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Charged black hole accelerated by spatially homogeneous electric field of Bertotti-Robinson (AdS2 x S2) space-time

G. A. Alekseev

Abstract

A simple exact solution of the Einstein - Maxwell field equations for charged non-rotating black hole accelerated by an external electric field is presented. The background space-time, described by the well known Bertotti-Robinson solution, contains a spatially homogeneous electric field and possess the topology AdS2 x S2. The black hole mass m, its charge e and the value of the background electric field E are free parameters of the constructed solution. In the "rigid" (non-inertial) reference frame comoving a black hole, this solution is static. The value of acceleration of a black hole due to its interaction with the external electric field is determined by the condition of vanishing of conical singularities on the axis of symmetry. The dynamics of a charged black hole in the external electric field is compared with the behaviour of a charged test particle with the same charge to mass ratio.

Charged black hole accelerated by spatially homogeneous electric field of Bertotti-Robinson (AdS2 x S2) space-time

Abstract

A simple exact solution of the Einstein - Maxwell field equations for charged non-rotating black hole accelerated by an external electric field is presented. The background space-time, described by the well known Bertotti-Robinson solution, contains a spatially homogeneous electric field and possess the topology AdS2 x S2. The black hole mass m, its charge e and the value of the background electric field E are free parameters of the constructed solution. In the "rigid" (non-inertial) reference frame comoving a black hole, this solution is static. The value of acceleration of a black hole due to its interaction with the external electric field is determined by the condition of vanishing of conical singularities on the axis of symmetry. The dynamics of a charged black hole in the external electric field is compared with the behaviour of a charged test particle with the same charge to mass ratio.

Paper Structure

This paper contains 7 sections, 17 equations, 1 figure.

Table of Contents

  1. Introduction and results
  2. Background A$\text{d}$S${}^2\times \mathbb{S}^2$ space-time with spatially homogeneous electric field
  3. Reissner-Nordström black hole immersed into A$\text{d}$S${}^2\times \mathbb{S}^2$ electric universe
  4. On the parameters of the solution (metric)--(alphabeta).
  5. The equation of motion of a charged black hole derived from the regularity axis condition
  6. Comments and Conclusions

Figures (1)

  • Figure 1: The lines of constant values of metric function $\log (-g_{tt})$ on $(\rho,z)$ plane outside a charged non-rotating black hole accelerated by the external spatially homogeneous (in the absence of a black hole) electric field. The top and bottom boundaries of the picture represent the same axis of symmetry antipodal to the axis where a black hole is located. The black object on this antipodal axis is a singularity arising due to focussing there of the "force" lines.