Removal of the nodal singularity of the C-metric

Abstract

The charged C-metric is transformed into another exact solution of the Einstein–Maxwell field equations corresponding to a massive charged particle accelerated by an electric field. When the appropriate equations of motion are satisfied, the nodal singularity associated with the C-metric disappears.

Supergravity Approach to Tachyon Potential in Brane-Antibrane Systems

“…The parameter a can be thought of as representing the separation between the brane and antibrane (we will elaborate on this shortly) and changing the sign of a amounts to reversing the orientation of the brane pair, so here we will choose, without loss of generality, a ≥ 0. m is the ADM mass of each brane and the ADM mass of the whole D6 −D6 system is M ADM = 2m which should be obvious as it would be the sum of ADM mass of each brane when they are well separated. It is also noteworthy that, similarly to what happens in the Ernst solution [16] in D = 4 Einstein-Maxwell theory describing a pair of oppositely-charged black holes accelerating away from each other (due to the Melvin magnetic universe content), this D6 −D6 solution in IIA theory is also static but axisymmetric in these Boyer-Lindquisttype coordinates. As has been pointed out by Sen [10] in the M-theory KK − dipole solution case and by Emparan [13] in the case of generalized Bonnor's solution, the IIA theory D6−D6…”

“…By properly tuning the strength of the magnetic field, the attractive inter-brane force along the axis would be rendered to vanish. Indeed this conical singularity structure of the D6 −D6 system and its cure via the introduction of the external magnetic field of proper strength is reminiscent of Ernst's prescription [16] for the elimination of conical singularities of the charged C-metric and of Emparan's treatment [13] to remove the analogous conical singularities of the Bonnor's magnetic dipole solution in Einstein-Maxwell and Einstein-Maxwell-dilaton theories and in the present work, we are closely following the formulation of Emparan [13].…”

Smooth metrics for snapping strings

“…The tunneling rate can be estimated to be proportional to exp(−πm 2 /µ), where m is the mass of the black holes and µ the string tension. We point out that as far as strings at the Grand Unification scale are concerned, the tunneling rate is greatest for instantons where the black hole radius 2m is much smaller than the thickness of the string ∼ µ −1/2 , and so the process of splitting is really described by a different metric, which should resemble the Ernst [12] metric in the vicinity of the black holes. We estimate the rate, and find it still to be negligibly small for Grand Unified scale strings, but of possible significance for cosmic superstrings [13], whose string tension is much higher.…”

“…We would expect this magnetic field to be able to nucleate magnetically charged black holes, and that the instanton describing this process to resemble locally the euclideanised Ernst metric [16,17] rather than the C-metric. The Ernst metric [12], we recall, is an exact solution to the coupled Einstein-Maxwell field equations, describing a pair of oppositely charged black holes accelerating under the influence of a magnetic field. However, the real metric describing a string splitting into a pair of small black holes in the Einstein-Abelian-Higgs system must confine the magnetic flux to within a distance m −1 v of the axis of symmetry, and thus we would expect to recover the C-metric at spacelike separations much greater than this.…”

Nonvanishing magnetic flux through the slightly charged Kerr black hole

“…Because of this negative implication of the result, there have also been some other works employing more careful treatments to turn the conclusion around and hence save the mechanism. The work performed by Dokuchaev [4] employing the Ernst-Wild solution [5] to the coupled Einstein-Maxwell equations belongs to this category. Starting from the exact Ernst-Wild solution, he showed that the magnetic flux through the hole becomes independent of the hole's angular momentum when the hole builds up equilibrium (Wald) charge.…”