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

Abstract

The presence of tidal charge and cosmological constant has considerable consequences on the spacetime geometry and its study is much more 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, effective potential and the innermost stable circular orbits on the equatorial plane. We noted that the negative values of tidal charge and cosmological constant decrease the energy of particles. In addition, the negative value of the cosmological constant leads us to 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 towards the rotational axis. Besides, black hole spin and positive charge distort shadow and its distortion becomes 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.