Particle motion and gravitational lensing in the metric of a dilaton black hole in a de Sitter universe

Abstract

We consider the metric exterior to a charged dilaton black hole in a de Sitter universe. We study the motion of a test particle in this metric. Conserved quantities are identified and the Hamilton-Jacobi method is employed for the solutions of the equations of motion. At large distances from the black hole the Hubble expansion of the universe modifies the effective potential such that bound orbits could exist up to an upper limit of the angular momentum per mass for the orbiting test particle. We then study the phenomenon of strong field gravitational lensing by these black holes by extending the standard formalism of strong lensing to the non-asymptotically flat dilaton-de Sitter metric. Expressions for the various lensing quantities are obtained in terms of the metric coefficients.

Gravitational lensing by black holes

“…Relativity in strong fields [36][37][38][39][40][41][42][43][44][45][46][47][48]. In the Schwarzschild casē…”

“…From the point of view of the observer at infinity, thanks to Eqs. (43) and (44), all geodesics asymptotically starting in an orbit at fixed radiusr , described by Eqs. (45) and (46), also describe a locus in the sky coordinates (θ 1 , θ 2 ).…”

Strong deflection lensing by charged black holes in scalar–tensor gravity

“…(34), and calculated numerically for any q, using the corresponding metric in Eq. (26). The plots of the strong deflection limit coefficients c 1 and c 2 as functions of the charge, for different values of the parameterb, are shown in Fig.…”

“…Using this method, which consists in a logarithmic approximation of the deflection angle for light rays deflecting close to the photon sphere, it is possible to obtain the positions, the magnifications, and the time delays of the relativistic images. Many works considering strong deflection lenses with spherical symmetry, most of them analytical and the others numerical, can be found in a e-mail: eiroa@iafe.uba.ar b e-mail: cmsendra@iafe.uba.ar the literature [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. The lensing effects of rotating black holes were also analyzed in several articles [39][40][41][42][43][44][45]; a related interesting aspect is that the apparent shapes (or shadows) of rotating black holes have a deformation produced by the spin [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60].…”

Gravitational lensing by phantom black holes

“…the EMD black hole has been already reported by Bhadra [21]. The lensing by EMD black holes with de-Sitter and anti-de-Sitter asymptotics have been studied by [22] and [23], respectively. In the last two cases the scalar field has a non zero potential.…”