12,171 research outputs found
Complex Numbers, Quantum Mechanics and the Beginning of Time
A basic problem in quantizing a field in curved space is the decomposition of
the classical modes in positive and negative frequency. The decomposition is
equivalent to a choice of a complex structure in the space of classical
solutions. In our construction the real tunneling geometries provide the link
between the this complex structure and analytic properties of the classical
solutions in a Riemannian section of space. This is related to the Osterwalder-
Schrader approach to Euclidean field theory.Comment: 27 pages LATEX, UCSBTH-93-0
Coupling a Self-Dual Tensor to Gravity in Six Dimensions
A recent result concerning interacting theories of self-dual tensor gauge
fields in six dimensions is generalized to include coupling to gravity. The
formalism makes five of the six general coordinate invariances manifest,
whereas the sixth one requires a non-trivial analysis. The result should be
helpful in formulating the world-volume action of the M theory five-brane.Comment: 7 pages, latex, no figure
Orientifolds and Slumps in G_2 and Spin(7) Metrics
We discuss some new metrics of special holonomy, and their roles in string
theory and M-theory. First we consider Spin(7) metrics denoted by C_8, which
are complete on a complex line bundle over CP^3. The principal orbits are S^7,
described as a triaxially squashed S^3 bundle over S^4. The behaviour in the
S^3 directions is similar to that in the Atiyah-Hitchin metric, and we show how
this leads to an M-theory interpretation with orientifold D6-branes wrapped
over S^4. We then consider new G_2 metrics which we denote by C_7, which are
complete on an R^2 bundle over T^{1,1}, with principal orbits that are
S^3\times S^3. We study the C_7 metrics using numerical methods, and we find
that they have the remarkable property of admitting a U(1) Killing vector whose
length is nowhere zero or infinite. This allows one to make an everywhere
non-singular reduction of an M-theory solution to give a solution of the type
IIA theory. The solution has two non-trivial S^2 cycles, and both carry
magnetic charge with respect to the R-R vector field. We also discuss some
four-dimensional hyper-Kahler metrics described recently by Cherkis and
Kapustin, following earlier work by Kronheimer. We show that in certain cases
these metrics, whose explicit form is known only asymptotically, can be related
to metrics characterised by solutions of the su(\infty) Toda equation, which
can provide a way of studying their interior structure.Comment: Latex, 45 pages; minor correction
Kerr-de Sitter Black Holes with NUT Charges
The four-dimensional Kerr-de Sitter and Kerr-AdS black hole metrics have
cohomogeneity 2, and they admit a generalisation in which an additional
parameter characterising a NUT charge is included. In this paper, we study the
higher-dimensional Kerr-AdS metrics, specialised to cohomogeneity 2 by
appropriate restrictions on their rotation parameters, and we show how they too
admit a generalisation in which an additional NUT-type parameter is introduced.
We discuss also the supersymmetric limits of the new metrics. If one performs a
Wick rotation to Euclidean spacetime signature, these yield new Einstein-Sasaki
metrics in odd dimensions, and Ricci-flat metrics in even dimensions. We also
study the five-dimensional Kerr-AdS black holes in detail. Although in this
particular case the NUT parameter is trivial, our investigation reveals the
remarkable feature that a five-dimensional Kerr-AdS ``over-rotating'' metric is
equivalent, after performing a coordinate transformation, to an under-rotating
Kerr-AdS metric.Comment: Latex, 21 page
Horava-Witten Stability: eppur si muove
We construct exact time-dependent solutions of the supergravity equations of
motion in which two initially non-singular branes, one with positive and the
other with negative tension, move together and annihilate each other in an
all-enveloping spacetime singularity. Among our solutions are the Horava-Witten
solution of heterotic M-theory and a Randall-Sundrum I type solution, both of
which are supersymmetric, i.e. BPS, in the time-independent case. In the
absence of branes our solutions are of Kasner type, and the source of
instability may ascribed to a failure to stabilise some of the modulus fields
of the compactification. It also raises questions about the viability of models
based on some sorts of negative tension brane.Comment: Latex, 22 pages, extended discussion of the global spacetime
structure, and reference adde
Moduli, Scalar Charges, and the First Law of Black Hole Thermodynamics
We show that under variation of moduli fields the first law of black
