195 research outputs found

### Conserved charges for black holes in Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics in AdS space

Motivated by possible applications within the framework of anti-de Sitter
gravity/Conformal Field Theory (AdS/CFT) correspondence, charged black holes
with AdS asymptotics, which are solutions to Einstein-Gauss-Bonnet gravity in D
dimensions, and whose electric field is described by a nonlinear
electrodynamics (NED) are studied. For a topological static black hole ansatz,
the field equations are exactly solved in terms of the electromagnetic stress
tensor for an arbitrary NED Lagrangian, in any dimension D and for arbitrary
positive values of Gauss-Bonnet coupling. In particular, this procedure
reproduces the black hole metric in Born-Infeld and conformally invariant
electrodynamics previously found in the literature. Altogether, it extends to
D>4 the four-dimensional solution obtained by Soleng in logarithmic
electrodynamics, which comes from vacuum polarization effects. Fall-off
conditions for the electromagnetic field that ensure the finiteness of the
electric charge are also discussed. The black hole mass and vacuum energy as
conserved quantities associated to an asymptotic timelike Killing vector are
computed using a background-independent regularization of the gravitational
action based on the addition of counterterms which are a given polynomial in
the intrinsic and extrinsic curvatures.Comment: 30 pages, no figures; a few references added; final version for PR

### Holographic correlation functions in Critical Gravity

We compute the holographic stress tensor and the logarithmic energy-momentum
tensor of Einstein-Weyl gravity at the critical point. This computation is
carried out performing a holographic expansion in a bulk action supplemented by
the Gauss-Bonnet term with a fixed coupling. The renormalization scheme defined
by the addition of this topological term has the remarkable feature that all
Einstein modes are identically cancelled both from the action and its
variation. Thus, what remains comes from a nonvanishing Bach tensor, which
accounts for non-Einstein modes associated to logarithmic terms which appear in
the expansion of the metric. In particular, we compute the holographic
$1$-point functions for a generic boundary geometric source.Comment: 21 pages, no figures,extended discussion on two-point functions,
final version to appear in JHE

### Magnetic Mass in 4D AdS Gravity

We provide a fully-covariant expression for the diffeomorphic charge in 4D
anti-de Sitter gravity, when the Gauss-Bonnet and Pontryagin terms are added to
the action. The couplings of these topological invariants are such that the
Weyl tensor and its dual appear in the on-shell variation of the action, and
such that the action is stationary for asymptotic (anti) self-dual solutions in
the Weyl tensor. In analogy with Euclidean electromagnetism, whenever the
self-duality condition is global, both the action and the total charge are
identically vanishing. Therefore, for such configurations the magnetic mass
equals the Ashtekhar-Magnon-Das definition.Comment: 21 pages, no figures; one reference added; final version for PR

### Renormalized AdS action and Critical Gravity

It is shown that the renormalized action for AdS gravity in even spacetime
dimensions is equivalent -on shell- to a polynomial of the Weyl tensor, whose
first non-vanishing term is proportional to $Weyl^2$. Remarkably enough, the
coupling of this last term coincides with the one that appears in Critical
Gravity.Comment: 15 pages, references added, version accepted to JHE

### Charged Rotating Black Hole Formation from Thin Shell Collapse in Three Dimensions

The thin shell collapse leading to the formation of charged rotating black
holes in three dimensions is analyzed in the light of a recently developed
Hamiltonian formalism for these systems. It is proposed to demand, as a way to
reconcile the properties of an infinitely extended solenoid in flat space with
a magnetic black hole in three dimensions, that the magnetic field should
vanish just outside the shell. The adoption of this boundary condition results
in an exterior solution with a magnetic field different from zero at a finite
distance from the shell. The interior solution is also found and assigns
another interpretation, in a different context, to the magnetic solution
previously obtained by Cl\'{e}ment and by Hirschmann and Welch.Comment: 15 pages, no figures. Discussion on junction conditions and
conclusions enlarged. Few references added. Final version for MPL

### Noether-Wald energy in Critical Gravity

Criticality represents a specific point in the parameter space of a
higher-derivative gravity theory, where the linearized field equations become
degenerate. In 4D Critical Gravity, the Lagrangian contains a Weyl-squared
term, which does not modify the asymptotic form of the curvature. The
Weyl$^{2}$ coupling is chosen such that it eliminates the massive scalar mode
and it renders the massive spin-2 mode massless. In doing so, the theory turns
consistent around the critical point.
Here, we employ the Noether-Wald method to derive the conserved quantities
for the action of Critical Gravity. It is manifest from this energy definition
that, at the critical point, the mass is identically zero for Einstein
spacetimes, what is a defining property of the theory. As the entropy is
obtained from the Noether-Wald charges at the horizon, it is evident that it
also vanishes for any Einstein black hole.Comment: 7 pages, no figures, Final version for PL

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