9,963 research outputs found
Branes as BIons
A BIon may be defined as a finite energy solution of a non-linear field
theory with distributional sources. By contrast a soliton is usually defined to
have no sources. I show how harmonic coordinates map the exteriors of the
topologically and causally non-trivial spacetimes of extreme p-branes to BIonic
solutions of the Einstein equations in a topologically trivial spacetime in
which the combined gravitational and matter energy momentum is located on
distributional sources. As a consequence the tension of BPS p-branes is
classically unrenormalized. The result holds equally for spacetimes with
singularities and for those, like the M-5-brane, which are everywhere
singularity free.Comment: Latex, 9 pages, no figure
A remark on kinks and time machines
We describe an elementary proof that a manifold with the topology of the
Politzer time machine does not admit a nonsingular, asymptotically flat Lorentz
metric.Comment: 4 page
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
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
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
On the stability of naked singularities
We study the linearised stability of the nakedly singular negative mass
Schwarzschild solution against gravitational perturbations. There is a one
parameter family of possible boundary conditions at the singularity. We give a
precise criterion for stability depending on the boundary condition. We show
that one particular boundary condition is physically preferred and show that
the spacetime is stable with this boundary condition.Comment: 20 pages. 5 figure
Conformal Carroll groups and BMS symmetry
The Bondi-Metzner-Sachs (BMS) group is shown to be the conformal extension of
Levy-Leblond's "Carroll" group. Further extension to the Newman-Unti (NU) group
is also discussed in the Carroll framework.Comment: 10 pages, no figure. Fast Track COmmunication, to appear in Class.
Quant. Gra
Conformal Carroll groups
Conformal extensions of Levy-Leblond's Carroll group, based on geometric
properties analogous to those of Newton-Cartan space-time are proposed. The
extensions are labelled by an integer . This framework includes and extends
our recent study of the Bondi-Metzner-Sachs (BMS) and Newman-Unti (NU) groups.
The relation to Conformal Galilei groups is clarified. Conformal Carroll
symmetry is illustrated by "Carrollian photons". Motion both in the
Newton-Cartan and Carroll spaces may be related to that of strings in the
Bargmann space.Comment: 31 pages, no figures. Minor misprints corrected and clarifications
added. To be published in J. Phys.
Properties of some five dimensional Einstein metrics
The volumes, spectra and geodesics of a recently constructed infinite family
of five-dimensional inhomogeneous Einstein metrics on the two bundles
over are examined. The metrics are in general of cohomogeneity one but
they contain the infinite family of homogeneous metrics . The geodesic
flow is shown to be completely integrable, in fact both the Hamilton-Jacobi and
the Laplace equation separate. As an application of these results, we compute
the zeta function of the Laplace operator on for large . We
discuss the spectrum of the Lichnerowicz operator on symmetric transverse
tracefree second rank tensor fields, with application to the stability of
Freund-Rubin compactifications and generalised black holes.Comment: 1+43 pages, 2 figures, LaTeX. Minor typos correcte
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