22 research outputs found
More about Birkhoff's Invariant and Thorne's Hoop Conjecture for Horizons
A recent precise formulation of the hoop conjecture in four spacetime
dimensions is that the Birkhoff invariant (the least maximal length of
any sweepout or foliation by circles) of an apparent horizon of energy and
area should satisfy . This conjecture together with the
Cosmic Censorship or Isoperimetric inequality implies that the length of
the shortest non-trivial closed geodesic satisfies . We have
tested these conjectures on the horizons of all four-charged rotating black
hole solutions of ungauged supergravity theories and find that they always
hold. They continue to hold in the the presence of a negative cosmological
constant, and for multi-charged rotating solutions in gauged supergravity.
Surprisingly, they also hold for the Ernst-Wild static black holes immersed in
a magnetic field, which are asymptotic to the Melvin solution. In five
spacetime dimensions we define as the least maximal area of all
sweepouts of the horizon by two-dimensional tori, and find in all cases
examined that , which we conjecture holds
quiet generally for apparent horizons. In even spacetime dimensions ,
we find that for sweepouts by the product , is
bounded from above by a certain dimension-dependent multiple of the energy .
We also find that is bounded from above by a certain
dimension-dependent multiple of the horizon area . Finally, we show that
is bounded from above by a certain dimension-dependent multiple of
the energy, for all Kerr-AdS black holes.Comment: 25 page
Equal charge black holes and seven dimensional gauged supergravity
We present various supergravity black holes of different dimensions with some
U(1) charges set equal in a simple, common form. Black hole solutions of seven
dimensional U(1)^2 gauged supergravity with three independent angular momenta
and two equal U(1) charges are obtained. We investigate the thermodynamics and
the BPS limit of this solution, and find that there are rotating supersymmetric
black holes without naked closed timelike curves. There are also supersymmetric
topological soliton solutions without naked closed timelike curves that have a
smooth geometry.Comment: 24 pages; v2, v3: minor change
Cohomogeneity One Manifolds of Spin(7) and G(2) Holonomy
In this paper, we look for metrics of cohomogeneity one in D=8 and D=7
dimensions with Spin(7) and G_2 holonomy respectively. In D=8, we first
consider the case of principal orbits that are S^7, viewed as an S^3 bundle
over S^4 with triaxial squashing of the S^3 fibres. This gives a more general
system of first-order equations for Spin(7) holonomy than has been solved
previously. Using numerical methods, we establish the existence of new
non-singular asymptotically locally conical (ALC) Spin(7) metrics on line
bundles over \CP^3, with a non-trivial parameter that characterises the
homogeneous squashing of CP^3. We then consider the case where the principal
orbits are the Aloff-Wallach spaces N(k,\ell)=SU(3)/U(1), where the integers k
and \ell characterise the embedding of U(1). We find new ALC and AC metrics of
Spin(7) holonomy, as solutions of the first-order equations that we obtained
previously in hep-th/0102185. These include certain explicit ALC metrics for
all N(k,\ell), and numerical and perturbative results for ALC families with AC
limits. We then study D=7 metrics of holonomy, and find new explicit
examples, which, however, are singular, where the principal orbits are the flag
manifold SU(3)/(U(1)\times U(1)). We also obtain numerical results for new
non-singular metrics with principal orbits that are S^3\times S^3. Additional
topics include a detailed and explicit discussion of the Einstein metrics on
N(k,\ell), and an explicit parameterisation of SU(3).Comment: Latex, 60 pages, references added, formulae corrected and additional
discussion on the asymptotic flow of N(k,l) cases adde
Single-charge rotating black holes in four-dimensional gauged supergravity
We consider four-dimensional U(1)^4 gauged supergravity, and obtain
asymptotically AdS_4, non-extremal, charged, rotating black holes with one
non-zero U(1) charge. The thermodynamic quantities are computed. We obtain a
generalization that includes a NUT parameter. The general solution has a
discrete symmetry involving inversion of the rotation parameter, and has a
string frame metric that admits a rank-2 Killing-Stackel tensor.Comment: 9 page
Charged rotating black holes in six-dimensional gauged supergravity
We obtain non-extremal charged rotating black holes in six-dimensional SU(2)
gauged supergravity with two independent angular momenta and one U(1) charge.
These include supersymmetric black holes without naked closed timelike curves.Comment: 9 pages; v2: minor change
Exact Absorption Probability in the Extremal Six-Dimensional Dyonic String Background
We show that the minimally coupled massless scalar wave equation in the
background of an six-dimensional extremal dyonic string (or D1-D5 brane
intersection) is exactly solvable, in terms of Mathieu functions. Using this
fact, we calculate absorption probabilities for these scalar waves, and present
the explicit results for the first few low energy corrections to the
leading-order expressions. For a specific tuning of the dyonic charges one can
reach a domain where the low energy absorption probability goes to zero with
inverse powers of the logarithm of the energy. This is a dividing domain
between the regime where the low energy absorption probability approaches zero
with positive powers of energy and the regime where the probability is an
oscillatory function of the logarithm of the energy. By the conjectured AdS/CFT
correspondence, these results shed novel light on the strongly coupled
two-dimensional field theory away from its infrared conformally invariant fixed
point (the strongly coupled ``non-critical'' string).Comment: Latex (3 times), 23 page
M-theory Conifolds
Seven-manifolds of G2 holonomy provide a bridge between M-theory and string theory, via Kaluza-Klein reduction to Calabi-Yau six-manifolds. We find first-order equations for a new family of G2 metrics D7, with S3 × S3 principal orbits. These are related at weak string coupling to the resolved conifold, paralleling earlier examples B7 that are related to the deformed conifold, allowing a deeper study of topology change and mirror symmetry in M-theory. The D7 metrics ’ non-trivial parameter characterises the squashing of an S3 bolt, which limits to S2 at weak coupling. In general the D7 metrics are asymptotically locally conical, with a nowhere-singular circle action