604 research outputs found
Extended Klein-Gordon Action, Gravity and Non-Relativistic Fluid
We consider a scalar field action for which the Lagrangian density is a power
of the massless Klein-Gordon Lagrangian. The coupling of gravity to this matter
action is considered. In this case, we show the existence of nontrivial scalar
field configurations with vanishing energy-momentum tensor on any static,
spherically symmetric vacuum solutions of the Einstein equations. These
configurations in spite of being coupled to gravity do not affect the curvature
of spacetime. The properties of this particular matter action are also
analyzed. For a particular value of the exponent, the extended Klein-Gordon
action is shown to exhibit a conformal invariance without requiring the
introduction of a nonminimal coupling. We also establish a correspondence
between this action and a non-relativistic isentropic fluid in one fewer
dimension. This fluid can be identified with the (generalized) Chaplygin gas
for a particular value of the power. It is also shown that the non-relativistic
fluid admits, apart from the Galileo symmetry, an additional symmetry whose
action is a rescaling of the time.Comment: 7 pages, two columns. Minor change
Thermodynamics of Lovelock black holes with a nonminimal scalar field
We source the Lovelock gravity theories indexed by an integer k and fixed by
requiring a unique anti-de Sitter vacuum with a self-interacting nonminimal
scalar field in arbitrary dimension d. For each inequivalent Lovelock gravity
theory indexed by the integer k, we establish the existence of a two-parametric
self-interacting potential that permits to derive a class of black hole
solutions with planar horizon for any arbitrary value of the nonminimal
coupling parameter. In the thermodynamical analysis of the solution, we show
that, once regularized the Euclidean action, the mass contribution coming form
the gravity side exactly cancels, order by order, the one arising from the
matter part yielding to a vanishing mass. This result is in accordance with the
fact that the entropy of the solution, being proportional to the lapse function
evaluated at the horizon, also vanishes. Consequently, the integration constant
appearing in the solution is interpreted as a sort of hair which turns out to
vanish at high temperature.Comment: 11 page
Planar AdS black holes in Lovelock gravity with a nonminimal scalar field
In arbitrary dimension D, we consider a self-interacting scalar field
nonminimally coupled with a gravity theory given by a particular Lovelock
action indexed by an integer k. To be more precise, the coefficients appearing
in the Lovelock expansion are fixed by requiring the theory to have a unique
AdS vacuum with a fixed value of the cosmological constant. This yields to
k=1,2,...,[(D-1)/2] inequivalent possible gravity theories; here the case k=1
corresponds to the standard Einstein-Hilbert Lagrangian. For each par (D,k), we
derive two classes of AdS black hole solutions with planar event horizon
topology for particular values of the nonminimal coupling parameter. The first
family of solutions depends on a unique constant and is valid only for k>1. In
fact, its GR counterpart k=1 reduces to the pure AdS metric with a vanishing
scalar field. The second family of solutions involves two independent constants
and corresponds to a stealth black hole configuration; that is a nontrivial
scalar field together with a black hole metric such that both side of the
Einstein equations (gravity and matter parts) vanishes identically. In this
case, the standard GR case k=1 reduces to the Schwarzschild-AdS-Tangherlini
black hole metric with a trivial scalar field. In both cases, the existence of
these solutions is strongly inherent of the presence of the higher order
curvature terms k>1 of the Lovelock gravity. We also establish that these
solutions emerge from a stealth configuration defined on the pure AdS metric
through a Kerr-Schild transformation. Finally, in the last part, we include
multiple exact (D-1)-forms homogenously distributed and coupled to the scalar
field. For a specific coupling, we obtain black hole solutions for arbitrary
value of the nonminimal coupling parameter generalizing those obtained in the
pure scalar field case.Comment: 19 pages. Some misprints corrected, some references and comments
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Thermodynamics of a BTZ black hole solution with an Horndeski source
In three dimensions, we consider a particular truncation of the Horndeski
action that reduces to the Einstein-Hilbert Lagrangian with a cosmological
constant and a scalar field whose dynamics is governed by its usual
kinetic term together with a nonminimal kinetic coupling. Requiring the radial
component of the conserved current to vanish, the solution turns out to be the
BTZ black hole geometry with a radial scalar field well-defined at the horizon.
This means in particular that the stress tensor associated to the matter source
behaves on-shell as an effective cosmological constant term. We construct an
Euclidean action whose field equations are consistent with the original ones
and such that the constraint on the radial component of the conserved current
also appears as a field equation. With the help of this Euclidean action, we
derive the mass and the entropy of the solution, and found that they are
proportional to the thermodynamical quantities of the BTZ solution by an
overall factor that depends on the cosmological constant. The reality condition
and the positivity of the mass impose the cosmological constant to be bounded
from above as where the limiting case
reduces to the BTZ solution with a vanishing scalar
field. Exploiting a scaling symmetry of the reduced action, we also obtain the
usual three-dimensional Smarr formula. In the last section, we extend all these
results in higher dimensions where the metric turns out to be the
Schwarzschild-AdS spacetime with planar horizon.Comment: 7 page
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