13,132 research outputs found
Two loop and all loop finite 4-metrics
In pure Einstein theory, Ricci flat Lorentzian 4-metrics of Petrov types III
or N have vanishing counter terms up to and including two loops. Moreover for
pp-waves and type-N spacetimes of Kundt's class which admit a non-twisting, non
expanding, null congruence all possible invariants formed from the Weyl tensor
and its covariant derivatives vanish. Thus these Lorentzian metrics suffer no
quantum corrections to all loop orders. By contrast for complete non-singular
Riemannian metrics the two loop counter term vanishes only if the metric is
flat.Comment: 4 pages Latex file, no figure
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
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
Black-Hole-Wave Duality in String Theory
Extreme 4-dimensional dilaton black holes embedded into 10-dimensional
geometry are shown to be dual to the gravitational waves in string theory. The
corresponding gravitational waves are the generalization of pp-fronted waves,
called supersymmetric string waves. They are given by Brinkmann metric and the
two-form field, without a dilaton. The non-diagonal part of the metric of the
dual partner of the wave together with the two-form field correspond to the
vector field in 4-dimensional geometry of the charged extreme black holes.Comment: 12 pages, LaTeX, preprint UG-3/94, SU-ITP-94-11, QMW-PH-94-1
Vacuum decay via Lorentzian wormholes
We speculate about the spacetime description due to the presence of
Lorentzian wormholes (handles in spacetime joining two distant regions or other
universes) in quantum gravity. The semiclassical rate of production of these
Lorentzian wormholes in Reissner-Nordstr\"om spacetimes is calculated as a
result of the spontaneous decay of vacuum due to a real tunneling
configuration. In the magnetic case it only depends on the field theoretical
fine structure constant. We predict that the quantum probability corresponding
to the nucleation of such geodesically complete spacetimes should be actually
negligible in our physical Universe
Branes, AdS gravitons and Virasoro symmetry
We consider travelling waves propagating on the anti-de Sitter (AdS)
background. It is pointed out that for any dimension d, this space of solutions
has a Virasoro symmetry with a non-zero central charge. This result is a
natural generalization to higher dimensions of the three-dimensional
Brown-Henneaux symmetry.Comment: 4 pages REVTe
Quantum Topological Invariants, Gravitational Instantons and the Topological Embedding
Certain topological invariants of the moduli space of gravitational
instantons are defined and studied. Several amplitudes of two and four
dimensional topological gravity are computed. A notion of puncture in four
dimensions, that is particularly meaningful in the class of Weyl instantons, is
introduced. The topological embedding, a theoretical framework for constructing
physical amplitudes that are well-defined order by order in perturbation theory
around instantons, is explicitly applied to the computation of the correlation
functions of Dirac fermions in a punctured gravitational background, as well as
to the most general QED and QCD amplitude. Various alternatives are worked out,
discussed and compared. The quantum background affects the propagation by
generating a certain effective ``quantum'' metric. The topological embedding
could represent a new chapter of quantum field theory.Comment: LaTeX, 18 pages, no figur
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
The Decay of Magnetic Fields in Kaluza-Klein Theory
Magnetic fields in five-dimensional Kaluza-Klein theory compactified on a
circle correspond to ``twisted'' identifications of five dimensional Minkowski
space. We show that a five dimensional generalisation of the Kerr solution can
be analytically continued to construct an instanton that gives rise to two
possible decay modes of a magnetic field. One decay mode is the generalisation
of the ``bubble decay" of the Kaluza-Klein vacuum described by Witten. The
other decay mode, rarer for weak fields, corresponds in four dimensions to the
creation of monopole-anti-monopole pairs. An instanton for the latter process
is already known and is given by the analytic continuation of the \KK\ Ernst
metric, which we show is identical to the five dimensional Kerr solution. We
use this fact to illuminate further properties of the decay process. It appears
that fundamental fermions can eliminate the bubble decay of the magnetic field,
while allowing the pair production of Kaluza-Klein monopoles.Comment: 25 pages, one figure. The discussion of fermions has been revised: We
show how fundamental fermions can eliminate the bubble-type instability but
still allow pair creation of monopole
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