87 research outputs found
No Scalar-Haired Cauchy Horizon Theorem in Charged Gauss-Bonnet Black Holes
Recently, a ``no inner (Cauchy) horizon theorem" for static black holes with
non-trivial scalar hairs has been proved in Einstein-Maxwell-scalar theories
and also in Einstein-Maxwell-Horndeski theories with the non-minimal coupling
of a charged (complex) scalar field to Einstein tensor. In this paper, we study
an extension of the theorem to the static black holes in
Einstein-Maxwell-Gauss-Bonnet-scalar theories, or simply, charged Gauss-Bonnet
(GB) black holes. We find that no inner horizon with charged scalar hairs is
allowed for the planar (k=0) black holes, as in the case without GB term. On
the other hand, for the non-planar (k=+1,-1) black holes, we find that the
haired inner horizon can not be excluded due to GB effect generally, though we
can not find a simple condition for its existence. As some explicit examples of
the theorem, we study numerical GB black hole solutions with charged scalar
hairs and Cauchy horizons in asymptotically anti-de Sitter space, and find good
agreements with the theorem. As a byproduct, we find a ``no-go theorem" for
charged de Sitter GB black holes with charged scalar hairs in arbitrary
dimensions.Comment: 21 pages, 8 figure
Symmetries and Conservation Laws in Horava Gravity
Horava gravity has been proposed as a renormalizable quantum gravity without
the ghost problem through anisotropic scaling dimensions which break Lorentz
symmetry in UV. In the Hamiltonian formalism, due to the Lorentz-violating
terms, the constraint structure looks quite different from that of general
relativity (GR) but we have recently found that "there exists the case where we
can recover the same number of degrees of freedom as in GR", in a rather
general set-up. In this paper, we study its Lagrangian perspectives and examine
the full diffeomorphism (Diff) symmetry and its associated conservation laws in
Horava gravity. Surprisingly, we find that the full Diff symmetry in the action
can also be recovered when a certain condition, called "super-condition", which
super-selects the Lorentz-symmetric sector in Horava gravity, is satisfied.
This indicates that the broken Lorentz symmetry, known as
"foliation-preserving" Diff, is just an "apparent" symmetry of the Horava
gravity action and rather its "full action symmetry can be as large as the Diff
in GR ". The super-condition exactly corresponds to the tertiary constraint in
Hamiltonian formalism which is the second-class constraint and provides a
non-trivial realization of the Lorentz symmetry otherwise being absent
apparently. From the recovered Lorentz symmetry in the action, we obtain the
conservation laws with the Noether currents as in covariant theories. The
general formula for the conserved Noether charges reproduces the mass of
four-dimensional static black holes with an "arbitrary" cosmological constant
in Horava gravity, and is independent of ambiguities associated with the choice
of asymptotic boundaries. We also discuss several challenging problems,
including its implications to Hamiltonian formalism, black hole thermodynamics,
radiations from colliding black holes.Comment: 18 pages, no figure
The Hamiltonian Dynamics of Horava Gravity
We consider the Hamiltonian formulation of Horava gravity in arbitrary
dimensions, which has been proposed as a renormalizable gravity model for
quantum gravity without the ghost problem. We study the "full" constraint
analysis of the "non-projectable" Horava gravity whose potential, V(R), is an
arbitrary function of the (intrinsic) Ricci scalar R. We find that there exist
generally distinct cases of this theory, depending on (i) whether the
Hamiltonian constraint generates new (second-class) constraints (Cases A, C) or
just fixes the associated Lagrange multipliers (Case B), or (ii) whether the IR
Lorentz-deformation parameter \lambda is at the conformal point (Case C) or not
(Cases A, B). It is found that, for Cases A and C, the dynamical degrees of
freedom are the same as in general relativity, while, for Case B, there is "one
additional phase-space degree of freedom", representing an extra (odd) scalar
graviton mode. This would resolve the long-standing debates about the extra
graviton modes and achieves the dynamical consistency of the Horava gravity, at
the "fully non-linear" level. Several exact solutions are also considered as
some explicit examples of the new constraints. The structure of the newly
obtained, "extended" constraint algebra seems to be generic to Horava gravity
and its general proof would be a challenging problem. Some other challenging
