arXiv subjects

Ivan Perez-Roman

Publications and source records attributed to Ivan Perez-Roman.

3 recordsLinked to original sources

arXiv2026

Frenet-Serret equations with variable proper acceleration in Minkowski spacetime

We study Frenet-Serret equations for timelike worldlines in Minkowski spacetime with proper-time-dependent curvature and torsion. This corresponds to relativistic motion with non-uniform proper acceleration and, when torsion is included, to trajectories whose Frenet-Serret frame rotates beyond the acceleration plane. Using the Gram-Schmidt construction of the tetrad from the four-velocity and its derivatives, we relate the intrinsic Frenet-Serret parameters to kinematic quantities such as proper acceleration, four-jerk, and four-snap. We then consider simple analytic cases for the jerk invariant and torsion, obtaining explicit curvature profiles and reduced Frenet-Serret equations. These examples clarify how non-constant acceleration and torsion modify the geometry of accelerated relativistic motion.

gr-qc↗

arXiv2022

Relativistic hyperbolic motion and its higher order kinematic quantities

We investigate the kinematics of the motion of an observer with constant proper acceleration (relativistic hyperbolic motion) in 1+1 and 1+3 dimensional Minkowski spacetimes. We provide explicit formulas for all the kinematic quantities up to the fourth proper time derivative (the Snap). In the 1+3 case, following a recent work of Pons and de Palol [Gen. Rel. Grav. 51 (2019) 80], a vectorial differential equation for the acceleration is obtained which by considering constant proper acceleration is turned into a nonlinear second order differential equation in terms of derivatives of the radius vector. If, furthermore, the velocity is parameterized in terms of hyperbolic functions, one obtains a differential equation to solve for the argument f(s) of the velocity. Differently from Pons and de Palol, who employed the particular solution, linear in the proper time s, we obtain the general solution and use it to work out more general expressions for the kinematical quantities. As a byproduct, we obtain a class of modified Rindler hyperbolic worldlines characterized by supplementary contributions to the components of the kinematical quantities.

gr-qc↗

arXiv2018

The region interior to the event horizon of the Regular Hayward Black Hole

The Painlevé-Gullstrand coordinates allow us to explore the interior of the regular Hayward black hole. The behavior of an infalling particle in traversing the Hayward black hole is compared with the one inside the Schwarzschild and Reissner-Nordstrom singular black holes. When approaching the origin the test particle trajectories present differences depending if the center is regular or singular. The velocities of the infalling test particle into the modified Hayward black hole are analyzed as well. As compared with the normal Hayward, in the modified Hayward black hole the particle moves faster and the surface gravity is smaller.

gr-qc↗