RECORD
Charged massive particle at rest in the field of a Reissner-Nordstr\"om black hole
General Relativity and Quantum Cosmology · Submitted 12 Sep 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
The interaction of a Reissner-Nordstr\"om 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 at 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-Nordstr\"om 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The interaction of a Reissner-Nordstr\"om black hole and a charged massive particle is studied in the framework of perturbation theory. | contribution 0.70 | 0.85 | 0.04 | asserted 0.98 |
| s1 | The particle backreaction is taken into account, studying the effect of general static perturbations of the hole following the approach of Zerilli. | method 0.94 | 0.87 | 0.04 | asserted 0.98 |
| s2 | The solutions of the combined Einstein-Maxwell equations for both perturbed gravitational and electromagnetic fields at first order of the perturbation are exactly reconstructed by summing all multipoles, and are given explicit closed form expressions. | result 0.63 | 0.94 | 0.15 | asserted 1.00 |
| s3 | 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. | result 1.00 | 0.85 | 0.51 | asserted 1.00 |
| s4 | 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. | result 0.99 | 0.79 | 0.14 | asserted 1.00 |
| s5 | 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-Nordstr\"om black holes. | result 0.91 | 0.82 | 0.18 | asserted 0.99 |
| s6 | 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. | contribution 0.62 | 0.91 | 0.05 | asserted 1.00 |
| s7 | The relations between our perturbative solutions and the corresponding exact two-body solutions belonging to the Weyl class are also discussed. | contribution 0.74 | 0.73 | 0.05 | asserted 0.60 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
The interaction of a Reissner-Nordstr\"om 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 at 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-Nordstr\"om 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.
Human review
How the literature uses it
7 arXiv papers cite this in 13 sentences
Papers citing it · 8 sentences without a confident label
Builds on it 1 paper
-
Our calculations generalize those of Ref. [ref] , in which the condition of balanced gravitational and electrostatic forces was enforced.
Tidally induced multipole moments of a nonrotating black hole vanish to all post-Newtonian orders · Perturbed spacetime: General case · 1.00
Uses its method or tool 2 papers
-
In solving these equations, the method of Ref. [ref] is very helpful.
Distorted static photon surfaces in perturbed Reissner-Nordstr\"om spacetimes · Solving the perturbative equations for $ℓ≥2$ · 1.00
-
We choose $S$ to be a surface of constant $t$ and $r$, set [equation] and obtain [equation] To evaluate this we follow Ref. [ref] and write $f^1/2 A_p = (k_A/r_0 r) (∂_θD/sinθ)$.
Tidally induced multipole moments of a nonrotating black hole vanish to all post-Newtonian orders · Gauss' law · 0.97
Cites it as background 1 paper
-
An interesting subset of this literature [ref] is concerned with the equilibrium of two (or more) massive and charged objects.
Self-force from conical singularity, without renormalization · Introduction and summary · 0.93
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.