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 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.

Self-forces on static bodies in arbitrary dimensions

“…Although the staticity constraint might appear to be overly restrictive, it already allows for a number of interesting statements. The aforementioned disagreements in the existing literature [14,15] appear, for example, in the static regime. Focusing attention on the static problem can also highlight interesting features which are not otherwise apparent-even in cases where the dynamical equations are already known.…”

“…For spacetime dimensions not equal to four, the selfforce program is considerably less mature. Absent any rigorous derivations, a number of ad hoc methods have been suggested to compute (mostly higher-dimensional) self-forces in various contexts [14][15][16][17][18][19][20][21]. Although it is not possible to compare all of these methods directly, it is known that at least some of them are inequivalent.…”

“…For example, the work of Beach, Poisson, and Nickel [15] suggested that the self-force on a charged particle in five spacetime dimensions might depend in an essential way on the details of that particle's internal structure, even if it were spherically symmetric. An analysis of the same system by Taylor and Flanagan [14] utilized a different method and found conflicting results. Unexplained ambiguities arose in both cases, although these had very different characters.…”

Electromagnetic self-force in the five dimensional Myers–Perry space–time

“…Also in five dimensional black hole with the Schwarzschild-Tangherlini metric, the electromagnetic self-force for a charged particle was computed in [8]. For some recent works on self-force see [9][10][11][12][13][14][15][16]. Recently a new approach was presented to find the effects of self-force (electromagnetic) on a charged particle in Kerr space-time based on the Janis-Newman (JN) algorithm [17].…”

Self-force as a probe of global structure

“…1 The self-force points away from the black hole, meaning that the external force required to keep the particle in place is smaller when the particle is charged, compared to what it would be in the case of a neutral particle. This iconic result was later generalized to electric charges in the Reissner-Nordström spacetime [8,9], to scalar charges [10][11][12], and to higher-dimensional black holes [13][14][15][16][17]. Drivas and Gralla [18] have shown that the Smith-Will force of Eq.…”