problems, which include the path integral quantization and the Dirac bracket
quantization are discussed also.Comment: Matches published version, Typos correcte
Spatially homogeneous Lifshitz black holes in five dimensional higher derivative gravity
We consider spatially homogeneous Lifshitz black hole solutions in five
dimensional higher derivative gravity theories, which can be possible near
horizon geometries of some systems that are interesting in the framework of
gauge/gravity duality. We show the solutions belonging to the nine Bianchi
classes in the pure R^2 gravity. We find that these black holes have zero
entropy at non-zero temperatures and this property is the same as the case of
BTZ black holes in new massive gravity at the critical point. In the most
general quadratic curvature gravity theories, we find new solutions in Bianchi
Type I and Type IX cases.Comment: 15 pages, no figure; v2, refs added, version to appear in JHE
Absorption cross section in Lifshitz black hole
We derive the absorption cross section of a minimally coupled scalar in the
Lifshitz black hole obtained from the new massive gravity. The absorption cross
section reduces to the horizon area in the low energy and massless limit of
s-wave mode propagation, indicating that the Lifshitz black hole also satisfies
the universality of low energy absorption cross section for black holes.Comment: 13 pages, 1 figure, version to appear in EPJ
Phase transitions for the Lifshitz black holes
We study possibility of phase transitions between Lifshitz black holes and
other configurations by using free energies explicitly. A phase transition
between Lifshitz soliton and Lifshitz black hole might not occur in three
dimensions. We find that a phase transition between Lifshitz and BTZ black
holes unlikely occurs because they have different asymptotes. Similarly, we
point out that any phase transition between Lifshitz and black branes unlikely
occurs in four dimensions since they have different asymptotes. This is
consistent with a necessary condition for taking a phase transition in the
gravitational system, which requires the same asymptote.Comment: 19 pages, 7 figures, a revised version to appear in EPJ
Field theories with anisotropic scaling in 2D, solitons and the microscopic entropy of asymptotically Lifshitz black holes
Field theories with anisotropic scaling in 1+1 dimensions are considered. It
is shown that the isomorphism between Lifshitz algebras with dynamical
exponents z and 1/z naturally leads to a duality between low and high
temperature regimes. Assuming the existence of gap in the spectrum, this
duality allows to obtain a precise formula for the asymptotic growth of the
number of states with a fixed energy which depends on z and the energy of the
ground state, and reduces to the Cardy formula for z=1. The holographic
realization of the duality can be naturally inferred from the fact that
Euclidean Lifshitz spaces in three dimensions with dynamical exponents and
characteristic lengths given by z, l, and 1/z, l/z, respectively, are
diffeomorphic. The semiclassical entropy of black holes with Lifshitz
asymptotics can then be recovered from the generalization of Cardy formula,
where the ground state corresponds to a soliton. An explicit example is
provided by the existence of a purely gravitational soliton solution for BHT
massive gravity, which precisely has the required energy that reproduces the
entropy of the analytic asymptotically Lifshitz black hole with z=3.
Remarkably, neither the asymptotic symmetries nor central charges were
explicitly used in order to obtain these results.Comment: 17 pages, no figures, references corrected and update
Lifshitz black holes in Brans-Dicke theory
We present an exact asymptotically Lifshitz black hole solution in
Brans-Dicke theory of gravity in arbitrary dimensions in presence of
a power-law potential. In this solution, the dynamical exponent is
determined in terms of the Brans-Dicke parameter and . Asymptotic
Lifshitz condition at infinity requires , which corresponds to
. On the other hand, the no-ghost condition
for the scalar field in the Einstein frame requires . We
compute the Hawking temperature of the black hole solution and discuss the
problems encountered and the proposals in defining its thermodynamic
properties. A generalized solution charged under the Maxwell field is also
presented.Comment: 32 pages, no figure. v2: revised version. Section 3.1 and Appendix B
improved. The argument in Appendix A clarified. v3: References added. v4:
analysis on the black hole thermodynamical properties corrected. Final
version to appear in JHE
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