Geodesics and optical properties of rotating black hole in Randall-Sundrum brane with a cosmological constant

TL;DR

This paper studies how tidal charge and a cosmological constant influence the spacetime geometry, particle dynamics, and shadow of a rotating Randall-Sundrum braneworld black hole, revealing effects on stability, size, and shape of the shadow.

Contribution

It provides new analytical expressions for geodesics and explores the combined effects of tidal charge and cosmological constant on black hole shadows and particle stability.

Findings

Negative tidal charge and cosmological constant lower particle energy.

Positive cosmological constant stabilizes circular orbits.

Cosmological constant reduces the black hole shadow radius.

Abstract

The presence of tidal charge and a cosmological constant has considerable consequences on the spacetime geometry and its study is much important from the observational point of view. Henceforth, we investigate their effects on particle dynamics and the shadow cast by a Randall-Sundrum braneworld black hole with a cosmological constant. On studying the circular geodesics of timelike particles, we have acquired the expressions of energy, angular momentum and effective potential. We noted that the negative values of tidal charge and cosmological constant decreases the energy of particles. In addition, the negative value of cosmological constant leads us to the stable circular orbits, whereas its positive value destabilizes the circular orbits. Our exploration shows that the cosmological constant diminishes the radius of the black hole shadow. In response to the dragging effect, black hole rotation elongates its shadow toward the rotational axis. Besides, black hole spin and positive charge distort shadow and its distortion become maximum as far as the black hole rotates faster. We also discussed the energy emission rate by considering different cases and compared our result with the standard Kerr black hole.