Regular magnetic black holes and monopoles from nonlinear electrodynamics

Abstract

It is shown that general relativity coupled to nonlinear electrodynamics (NED) with the Lagrangian L(F ) , F = Fµν F µν having a correct weak field limit, leads to nontrivial spherically symmetric solutions with a globally regular metric if and only if the electric charge is zero and L(F ) tends to a finite limit as F → ∞ . Properties and examples of such solutions, which include magnetic black holes and solitonlike objects (monopoles), are discussed. Magnetic solutions are compared with their electric counterparts. A duality between solutions of different theories specified in two alternative formulations of NED (called the F P duality) is used as a tool for this comparison.

Scalar Fields in Multidimensional Gravity. No-Hair and Other No-Go Theorems

“…[12] in a discussion of static, spherically symmetric solutions to the STT equations with U = 0 ). Wormholes, however, can even appear in normal STT, with l(φ) > 0 , due to the so-called conformal continuations [9]. Namely, it can happen that the transformation (7) maps a singular surface in M E to a regular surface in M J due to a singular behaviour of the conformal factor, which compensates the singularity in M E .…”

“…Extensions of Statements A and B generally require additional studies. Statement D proves to be the most universal, in particular, it holds [9,10] in STT and HOG under very general conditions. Unlike that, Statement C is violated in STT where wormhole solutions are found quite often.…”

“…In cases m < 0 and/or Λ < 0 there is at most one simple horizon. All the corresponding Carter-Penrose diagrams are well known ( [20], see also [9,10]) and will not be reproduced here. In (2+1)-dimensional gravity (d 0 = 1 ) we have a still shorter list of global structures: at most one simple horizon is possible.…”

“…Namely, it can happen that the transformation (7) maps a singular surface in M E to a regular surface in M J due to a singular behaviour of the conformal factor, which compensates the singularity in M E . Then M J can be continued in a regular manner through this surface (the so-called conformal continuation [9]), and the global properties of M J can be considerably richer than those of M E . Ref.…”

“…This follows from the simplest example of CCs in the solutions with a conformal scalar field in GR, leading to black holes [28,29] and wormholes [12,30] and known since the 70s although the term "conformal continuation" was introduced only recently [9]. Let us also recall that a wormhole was shown to be one of the generic structures appearing as a result of CCs in scalar-tensor theories [10].…”