hole thermodynamics becomes , where are the scalar charges. We also show
that the ADM mass is extremized at fixed , , when the moduli
fields take the fixed value which depend only on electric
and magnetic charges. It follows that the least mass of any black hole with
fixed conserved electric and magnetic charges is given by the mass of the
double-extreme black hole with these charges. Our work allows us to interpret
the previously established result that for all extreme black holes the moduli
fields at the horizon take a value depending only
on the electric and magnetic conserved charges: is such
that the scalar charges .Comment: 3 pages, no figures, more detailed versio
New Complete Non-compact Spin(7) Manifolds
We construct new explicit metrics on complete non-compact Riemannian
8-manifolds with holonomy Spin(7). One manifold, which we denote by A_8, is
topologically R^8 and another, which we denote by B_8, is the bundle of chiral
spinors over . Unlike the previously-known complete non-compact metric of
Spin(7) holonomy, which was also defined on the bundle of chiral spinors over
S^4, our new metrics are asymptotically locally conical (ALC): near infinity
they approach a circle bundle with fibres of constant length over a cone whose
base is the squashed Einstein metric on CP^3. We construct the
covariantly-constant spinor and calibrating 4-form. We also obtain an
L^2-normalisable harmonic 4-form for the A_8 manifold, and two such 4-forms (of
opposite dualities) for the B_8 manifold. We use the metrics to construct new
supersymmetric brane solutions in M-theory and string theory. In particular, we
construct resolved fractional M2-branes involving the use of the L^2 harmonic
4-forms, and show that for each manifold there is a supersymmetric example. An
intriguing feature of the new A_8 and B_8 Spin(7) metrics is that they are
actually the same local solution, with the two different complete manifolds
corresponding to taking the radial coordinate to be either positive or
negative. We make a comparison with the Taub-NUT and Taub-BOLT metrics, which
by contrast do not have special holonomy. In an appendix we construct the
general solution of our first-order equations for Spin(7) holonomy, and obtain
further regular metrics that are complete on manifolds B^+_8 and B^-_8 similar
to B_8.Comment: Latex, 29 pages. Appendix obtaining general solution of first-order
equations and additional complete Spin(7) manifolds adde
Time-Dependent Multi-Centre Solutions from New Metrics with Holonomy Sim(n-2)
The classifications of holonomy groups in Lorentzian and in Euclidean
signature are quite different. A group of interest in Lorentzian signature in n
dimensions is the maximal proper subgroup of the Lorentz group, SIM(n-2).
Ricci-flat metrics with SIM(2) holonomy were constructed by Kerr and Goldberg,
and a single four-dimensional example with a non-zero cosmological constant was
exhibited by Ghanam and Thompson. Here we reduce the problem of finding the
general -dimensional Einstein metric of SIM(n-2) holonomy, with and without
a cosmological constant, to solving a set linear generalised Laplace and
Poisson equations on an (n-2)-dimensional Einstein base manifold. Explicit
examples may be constructed in terms of generalised harmonic functions. A
dimensional reduction of these multi-centre solutions gives new time-dependent
Kaluza-Klein black holes and monopoles, including time-dependent black holes in
a cosmological background whose spatial sections have non-vanishing curvature.Comment: Typos corrected; 29 page
New Black Holes in Five Dimensions
We construct new stationary Ricci-flat metrics of cohomogeneity 2 in five
dimensions, which generalise the Myers-Perry rotating black hole metrics by
adding a further non-trivial parameter. We obtain them via a construction that
is analogous to the construction by Plebanski and Demianski in four dimensions
of the most general type D metrics. Limiting cases of the new metrics contain
not only the general Myers-Perry black hole with independent angular momenta,
but also the single rotation black ring of Emparan and Reall. In another limit,
we obtain new static metrics that describe black holes whose horizons are
distorted lens spaces L(n;m)= S^3/\Gamma(n;m), where m\ge n+2\ge 3. They are
asymptotic to Minkowski spacetime factored by \Gamma(m;n). In the general
stationary case, by contrast, the new metrics describe spacetimes with an
horizon and with a periodicity condition on the time coordinate; these examples
can be thought of as five-dimensional analogues of the four-dimensional
Taub-NUT metrics.Comment: 25 page
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