Tidal forces around the Letelier-Alencar cloud of strings black hole

Abstract

In this work, we investigate relativistic tidal forces around a black hole sourced by a cloud of strings, described by the generalized Letelier-Alencar solution. We first review the original Letelier spacetime and its recent generalization, computing the Kretschmann scalar and showing that the generalized model exhibits a stronger curvature divergence at $r \to 0$ than both Letelier and Schwarzschild cases. We then analyze geodesic motion in this background. For massless particles, we focus on circular photon orbits, while for massive particles, we consider both radial infall and circular motion. We find that the radii of the photon sphere and of the innermost stable circular orbit increase with the cloud of strings parameter $g_s$ and decrease with the length scale $l_s$, and circular orbits cease to exist in certain regions of the parameter space. For radial motion, we compute the radial acceleration and the corresponding tidal forces. In this case, we show that an inversion between stretching and compression may occur, although this regime is typically hidden inside the event horizon. Once the tidal forces are known, we computed the behavior of the displacement vector in order to verify whether the usual stretching behavior induced by tidal forces is preserved. Finally, we study tidal forces for observers in circular motion, showing that the cloud of strings modifies the Keplerian frequency and the tidal force profile even at large distances, and that in this case there is no sign change of the tidal components.