Gravitational Effects of Rotating Braneworld Black Holes

TL;DR

This paper investigates gravitational effects like light deflection and precession around rotating black holes in a braneworld scenario, providing analytical and numerical results that compare these black holes to Kerr black holes, highlighting potential observational distinctions.

Contribution

It offers the first analytical formula for light deflection in the weak field limit and numerical analysis in the strong field limit for braneworld black holes, comparing them to Kerr black holes.

Findings

Deflection angles become indistinguishable for certain parameters.

Relativistic precession frequencies show similar behavior at specific radii.

Angular momentum plays a key role in differentiating black hole types.

Abstract

We study the light deflection effect and the relativistic periastron and frame-dragging precessions for a rotating black hole localized on the brane in the Randall-Sundrum braneworld scenario. Focusing on a light ray, which passes through the field of the black hole in its equatorial plane, we first calculate the deflection angle in the weak field limit. We obtain an analytical formula, involving the related perturbative parameters of the field up to the second order. We then proceed with the numerical calculation of the deflection angle in the strong field limit, when the light ray passes at the closest distance of approach to the limiting photon orbit. We show that the deflection angles for the light ray, winding maximally rotating Kerr and braneworld black holes in the same direction as their rotation, become essentially indistinguishable from each other for a specific value of the negative tidal charge. The same feature occurs in the relativistic precession frequencies at characteristic radii, for which the radial epicyclic frequency of the test particle motion attains its highest value. Thus, the crucial role in a possible identification of the maximally rotating Kerr and braneworld black holes would play their angular momentum, which in the latter case breaches the Kerr bound in general relativity.