Dyson pairs and zero mass black holes

Abstract

It has been argued by Dyson in the context of QED in flat spacetime that perturbative expansions in powers of the electric charge e cannot be convergent because if e is purely imaginary then the vacuum should be unstable to the production of charged pairs. We investigate the spontaneous production of such Dyson pairs in electrodynamics coupled to gravity. They are found to consist of pairs of zero-rest mass black holes with regular horizons. The properties of these zero rest mass black holes are discussed. We also consider ways in which a dilaton may be included and the relevance of this to recent ideas in string theory. We discuss accelerating solutions and find that, in certain circumstances, the 'no strut' condition may be satisfied giving a regular solution describing a pair of zero rest mass black holes accelerating away from one another. We also study wormhole and tachyonic solutions and how they affect the stability of the vacuum. * Supported by EPSRC grant no. 9400616X.

Accretion of rotating fluids onto stationary solutions

“…To include in the investigation other types of black holes, including phantom [24][25][26] and regular [27][28][29] black holes, we consider the case…”

Thermal action and specific heat of the five-dimensional non-extremal black hole

“…This singularity is compared with that in the fourdimensional U(1) 2 dilaton black hole, where the singularity appears only when it has both electric and magnetic charges [19]. Similarly in the four-dimensional electrically singlycharged black hole paramertrized by a, which characterizes the coupling of the dilaton to the gauge field, the phase transition was found only for a 2 < 1 [12,16]. The specific heats for the a = 1 stringy black hole and the a = √ 3 Kaluza-Klein black hole are always negative, which are considered to correspond to the disappearances of singularities for the U(1) 2 dilaton black hole with only electric charge [19] and our Q = 0, P = 0 case in (49) respectively.…”

“…where Φ Q = LQ/2r 2 + is the electric potential on the horizon in five dimensions [12,16] and Φ P = 4P/L(r 0 cosh α) 2 may be regarded as the electric potential associated with G. To consider the thermodynamics of the five-dimensional black hole we define the Gibbs free energy…”

“…Based on such direct calculation of the partition function the thermodynamics was constructed for the fourdimensional rotating black holes [10] or the four-dimensional U(1) 2 dilaton black holes [11], where the rule that the entropy is one quarter of the area of the event horizon was discussed. Recently to study the zero mass black holes the four-dimensional anti-Maxwell dilaton Einstein theory as well as the usual Maxwell one, that are specified by a dimensionless dilaton coupling parameter a, were considered [12] and the on-shell actions for the electrically singly-charged non-extremal black holes were evaluated to be equal to the entropies. The specific heats characterized by a were shown to behave differently between both theories.…”

“…Our one result (39) is considered to exhibit the generalized Smarr formula in five dimensions, which corresponds to the Smarr formula M = 2ST +QΦ Q for the four-dimensional electrically singly-charged dilatonic black hole [12]. The other result that the Euclidean on-shell action is one half of the entropy in five dimensions is compared with the four-dimensional case where it equals to the entropy itself [11,12]. As seen above the two results are consistently related to each other.…”