9,086 research outputs found
Gravitational Instantons, Confocal Quadrics and Separability of the Schr\"odinger and Hamilton-Jacobi equations
A hyperk\"ahler 4-metric with a triholomorphic SU(2) action gives rise to a
family of confocal quadrics in Euclidean 3-space when cast in the canonical
form of a hyperk\"ahler 4-metric metric with a triholomorphic circle action.
Moreover, at least in the case of geodesics orthogonal to the U(1) fibres, both
the covariant Schr\"odinger and the Hamilton-Jacobi equation is separable and
the system integrable.Comment: 10 pages Late
Bohm and Einstein-Sasaki Metrics, Black Holes and Cosmological Event Horizons
We study physical applications of the Bohm metrics, which are infinite
sequences of inhomogeneous Einstein metrics on spheres and products of spheres
of dimension 5 <= d <= 9. We prove that all the Bohm metrics on S^3 x S^2 and
S^3 x S^3 have negative eigenvalue modes of the Lichnerowicz operator and by
numerical methods we establish that Bohm metrics on S^5 have negative
eigenvalues too. We argue that all the Bohm metrics will have negative modes.
These results imply that higher-dimensional black-hole spacetimes where the
Bohm metric replaces the usual round sphere metric are classically unstable. We
also show that the stability criterion for Freund-Rubin solutions is the same
as for black-hole stability, and hence such solutions using Bohm metrics will
also be unstable. We consider possible endpoints of the instabilities, and show
that all Einstein-Sasaki manifolds give stable solutions. We show how Wick
rotation of Bohm metrics gives spacetimes that provide counterexamples to a
strict form of the Cosmic Baldness conjecture, but they are still consistent
with the intuition behind the cosmic No-Hair conjectures. We show how the
Lorentzian metrics may be created ``from nothing'' in a no-boundary setting. We
argue that Lorentzian Bohm metrics are unstable to decay to de Sitter
spacetime. We also argue that noncompact versions of the Bohm metrics have
infinitely many negative Lichernowicz modes, and we conjecture a general
relation between Lichnerowicz eigenvalues and non-uniqueness of the Dirichlet
problem for Einstein's equations.Comment: 53 pages, 11 figure
Generalized Taub-NUT metrics and Killing-Yano tensors
A necessary condition that a St\"ackel-Killing tensor of valence 2 be the
contracted product of a Killing-Yano tensor of valence 2 with itself is
re-derived for a Riemannian manifold. This condition is applied to the
generalized Euclidean Taub-NUT metrics which admit a Kepler type symmetry. It
is shown that in general the St\"ackel-Killing tensors involved in the
Runge-Lenz vector cannot be expressed as a product of Killing-Yano tensors. The
only exception is the original Taub-NUT metric.Comment: 14 pages, LaTeX. Final version to appear in J.Phys.A:Math.Ge
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
Brane Worlds in Collision
We obtain an exact solution of the supergravity equations of motion in which
the four-dimensional observed universe is one of a number of colliding
D3-branes in a Calabi-Yau background. The collision results in the
ten-dimensional spacetime splitting into disconnected regions, bounded by
curvature singularities. However, near the D3-branes the metric remains static
during and after the collision. We also obtain a general class of solutions
representing -brane collisions in arbitrary dimensions, including one in
which the universe ends with the mutual annihilation of a positive-tension and
negative-tension 3-brane.Comment: RevTex, 4 pages, 1 figure, typos and minor errors correcte
Statistical Mechanics of Charged Particles in Einstein-Maxwell-Scalar Theory
We consider an -body system of charged particle coupled to gravitational,
electromagnetic, and scalar fields. The metric on moduli space for the system
can be considered if a relation among the charges and mass is satisfied, which
includes the BPS relation for monopoles and the extreme condition for charged
black holes. Using the metric on moduli space in the long distance
approximation, we study the statistical mechanics of the charged particles at
low velocities. The partition function is evaluated as the leading order of the
large expansion, where is the spatial dimension of the system and will
be substituted finally as .Comment: 11 pages, RevTeX3.
Killing vectors in asymptotically flat space-times: I. Asymptotically translational Killing vectors and the rigid positive energy theorem
We study Killing vector fields in asymptotically flat space-times. We prove
the following result, implicitly assumed in the uniqueness theory of stationary
black holes. If the conditions of the rigidity part of the positive energy
theorem are met, then in such space-times there are no asymptotically null
Killing vector fields except if the initial data set can be embedded in
Minkowski space-time. We also give a proof of the non-existence of non-singular
(in an appropriate sense) asymptotically flat space-times which satisfy an
energy condition and which have a null ADM four-momentum, under conditions
weaker than previously considered.Comment: 30 page
Rotating Black Holes which Saturate a Bogomol'nyi Bound
We construct and study the electrically charged, rotating black hole solution
in heterotic string theory compactified on a dimensional torus. This
black hole is characterized by its mass, angular momentum, and a
dimensional electric charge vector. One of the novel features of this solution
is that for , its extremal limit saturates the Bogomol'nyi bound. This is
in contrast with the case where the rotating black hole solution develops
a naked singularity before the Bogomol'nyi bound is reached. The extremal black
holes can be superposed, and by taking a periodic array in , one obtains
effectively four dimensional solutions without naked singularities.Comment: 13 pages, no figure
The Action of Instantons with Nut Charge
We examine the effect of a non-trivial nut charge on the action of
non-compact four-dimensional instantons with a U(1) isometry. If the instanton
action is calculated by dimensionally reducing along the isometry, then the nut
charge is found to make an explicit non-zero contribution. For metrics
satisfying AF, ALF or ALE boundary conditions, the action can be expressed
entirely in terms of quantities (including the nut charge) defined on the fixed
point set of the isometry. A source (or sink) of nut charge also implies the
presence of a Misner string coordinate singularity, which will have an
important effect on the Hamiltonian of the instanton.Comment: 25 page
General Very Special Relativity is Finsler Geometry
We ask whether Cohen and Glashow's Very Special Relativity model for Lorentz
violation might be modified, perhaps by quantum corrections, possibly producing
a curved spacetime with a cosmological constant. We show that its symmetry
group ISIM(2) does admit a 2-parameter family of continuous deformations, but
none of these give rise to non-commutative translations analogous to those of
the de Sitter deformation of the Poincar\'e group: spacetime remains flat. Only
a 1-parameter family DISIM_b(2) of deformations of SIM(2) is physically
acceptable. Since this could arise through quantum corrections, its
implications for tests of Lorentz violations via the Cohen-Glashow proposal
should be taken into account. The Lorentz-violating point particle action
invariant under DISIM_b(2) is of Finsler type, for which the line element is
homogeneous of degree 1 in displacements, but anisotropic. We derive
DISIM_b(2)-invariant wave equations for particles of spins 0, 1/2 and 1. The
experimental bound, , raises the question ``Why is the
dimensionless constant so small in Very Special Relativity?''Comment: 4 pages, minor corrections, references adde
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