94 research outputs found
Smarr's formula for black holes with non-linear electrodynamics
It is known that for nonlinear electrodynamics the First Law of Black Hole
Mechanics holds, however the Smarr's formula for the total mass does not. In
this contribution we discuss the point and determine the corresponding
expressions for the Bardeen black hole solution that represents a nonlinear
magnetic monopole. The same is done for the regular black hole solution derived
by Ayon-Beato and Garcia, showing that in the case that variations of the
electric charge are involved, the Smarr's formula does not longer is valid.Comment: 10 pages, 3 figures.Contribution to the Festscrift of Prof. A. Garci
Scalar Fields Nonminimally Coupled to pp Waves
Here, we report pp waves configurations of three-dimensional gravity for
which a scalar field nonminimally coupled to them acts as a source. In absence
of self-interaction the solutions are gravitational plane waves with a profile
fixed in terms of the scalar wave. In the self-interacting case, only power-law
potentials parameterized by the nonminimal coupling constant are allowed by the
field equations. In contrast with the free case the self-interacting scalar
field does not behave like a wave since it depends only on the wave-front
coordinate. We address the same problem when gravitation is governed by
topologically massive gravity and the source is a free scalar field. From the
pp waves derived in this case, we obtain at the zero topological mass limit,
new pp wave solutions of conformal gravity for any arbitrary value of the
nonminimal coupling parameter. Finally, we extend these solutions to the
self-interacting case of conformal gravity.Comment: 14 pages, RevTeX. Minor changes. To appear in Phys. Rev.
Higher-dimensional AdS waves and pp-waves with conformally related sources
AdS waves and pp-waves can only be supported by pure radiation fields, for which the only nonvanishing component of the energy-momentum tensor is the energy density along the retarded time. We show that the nonminimal coupling of self-gravitating scalar fields to the higher-dimensional versions of these exact gravitational waves can be done consistently. In both cases, the resulting pure radiation constraints completely fix the scalar field dependence and the form of the allowed self-interactions. More significantly, we establish that the two sets of pure radiation constraints are conformally related for any nonminimal coupling, in spite of the fact that the involved gravitational fields are not necessarily related. In this correspondence, the potential supporting the AdS waves emerges from the self-interaction associated to the pp-waves and a self-dual condition naturally satisfied by the pp-wave scalar fields
Stability properties of black holes in self-gravitating nonlinear electrodynamics
We analyze the dynamical stability of black hole solutions in
self-gravitating nonlinear electrodynamics with respect to arbitrary linear
fluctuations of the metric and the electromagnetic field. In particular, we
derive simple conditions on the electromagnetic Lagrangian which imply linear
stability in the domain of outer communication. We show that these conditions
hold for several of the regular black hole solutions found by Ayon-Beato and
Garcia.Comment: 15 pages, no figure
"No-Scalar-Hair" Theorems for Nonminimally Coupled Fields with Quartic Self-Interaction
Self-gravitating scalar fields with nonminimal coupling to gravity and having
a quartic self-interaction are considered in the domain of outer communications
of a static black hole. It is shown that there is no value of the nonminimal
coupling parameter for which nontrivial static black hole solutions
exist. This result establishes the correctness of Bekenstein ``no-scalar-hair''
conjecture for quartic self-interactions.Comment: 8 pages, RevTeX
Regular Magnetic Black Holes and Monopoles from Nonlinear Electrodynamics
It is shown that general relativity coupled to nonlinear electrodynamics
(NED) with the Lagrangian , having a correct weak field
limit, leads to nontrivial static, spherically symmetric solutions with a
globally regular metric if and only if the electric charge is zero and
tends to a finite limit as . Properties and examples of such
solutions, which include magnetic black holes and soliton-like 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 duality) is used as a tool for
this comparison.Comment: 6 pages, Latex2e. One more theorem, some comments and two references
have been added. Final journal versio
No-Hair Theorem for Spontaneously Broken Abelian Models in Static Black Holes
The vanishing of the electromagnetic field, for purely electric
configurations of spontaneously broken Abelian models, is established in the
domain of outer communications of a static asymptotically flat black hole. The
proof is gauge invariant, and is accomplished without any dependence on the
model. In the particular case of the Abelian Higgs model, it is shown that the
only solutions admitted for the scalar field become the vacuum expectation
values of the self-interaction.Comment: 8 pages, 2 figures, RevTeX; some changes to match published versio
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