3,092 research outputs found
On Black Hole Stability in Critical Gravities
We consider extended cosmological gravities with Ricci tensor and scalar
squared terms in diverse dimensions. These theories admit solutions of Einstein
metrics, including the Schwarzschild-Tangherlini AdS black holes, whose mass
and entropy vanish at the critical point. We perform linearized analysis around
the black holes and show that in general the spectrum consists of the usual
spin-2 massless and ghost massive modes. We demonstrate that there is no
exponentially-growing tachyon mode in the black holes. At the critical point,
the massless spin-2 modes have zero energy whilst the massive spin-2 modes are
replaced by the log modes. There always exist certain linear combination of
massless and log modes that has negative energy. Thus the stability of the
black holes requires that the log modes to be truncated out by the boundary
condition.Comment: 16 pages, minor corrections, further comments and references adde
General Kerr-NUT-AdS Metrics in All Dimensions
The Kerr-AdS metric in dimension D has cohomogeneity [D/2]; the metric
components depend on the radial coordinate r and [D/2] latitude variables \mu_i
that are subject to the constraint \sum_i \mu_i^2=1. We find a coordinate
reparameterisation in which the \mu_i variables are replaced by [D/2]-1
unconstrained coordinates y_\alpha, and having the remarkable property that the
Kerr-AdS metric becomes diagonal in the coordinate differentials dy_\alpha. The
coordinates r and y_\alpha now appear in a very symmetrical way in the metric,
leading to an immediate generalisation in which we can introduce [D/2]-1 NUT
parameters. We find that (D-5)/2 are non-trivial in odd dimensions, whilst
(D-2)/2 are non-trivial in even dimensions. This gives the most general
Kerr-NUT-AdS metric in dimensions. We find that in all dimensions D\ge4
there exist discrete symmetries that involve inverting a rotation parameter
through the AdS radius. These symmetries imply that Kerr-NUT-AdS metrics with
over-rotating parameters are equivalent to under-rotating metrics. We also
consider the BPS limit of the Kerr-NUT-AdS metrics, and thereby obtain, in odd
dimensions and after Euclideanisation, new families of Einstein-Sasaki metrics.Comment: Latex, 24 pages, minor typos correcte
A Killing tensor for higher dimensional Kerr-AdS black holes with NUT charge
In this paper, we study the recently discovered family of higher dimensional
Kerr-AdS black holes with an extra NUT-like parameter. We show that the inverse
metric is additively separable after multiplication by a simple function. This
allows us to separate the Hamilton-Jacobi equation, showing that geodesic
motion is integrable on this background. The separation of the Hamilton-Jacobi
equation is intimately linked to the existence of an irreducible Killing
tensor, which provides an extra constant of motion. We also demonstrate that
the Klein-Gordon equation for this background is separable.Comment: LaTeX, 14 pages. v2: Typo corrected and equation added. v3: Reference
added, introduction expanded, published versio
Mass of Rotating Black Holes in Gauged Supergravities
The masses of several recently-constructed rotating black holes in gauged
supergravities, including the general such solution in minimal gauged
supergravity in five dimensions, have until now been calculated only by
integrating the first law of thermodynamics. In some respects it is more
satisfactory to have a calculation of the mass that is based directly upon the
integration of a conserved quantity derived from a symmetry principal. In this
paper, we evaluate the masses for the newly-discovered rotating black holes
using the conformal definition of Ashtekar, Magnon and Das (AMD), and show that
the results agree with the earlier thermodynamic calculations. We also consider
the Abbott-Deser (AD) approach, and show that this yields an identical answer
for the mass of the general rotating black hole in five-dimensional minimal
gauged supergravity. In other cases we encounter discrepancies when applying
the AD procedure. We attribute these to ambiguities or pathologies of the
chosen decomposition into background AdS metric plus deviations when scalar
fields are present. The AMD approach, involving no decomposition into
background plus deviation, is not subject to such complications. Finally, we
also calculate the Euclidean action for the five-dimensional solution in
minimal gauged supergravity, showing that it is consistent with the quantum
statistical relation.Comment: Typos corrected and references update
Kerr-Schild Structure and Harmonic 2-forms on (A)dS-Kerr-NUT Metrics
We demonstrate that the general (A)dS-Kerr-NUT solutions in D dimensions with
([D/2], [(D+1)/2]) signature admit [D/2] linearly-independent,
mutually-orthogonal and affinely-parameterised null geodesic congruences. This
enables us to write the metrics in a multi-Kerr-Schild form, where the mass and
all of the NUT parameters enter the metrics linearly. In the case of D=2n, we
also obtain n harmonic 2-forms, which can be viewed as charged (A)dS-Kerr-NUT
solution at the linear level of small-charge expansion, for the
higher-dimensional Einstein-Maxwell theories. In the BPS limit, these 2-forms
reduce to n-1 linearly-independent ones, whilst the resulting Calabi-Yau metric
acquires a Kahler 2-form, leaving the total number the same.Comment: Latex, 11 pages, references adde
f(R) Theories of Supergravities and Pseudo-supergravities
We present f(R) theories of ten-dimensional supergravities, including the
fermionic sector up to the quadratic order in fermion fields. They are obtained
by performing the conformal scaling on the usual supergravities to the f(R)
frame in which the dilaton becomes an auxiliary field and can be integrated
out. The f(R) frame coincides with that of M-theory, D2-branes or NS-NS
5-branes. We study various BPS p-brane solutions and their near-horizon AdS
\times sphere geometries in the context of the f(R) theories. We find that new
solutions emerge with global structures that do not exist in the corresponding
solutions of the original supergravity description. In lower dimensions, We
construct the f(R) theory of N=2, D=5 gauged supergravity with a vector
multiplet, and that for the four-dimensional U(1)^4 gauged theory with three
vector fields set equal. We find that some previously-known BPS singular
"superstars" become wormholes in the f(R) theories. We also construct a large
class of f(R) (gauged) pseudo-supergravities. In addition we show that the
breathing mode in the Kaluza-Klein reduction of Gauss-Bonnet gravity on S^1 is
an auxiliary field and can be integrated out.Comment: Latex, 46 page
Separability and Killing Tensors in Kerr-Taub-NUT-de Sitter Metrics in Higher Dimensions
A generalisation of the four-dimensional Kerr-de Sitter metrics to include a
NUT charge is well known, and is included within a class of metrics obtained by
Plebanski. In this paper, we study a related class of Kerr-Taub-NUT-de Sitter
metrics in arbitrary dimensions D \ge 6, which contain three non-trivial
continuous parameters, namely the mass, the NUT charge, and a (single) angular
momentum. We demonstrate the separability of the Hamilton-Jacobi and wave
equations, we construct a closely-related rank-2 Staeckel-Killing tensor, and
we show how the metrics can be written in a double Kerr-Schild form. Our
results encompass the case of the Kerr-de Sitter metrics in arbitrary
dimension, with all but one rotation parameter vanishing. Finally, we consider
the real Euclidean-signature continuations of the metrics, and show how in a
limit they give rise to certain recently-obtained complete non-singular compact
Einstein manifolds.Comment: Author added, title changed, references added, focus of paper changed
to Killing tensors and separability. Latex, 13 page
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