Inomjon Ibragimov

This study examines the dynamical evolution of self-gravitating systems in the presence of exotic matter within the framework of f ( R ) gravity. Specifically, we have adopted the Starobinsky model $$f(R) = R + \alpha R^2$$ f ( R ) = R + α R 2 , which incorporates higher-order curvature corrections to describe nonlinear gravitational behavior. The analysis focuses on the nonlinear spherical evolution of anisotropic matter configurations and explains how dark matter influences their physical characteristics. The presence of dark matter is found to significantly affect the radial and tangential pressure distributions, thereby altering the overall dynamics of the system. The model is employed for compact object $$ Her~X-1$$ H e r X - 1 described by the generalized Tolman–Kuchowicz metric, demonstrating a singularity-free behavior of the physical parameters. The results reveal that increasing the parameter n of the generalized Tolman–Kuchowicz metric leads to striking variations in the model characteristics, highlighting its essential role in governing internal structure and evolution of the compact object. The model remains physically viable under different testing criteria like energy conditions, hydrostatic equilibrium condition, adiabatic index, causality conditions, Herrera’s Cracking condition and mass-radius relation presented in this work.

This study examines the dynamical evolution of self-gravitating systems in the presence of exotic matter within the framework of $f(R)$ gravity. Specifically, we have adopted the Starobinsky model $f(R) = R + αR^2$, which incorporates higher-order curvature corrections to describe nonlinear gravitational behavior. The analysis focuses on the nonlinear spherical evolution of anisotropic matter configurations and explains how dark matter influences their physical characteristics. The presence of dark matter is found to significantly affect the radial and tangential pressure distributions, thereby altering the overall dynamics of the system. The model is employed for the compact object $ Her~X-1$ described by the generalized Tolman-Kuchowicz metric, demonstrating a singularity-free behavior of the physical parameters. The results reveal that increasing the parameter $n$ of the generalized Tolman-Kuchowicz metric leads to striking variations in the model characteristics, highlighting its essential role in governing internal structure and evolution of the compact object. The model remains physically viable under different testing criteria like energy conditions, hydrostatic equilibrium condition, adiabatic index, causality conditions, Herrera's Cracking condition and mass-radius relation presented in this work.

This study investigates the dynamics of spinning charged test particles in the spacetime of a Reissner–Nordström (RN) black hole immersed in an asymptotically uniform magnetic field, using the Mathisson–Papapetrou–Dixon (MPD) equations supplemented with the Tulczyjew spin condition. We derive the equations of motion incorporating spin-curvature coupling, electromagnetic interactions, and magnetic field effects, leading to an effective potential that governs equatorial circular orbits. The analysis focuses on how particle spin s , charge q , black hole charge Q , and magnetic coupling $$\omega $$ ω modify the effective potential, innermost stable circular orbits (ISCO), critical angular momentum for capture, and center-of-mass energy in particle collisions. The obtained results show that a positive spin flattens the potential and shifts the minima inward, enabling closer orbits, while a negative spin steepens it for repulsion. ISCO radii decrease with aligned spin and magnetic coupling, reducing specific energy and angular momentum. Critical angular momentum increases with magnetic strength and charge, exhibiting non-monotonic spin dependence due to competing Lorentz and spin-curvature forces. For collisions, the center-of-mass energy spikes near the horizon, enhanced by opposite spins and counter-rotating orbits, but suppressed by strong magnetic repulsion. At ISCO, energies peak for weak or negative coupling. These findings reveal that spin-magnetic interactions expand stable orbital regimes and boost collision energies, with implications for high-energy astrophysics near magnetized charged black holes, such as particle acceleration in accretion disks or cosmic ray production. We treat the external magnetic field as a test field on a fixed RN geometry and assume it is sufficiently weak at the ISCO so that backreaction is negligible. Scans labeled by $$\omega = qB_0$$ ω = q B 0 are evaluated at fixed small $$B_0$$ B 0 by varying the particle charge q ; for ISCO collisions, the first and the second particle orbit and collide at the same ISCO radius.