Force on a static charge outside a Schwarzschild black hole

Smith, Andrew; Will, Clifford M.

doi:10.1103/physrevd.22.1276

Cited by 133 publications

(193 citation statements)

References 6 publications

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“…For example, the self-force on a static scalar charge diverges on the ergosphere in the Kerr spacetime [43] since it requires infinite acceleration to hold the charge fixed there. On the other hand, this "intuition" fails in certain cases, for example, the electrostatic self-force invariant in Schwarzschild spacetime is F = e 2 M/r 3 [44], which is everywhere regular. Presumably, the regularity of the force on the horizon is a coincidence of the Schwarzschild geometry in four dimensions and there appears to be no reason to expect this to be true in general.…”

Section: Electrostatic Self-forcementioning

confidence: 99%

Static self-forces in a five-dimensional black hole spacetime

Taylor

Flanagan

2015

Phys. Rev. D

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We obtain the electric field and scalar field for a static point charge in closed form in the 5D Schwarzschild-Tangherlini black hole spacetime. We then compute the static self-force in each of these cases by assuming that the appropriate singular field is a 4D Hadamard Green's function on the constant time Riemannian slice. It is well known that the Hadamard representation of a Green's function involves an arbitrary regular biscalar W0(x, x ), whose coincidence limit w(x) appears in the expression for the self-force. We develop an axiomatic approach to reduce this arbitrary function to a single arbitrary dimensionless coefficient. We show that in the context of this approach to regularization, the self-force does not depend on any undetermined length-scale and need not depend on the internal structure of the charge.

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Section: Electrostatic Self-forcementioning

confidence: 99%

Static self-forces in a five-dimensional black hole spacetime

Taylor

Flanagan

2015

Phys. Rev. D

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“…For a weakly curved spacetime the above mentioned explicit self-forces expressions were derived by DeWitt and DeWitt [5], and by Pfenning an Poisson [6]. The self-force on a static particle was investigated analytically by several authors: Smith and Will have obtained a non-vanishing result for the electromagnetic self-force on a static particle in Schwarzschild [7]. Later Lohiya [8] derived the electromagnetic self-force on a static particle for other types of background spacetimes.…”

Section: Introductionmentioning

confidence: 99%

Scalar self-force on a static particle in Schwarzschild spacetime using the massive field approach

Rosenthal

2004

Phys. Rev. D

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We use the recently developed massive field approach to calculate the scalar self-force on a static particle in a Schwarzschild spacetime. In this approach the scalar self-force is obtained from the difference between the (massless) scalar field, and an auxiliary massive scalar field combined with a certain limiting process. By applying this approach to a static particle in Schwarzschild we show that the scalar self-force vanishes in this case. This result conforms with a previous analysis by Wiseman [9].

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“…This test field approach has been largely used in the current literature [10,19,28,29]. It is interesting to analyze what conceptual differences are introduced in the properties of the electric field of the test particle in the context of a charged Reissner-Nordström geometry compared and contrasted with the Schwarzschild case.…”

Section: B Electric Test Field Solution On a Reissner-nordström Backmentioning

confidence: 99%

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

2007

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The interaction of a Reissner-Nordström 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 EinsteinMaxwell 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-Nordström 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.

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Force on a static charge outside a Schwarzschild black hole

Cited by 133 publications

References 6 publications

Static self-forces in a five-dimensional black hole spacetime

Static self-forces in a five-dimensional black hole spacetime

Scalar self-force on a static particle in Schwarzschild spacetime using the massive field approach

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

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