Gravitational Effects of Rotating Braneworld Black Holes

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. * Dedicated to Sergei Odintsov on the occasion of his fiftieth birthday.

Strong gravitational lensing in a squashed Kaluza-Klein Gödel black hole

“…It is shown that the relativistic images can provide us not only some important signatures about black holes in the Universe, but also profound verification of alternative theories of gravity in their strong field regime. Thus, the strong gravitational lensing by black holes has been studied extensively in various theories of gravity [5][6][7][8][9][10][11][14][15][16][17]. Most studies of the strong gravitational lensing are focused on black holes immersed in the rather idealized isotropic homogeneous Universe.…”

Analytical Kerr-Sen dilaton-axion black hole lensing in the weak deflection limit

“…As a consequence, in the field of study a wave of a profound examinations arose. Many authors have discussed gravitational lensing in the strong deflection limit approximation in various metrics from general relativity, string theory and braneworld gravity [17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36]. Amore and Arceo [37] as well as Iyer and Petters [38] have presented a procedures interpolating between the weak and the strong deflection limits analysis.…”

Strong gravitational lensing in a rotating Kaluza-Klein black hole with squashed horizons

“…With these quantities, we can find that all of coefficients in the metric ( 19) can be expressed as the functions of the parameters ρ 0 , ρ M and b, which means that we can study the strong gravitational lensing in the rotating squashed KK black hole spacetime (6) through the standard form used in [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

“…As photons pass close to the photon sphere, the deflection angles of of the light rays become very large, which yields that there exist two infinite sets of faint relativistic images on each side of the black hole. With these relativistic images, we could extract the information about black holes in the Universe and verify profoundly alternative theories of gravity in their strong field regime [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. Recently, we have studied the strong gravitational lensing in the background of a Schwarzschild squashed KK black hole [33] and a squashed KK Gödel black hole [34] and find that the size of the extra dimension and the the global rotation parameter j of the Gödel Universe affects the photon sphere radius, the deflection angle and the corresponding observational variables in the strong gravitational lensing.…”