Asymmetric black dyonic holes

Abstract

A 6-parametric asymptotically flat exact solution, describing a two-body system of asymmetric black dyons, is studied. The system consists of two unequal counterrotating Kerr-Newman black holes, endowed with electric and magnetic charges which are equal but opposite in sign, separated by a massless strut. The Smarr formula is generalized in order to take into account their contribution to the mass. The expressions for the horizon half-length parameters σ 1 and σ 2 , as functions of the Komar parameters and of the coordinate distance, are displayed, and the thermodynamic properties of the twobody system are studied. Furthermore, the seven physical parameters satisfy a simple algebraic relation which can be understood as a dynamical scenario, in which the physical properties of one body are affected by the ones of the other body.

Discreteness of Dyonic Dilaton Black Holes

“…One can expect that for rotating solutions the discreteness in the parameter space also manifests itself in a nontrivial fashion. It would be especially interesting to explore the system of dyonic diholes [22,23,24] in presence of a dilaton field.…”

On the Smarr formula for rotating dyonic black holes

“…On the other hand, when the Tomimatsu formulas (completed by an analogous expression for magnetic charge) were applied to multi-dyons [5,7,8,9,10], it was observed that the resulting values for the black hole parameters failed to obey the standard Smarr relation, but obeyed a generalized Smarr relation with both electric and magnetic contributions. However, the derivation by Tomimatsu [5] gives little details of the underlying calculations, so to clarify the situation a new derivation is necessary.…”

A note on static dyonic diholes

“…Therefore, our analysis makes it very clear that the dyonic generalizations of the known electrostatic solutions for black diholes [2,3] are static as well, despite the presence in them of both electric and magnetic charges. The erroneous physical interpretations of the dyonic configurations made in the paper [1] spring from improper use by Cabrera-Munguia et al of Tomimatsu's formula for the angular momentum [14] that forced those authors to make some incorrect redefinitions (see [15,16] for details). We hope that our results may be helpful in the future for constructing more general static spacetimes, for instance in the presence of a dilaton field.…”

“…In a recent paper [1], Cabrera-Munguia et al presented an exact stationary axisymmetric solution of the Einstein-Maxwell equations for two unequal dyons and considered some of its limiting cases. In subsection 5.3 they assert that in the limit of vanishing total angular momentum, their binary dyonic configuration still has "non-vanishing global angular momentum" and, moreover, "the magnetic monopole charges arise from the rotation of the Reissner-Nordström black holes".…”