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

## Abstract

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-knownmore »

- Authors:

- Istituto per le Applicazioni del Calcolo 'M. Picone', CNR I-00161 Rome (Italy) and ICRA, University of Rome 'La Sapienza', I-00185 Rome (Italy)
- (Italy)
- (Italy) and ICRANet, I-65100 Pescara (Italy)

- Publication Date:

- OSTI Identifier:
- 21011077

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.75.044012; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 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

### Citation Formats

```
Bini, D., Geralico, A., Ruffini, R., Physics Department and ICRA, University of Rome 'La Sapienza', I-00185 Rome, and Physics Department and ICRA, University of Rome 'La Sapienza', I-00185 Rome.
```*Charged massive particle at rest in the field of a Reissner-Nordstroem black hole*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.044012.

```
Bini, D., Geralico, A., Ruffini, R., Physics Department and ICRA, University of Rome 'La Sapienza', I-00185 Rome, & Physics Department and ICRA, University of Rome 'La Sapienza', I-00185 Rome.
```*Charged massive particle at rest in the field of a Reissner-Nordstroem black hole*. United States. doi:10.1103/PHYSREVD.75.044012.

```
Bini, D., Geralico, A., Ruffini, R., Physics Department and ICRA, University of Rome 'La Sapienza', I-00185 Rome, and Physics Department and ICRA, University of Rome 'La Sapienza', I-00185 Rome. Thu .
"Charged massive particle at rest in the field of a Reissner-Nordstroem black hole". United States.
doi:10.1103/PHYSREVD.75.044012.
```

```
@article{osti_21011077,
```

title = {Charged massive particle at rest in the field of a Reissner-Nordstroem black hole},

author = {Bini, D. and Geralico, A. and Ruffini, R. and Physics Department and ICRA, University of Rome 'La Sapienza', I-00185 Rome and Physics Department and ICRA, University of Rome 'La Sapienza', I-00185 Rome},

abstractNote = {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.},

doi = {10.1103/PHYSREVD.75.044012},

journal = {Physical Review. D, Particles Fields},

number = 4,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}