Charged massive particle at rest in the field of a Reissner-Nordstroem black hole

Journal Article · Thu Feb 15 04:00:00 EST 2007 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.75.044012· OSTI ID:21011077

Bini, D; Geralico, A; Ruffini, R ^[1]

---

1. Istituto per le Applicazioni del Calcolo 'M. Picone', CNR I-00161 Rome (Italy) and ICRA, University of Rome 'La Sapienza', I-00185 Rome (Italy)

The interaction of a Reissner-Nordstroem black hole and a charged massive particle is studied in the framework of perturbation theory. The particle backreaction is taken into account, studying the effect of general static perturbations of the hole following the approach of Zerilli. The solutions of the combined Einstein-Maxwell equations for both perturbed gravitational and electromagnetic fields to first order of the perturbation are exactly reconstructed by summing all multipoles, and are given explicit closed form expressions. The existence of a singularity-free solution of the Einstein-Maxwell system requires that the charge-to-mass ratios of the black hole and of the particle satisfy an equilibrium condition which is in general dependent on the separation between the two bodies. If the black hole is undercritically charged (i.e. its charge-to-mass ratio is less than one), the particle must be overcritically charged, in the sense that the particle must have a charge-to-mass ratio greater than one. If the charge-to-mass ratios of the black hole and of the particle are both equal to one (so that they are both critically charged, or 'extreme'), the equilibrium can exist for any separation distance, and the solution we find coincides with the linearization in the present context of the well-known Majumdar-Papapetrou solution for two extreme Reissner-Nordstroem black holes. In addition to these singularity-free solutions, we also analyze the corresponding solution for the problem of a massive particle at rest near a Schwarzschild black hole, exhibiting a strut singularity on the axis between the two bodies. The relations between our perturbative solutions and the corresponding exact two-body solutions belonging to the Weyl class are also discussed.

• OSTI ID: 21011077
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 4 Vol. 75; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BLACK HOLES
COSMOLOGY
DISTURBANCES
EINSTEIN-MAXWELL EQUATIONS
ELECTROMAGNETIC FIELDS
MATHEMATICAL SOLUTIONS
MULTIPOLES
PARTICLE INTERACTIONS
PERTURBATION THEORY
QUANTUM FIELD THEORY
SCHWARZSCHILD METRIC
SINGULARITY
TWO-BODY PROBLEM