Static Self-Forces in a Five-Dimensional Black Hole Spacetime

Abstract

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 Green's function involves an arbitrary regular biscalar $W_0(x,x^{\prime })$, 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.

Agrees with published version

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Cited by in corpus (7)

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• Self-force on a static particle near a black hole
• Self-force on a scalar charge in a circular orbit about a Reissner-Nordström black hole
• Self-force as a probe of global structure
• Self-action in Gravity