175 research outputs found
Thermodynamics of Magnetised Kerr-Newman Black Holes
The thermodynamics of a magnetised Kerr-Newman black hole is studied to all
orders in the appended magnetic field . The asymptotic properties of the
metric and other fields are dominated by the magnetic flux that extends to
infinity along the axis, leading to subtleties in the calculation of conserved
quantities such as the angular momentum and the mass. We present a detailed
discussion of the implementation of a Wald-type procedure to calculate the
angular momentum, showing how ambiguities that are absent in the usual
asymptotically-flat case may be resolved by the requirement of gauge
invariance. We also present a formalism from which we are able to obtain an
expression for the mass of the magnetised black holes. The expressions for the
mass and the angular momentum are shown to be compatible with the first law of
thermodynamics and a Smarr type relation. Allowing the appended magnetic field
to vary results in an extra term in the first law of the form
where is interpreted as an induced magnetic moment. Minimising the total
energy with respect to the total charge at fixed values of the angular
momentum and energy of the seed metric allows an investigation of Wald's
process. The Meissner effect is shown to hold for electrically neutral extreme
black holes. We also present a derivation of the angular momentum for black
holes in the four-dimensional STU model, which is supergravity
coupled to three vector multiplets.Comment: 27 page
Compactifications of Deformed Conifolds, Branes and the Geometry of Qubits
We present three families of exact, cohomogeneity-one Einstein metrics in
dimensions, which are generalizations of the Stenzel construction of
Ricci-flat metrics to those with a positive cosmological constant. The first
family of solutions are Fubini-Study metrics on the complex projective spaces
, written in a Stenzel form, whose principal orbits are the Stiefel
manifolds divided by . The second family are
also Einstein-K\"ahler metrics, now on the Grassmannian manifolds
, whose principal orbits are the
Stiefel manifolds (with no factoring in this case). The
third family are Einstein metrics on the product manifolds , and are K\"ahler only for . Some of these metrics are believed
to play a role in studies of consistent string theory compactifications and in
the context of the AdS/CFT correspondence. We also elaborate on the geometric
approach to quantum mechanics based on the K\"ahler geometry of Fubini-Study
metrics on , and we apply the formalism to study the quantum
entanglement of qubits.Comment: 31 page
Bulk/Boundary Thermodynamic Equivalence, and the Bekenstein and Cosmic-Censorship Bounds for Rotating Charged AdS Black Holes
We show that one may pass from bulk to boundary thermodynamic quantities for
rotating AdS black holes in arbitrary dimensions so that if the bulk quantities
satisfy the first law of thermodynamics then so do the boundary CFT quantities.
This corrects recent claims that boundary CFT quantities satisfying the first
law may only be obtained using bulk quantities measured with respect to a
certain frame rotating at infinity, and which therefore do not satisfy the
first law. We show that the bulk black hole thermodynamic variables, or
equivalently therefore the boundary CFT variables, do not always satisfy a
Cardy-Verlinde type formula, but they do always satisfy an AdS-Bekenstein
bound. The universal validity of the Bekenstein bound is a consequence of the
more fundamental cosmic censorship bound, which we find to hold in all cases
examined. We also find that at fixed entropy, the temperature of a rotating
black hole is bounded above by that of a non-rotating black hole, in four and
five dimensions, but not in six or more dimensions. We find evidence for
universal upper bounds for the area of cosmological event horizons and
black-hole horizons in rotating black-hole spacetimes with a positive
cosmological constant.Comment: Latex, 42 page
Non-Abelian pp-waves in D=4 supergravity theories
The non-Abelian plane waves, first found in flat spacetime by Coleman and
subsequently generalized to give pp-waves in Einstein-Yang-Mills theory, are
shown to be 1/2 supersymmetric solutions of a wide variety of N=1 supergravity
theories coupled to scalar and vector multiplets, including the theory of SU(2)
Yang-Mills coupled to an axion \sigma and dilaton \phi recently obtained as the
reduction to four-dimensions of the six-dimensional Salam-Sezgin model. In this
latter case they provide the most general supersymmetric solution. Passing to
the Riemannian formulation of this theory we show that the most general
supersymmetric solution may be constructed starting from a self-dual Yang-Mills
connection on a self-dual metric and solving a Poisson equation for e^\phi. We
also present the generalization of these solutions to non-Abelian AdS pp-waves
which allow a negative cosmological constant and preserve 1/4 of supersymmetry.Comment: Latex, 1+12 page
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