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

Marcos V. de S. Silva, T. M. Crispim, R. R. Landim, Gonzalo Olmo, Diego Sáez-Chillón Gómez

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 that 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. 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.

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 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 and decrease with the length scale , and that 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. 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.

Paper Structure

This paper contains 12 sections, 69 equations, 11 figures.

Table of Contents

  1. Introduction
  2. spacetimes
  3. Letelier spacetime
  4. New cloud of strings spacetime: The Letelier-Alencar solution
  5. Geodesics
  6. Photons
  7. Massive particles in equatorial plane
  8. Massive particles in radial motion
  9. Geodesic deviation and tidal forces
  10. Relativistic tidal forces effects in radial geodesics
  11. Relativistic tidal forces effects in circular geodesics
  12. Conclusions

Figures (11)

  • Figure 1: Behavior of the function $f(r)$ as a function of the radial coordinate for different values of $g_s$ with $l_s/M = 1$ (top), and for $g_s = 0.4$ with different values of $l_s$ (bottom).
  • Figure 2: Behavior of the event horizon radius and the Cauchy horizon radius as functions of $g_s$ with $l_s/M = 1$ (top) and as a function of $l_s$ with $g_s=0.4$ (bottom).
  • Figure 3: Behavior of the effective potential for photons as a function of the radial coordinate for $l_s/M = 1$ and different values of $g_s$ (top), and for $g_s = 0.4$ with different values of $l_s$ (bottom).
  • Figure 4: Behavior of the unstable photon orbit as a function of $g_s$ with $l_s/M=1$ (top panel) and as a function of $l_s$ for $g_s=0.4$ (bottom panel).
  • Figure 5: Effective potential for massive particles under different parameter choices. Top panel: $L/M=4$, $l_s/M=1$, varying $g_s$. Middle panel: $L/M=4$, $g_s=0.4$, varying $l_s$. Bottom panel: $g_s=0.4$, $l_s/M=1$, varying $L$.
  • ...and 6 more figures