS 1915+105), intermediate-mass (M82 X-1), and supermassive (SgrA*) BHs within the relativistic precession model by employing a Markov chain Monte Carlo analysis.

Gravitational wave radiation from periodic orbits and quasi-periodic oscillations in an Einstein nonlinear Maxwell–Yukawa black hole

Various studies show that the gravitational collapse of inhomogeneous matter clouds leads to naked singularity formation. We investigate here the spin precession frequency of a test gyroscope attached to a stationary observer in a rotating naked singularity spacetime. In the weak field limit, Lense-Thirring precession for rotating naked singularity and geodetic precession in asymptotic limit for null naked singularity are found to be equal to that of a Kerr black hole and a Schwarzschild black hole respectively. In addition, we can distinguish rotating naked singularity and Kerr naked singularity for an observer in the equatorial plane using spin precession. To this end, we have found the constraints on the parameters of rotating naked singularity by employing Monte Carlo Markov Chain simulation and using the observation from five quasi-periodic sources within the relativistic precession model. Our analysis shows that the measurement of spin parameter estimate for GRO J1655-40 is in disagreement with the value found from the continuum-fitting method, while for XTEJ1859+226 and GRS 1915+105, it is inconsistent with spectral analysis results.

Türkiye

Mustapha Azreg-Aïnou

Spin precession frequencies of a test gyroscope around a naked singularity and quasi-periodic oscillations

In this paper, we study the universal thermodynamic topological classes of a family of black holes in a perfect fluid dark matter (PFDM) background. Recent research on black hole thermodynamics suggests that all black holes can be cast into four universal thermodynamic classes, denoted by $$W^{1-}$$ , $$W^{0+}$$ , $$W^{0-}$$ , and $$W^{1+}$$ . Our study reveals that the Schwarzschild black hole in PFDM belongs to the $$W^{1-}$$ class, and the independence of black hole size is thermodynamically unstable in both the low- and high-temperature limits. The Reissner–Nordström, Kerr, and Kerr–Newman black holes in the PFDM background belong to the same universal thermodynamic class, $$W^{0+}$$ , which represents small-stable black holes and large-unstable black holes at low-temperature limits, whereas no black hole state exists at high temperatures. The AdS black holes behave differently when compared to their counterparts in PFDM. The Schwarzschild–AdS black hole belongs to the $$W^{0-}$$ class, indicating that no black hole state exists at low temperatures, but small-unstable and large-stable black hole states exist at high temperatures. Furthermore, the Kerr–AdS black hole belongs to the $$W^{1+}$$ class, characterized by small-stable black holes at low temperatures, large-stable black holes at high temperatures, and unstable intermediate-sized black holes at both low and high temperatures. Thus, the presence of PFDM does not affect the stability of the black hole. These findings uncover the universal topological classifications underlying black hole thermodynamics, offering profound insights into the fundamental principles of quantum gravity.

Muhammad Rizwan

M. Moughal

Universal thermodynamic topological classes of black holes in a perfect fluid dark matter background

The study of astrophysical phenomena like black hole shadows is an effective approach to properly understand the modified gravity and explore its validity. Motivated by recent astrophysical observations, we consider a black hole (BH) in <math altimg='si1.svg'><mi>F</mi><mo stretchy='false'>(</mo><mi>R</mi><mo stretchy='false'>)</mo></math>-ModMax gravity and study the optical features such as the shadow's geometrical shape, energy emission rate, and deflection of light. More specifically, we show how the variation of the model parameters imprints specific signatures on these optical quantities. In the following, we consider such black holes as supermassive BHs and evaluate the parameters of the model with shadow size estimates done by the observations of M87* from the Event Horizon Telescope (EHT). According to our findings, the parameter <math altimg='si2.svg'><msub><mrow><mi>f</mi></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msub></math> plays an effective role in having results consistent with the EHT data such that the resulting shadow of AdS black holes in <math altimg='si1.svg'><mi>F</mi><mo stretchy='false'>(</mo><mi>R</mi><mo stretchy='false'>)</mo></math>-ModMax gravity agrees with the observational data for <math altimg='si3.svg'><msub><mrow><mi>f</mi></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>&lt;</mo><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>1</mn></math>. However, for dS black holes, a consistent result is observed for <math altimg='si4.svg'><msub><mrow><mi>f</mi></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>&gt;</mo><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>1</mn></math>.

