Self-force on a static particle near a black hole

Abstract

We study the self-force acting on a static charged point-like particle near a Schwarzschild black hole. We obtain the point-like particle as a limit of a spacetime describing a big neutral black hole with a small charged massive object nearby. The massive object is modeled by a black hole or a naked singularity. In this fully interacting system the massive object is supported above the black hole by a strut. Such a strut has a non-zero tension which corresponds to the external force compensating the gravitational force and the electromagnetic self-force acting on the massive object. We discuss details of the limiting procedure leading to the point-like particle situation. As a result, we obtain the standard gravitational force in the static frame of the Schwarzschild spacetime and the electromagnetic self-force. The electromagnetic-self force differs slightly from the classical results in a domain near the horizon. The difference is due to taking into account an influence of the strut on the electromagnetic field. We also demonstrate that higher order corrections to the gravitational force, a sort of the gravitational self-force, are not uniquely defined and they depend on details of the limiting procedure.

arXiv comment15 pages, 3 figures [v3: minor changes, references added]

References in corpus (42)

• The motion of point particles in curved spacetime
• Gravitational Radiation Reaction to a Particle Motion
• An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime
• Self-force and radiation reaction in general relativity
• Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism
• A Rigorous Derivation of Gravitational Self-force
• Interpreting the C-metric
• A Rigorous Derivation of Electromagnetic Self-force
• Nonlinear gravitational self-force: second-order equation of motion
• Self-force as a cosmic censor
• Regularization parameters for the self force in Schwarzschild spacetime: II. gravitational and electromagnetic cases
• Motion of small objects in curved spacetimes: An introduction to gravitational self-force
• The double-Reissner-Nordstrom solution and the interaction force between two spherically symmetric charged particles
• Equilibrium configurations of two charged masses in General Relativity
• The Motion of Small Bodies in Space-time
• Gauge and motion in perturbation theory
• Charged massive particle at rest in the field of a Reissner-Nordström black hole
• Analogs of the double-Reissner-Nordstrom solution in magnetostatics and dilaton gravity: mathematical description and some physical properties
• Scalar and electromagnetic fields of static sources in higher dimensional Majumdar-Papapetrou spacetimes
• Regularization of static self-forces
• Self-force as probe of internal structure
• Thermodynamics of two black holes
• Static Kerr Green's Function in Closed Form and an Analytic Derivation of the Self-Force for a Static Scalar Charge in Kerr Space-Time
• Gravitational self-force in nonvacuum spacetimes
• Self-force on a charge outside a five-dimensional black hole
• Self-forces on static bodies in arbitrary dimensions
• Unequal binary configurations of interacting Kerr black holes
• Self-energy of a scalar charge near higher-dimensional black holes
• Anomaly and the self-energy of electric charges
• Charged particles in higher dimensional homogeneous gravitational field: Self-energy and self-force
• Superposition of fields of two Reissner - Nordstrom sources
• Electromagnetic self-force on a static charge in Schwarzschild-de Sitter spacetimes
• Static Self-Forces in a Five-Dimensional Black Hole Spacetime
• Electrostatic self-energy in static black holes with spherical symmetry
• Soliton Nature of Equilibrium State of Two Charged Masses in General Relativity
• Self-force from conical singularity, without renormalization
• Self force on an accelerated particle
• Electromagnetic field near cosmic string
• Electromagnetic self-force in curved spacetime: New insights from the Janis-Newman algorithm
• Self-force as a probe of global structure
• Spin Self-Force
• Bi-conformal symmetry and static Green functions in the higher-dimensional Reissner-Nordstrom spacetimes

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