Iran

Khadije Jafarzade

Zeynab Bazyar

A study of black holes in <italic>F</italic>( <italic>R</italic>)-ModMax gravity: Gravitational lensing and constraints from EHT observations

In this manuscript, we provide a comprehensive study of gravitational lensing by dark compact objects predicted by modified gravity (MOG) based on the scalar–vector–tensor action, with the aim of providing new insights into the nature of gravitational interactions. We compute weak and strong deflection angles for the specified static, spherically symmetric MOG spacetime. Additionally, we dedicate a section to exploring observational implications in the weak field limit. By employing a supermassive galactic black hole as a gravitational lens, we compare various parameters in MOG with those of the Schwarzschild black hole as lens in strong-field scenarios. Specifically, we model the black holes $${\text {M}87}{^*}$$ and $${\text {Sgr}}\, {\text {A}}{^*}$$ as lenses within the MOG framework, calculating the corresponding lensing coefficients and distortion parameters in the weak field regime.

Nagina Rehman

Malaysia

Zoe Chan

Gravitational lensing by a dark compact object in modified gravity and observational constraints from Einstein rings

In this paper, our aim is to extend our earlier work [Ahmed et al. in Eur. Phys. J. C 76:280, 2016], investigating an axisymmetric plasma flow with angular momentum onto a spherical black hole. To accomplish that goal, we focus on the case in which the ideal magnetohydrodynamic approximation is valid, utilizing certain conservation laws which arise from particular symmetries of the system. After formulating a Hamiltonian of the physical system, we solve the Hamilton equations and look for critical solutions of (both in and out) flows. Reflecting the difference from the Schwarzschild spacetime, the positions of sonic points (fast magnetosonic point, slow magnetosonic point, Alfvén point) are altered. We explore several kinds of flows including critical, non-critical, global, magnetically arrested and shock induced. Lastly, we analyze the shock states near a specific quantum corrected Schwarzschild black hole and determine that quantum effects do not favor shock states by pushing the shock location outward.

Japan

Sousuke Noda

Hamiltonian formulation of relativistic magnetohydrodynamic accretion on a general spherically symmetric and static black hole: quantum effects on shock states

A novel class of Buchdahl-inspired metrics with closed-form expressions was recently obtained based on Buchdahl’s seminal work on searching for static, spherically symmetric metrics in  $${{\mathcal {R}}}^{2}$$  <math> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> </math>   gravity in vacuo. Buchdahl-inspired spacetimes provide an interesting framework for testing predictions of  $${{\mathcal {R}}}^{2}$$  <math> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> </math>   gravity models against observations. To test these Buchdahl-inspired spacetimes, we consider observational constraints imposed on the deviation parameter, which characterizes the deviation of the asymptotically flat Buchdahl-inspired metric from the Schwarzschild spacetime. We utilize several recent solar system experiments and observations of the S2 star in the galactic center and the black hole shadow. By calculating the effects of Buchdahl-inspired spacetimes on astronomical observations both within and outside of the solar system, including the deflection angle of light by the Sun, gravitational time delay, perihelion advance, shadow, and geodetic precession, we determine observational constraints on the corresponding deviation parameters by comparing theoretical predictions with the most recent observations. Among these constraints, we find that the tightest one comes from the Cassini mission’s measurement of gravitational time delay.

Tao Zhu

Romania

Hoang Nguyen

Observational tests of asymptotically flat  $${{\mathcal {R}}}^{2}$$  <math> <msup> <mrow> <mi>R</mi> </mrow> <mn>2</mn> </msup> </math>   spacetimes

Using the zero-point length effect, we construct a new class of charged black hole solutions in the framework of three-dimensional Gauss–Bonnet (GB) gravity with Maxwell electrodynamics. The gravitational and electromagnetic potentials and the spacetime curvature are finite and regular everywhere; however, the computation of scalar curvature invariants suggests the presence of a singularity at the origin. We also explore the thermodynamics of the solutions obtained and reveal that the entropy of the black hole decreases due to the stringy effects. The thermodynamics and conserved quantities are computed, and the validity of the first law of thermodynamics on the black hole horizon is verified. Finally, the spinning black hole solution is reported.