9,945 research outputs found
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
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
D-instanton sums for matter hypermultiplets
We calculate some non-perturbative (D-instanton) quantum corrections to the
moduli space metric of several (n>1) identical matter hypermultiplets for the
type-IIA superstrings compactified on a Calabi-Yau threefold, near conifold
singularities. We find a non-trivial deformation of the (real) 4n-dimensional
hypermultiplet moduli space metric due to the infinite number of D-instantons,
under the assumption of n tri-holomorphic commuting isometries of the metric,
in the hyper-K"ahler limit (i.e. in the absence of gravitational corrections).Comment: 11 pages, 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
Phases of 4D Scalar-tensor black holes coupled to Born-Infeld nonlinear electrodynamics
Recent results show that when non-linear electrodynamics is considered the
no-scalar-hair theorems in the scalar-tensor theories (STT) of gravity, which
are valid for the cases of neutral black holes and charged black holes in the
Maxwell electrodynamics, can be circumvented. What is even more, in the present
work, we find new non-unique, numerical solutions describing charged black
holes coupled to non-linear electrodynamics in a special class of scalar-tensor
theories. One of the phases has a trivial scalar field and coincides with the
corresponding solution in General Relativity. The other four phases that we
find are characterized by the value of the scalar field charge. The causal
structure and some aspects of the stability of the solutions have also been
studied. For the scalar-tensor theories considered, the black holes have a
single, non-degenerate horizon, i.e., their causal structure resembles that of
the Schwarzschild black hole. The thermodynamic analysis of the stability of
the solutions indicates that a phase transition may occur.Comment: 18 pages, 8 figures, new phases, figures, clarifying remarks and
acknowledgements adde
Almost Special Holonomy in Type IIA&M Theory
We consider spaces M_7 and M_8 of G_2 holonomy and Spin(7) holonomy in seven
and eight dimensions, with a U(1) isometry. For metrics where the length of the
associated circle is everywhere finite and non-zero, one can perform a
Kaluza-Klein reduction of supersymmetric M-theory solutions (Minkowksi)_4\times
M_7 or (Minkowksi)_3\times M_8, to give supersymmetric solutions
(Minkowksi)_4\times Y_6 or (Minkowksi)_3\times Y_7 in type IIA string theory
with a non-singular dilaton. We study the associated six-dimensional and
seven-dimensional spaces Y_6 and Y_7 perturbatively in the regime where the
string coupling is weak but still non-zero, for which the metrics remain
Ricci-flat but that they no longer have special holonomy, at the linearised
level. In fact they have ``almost special holonomy,'' which for the case of Y_6
means almost Kahler, together with a further condition. For Y_7 we are led to
introduce the notion of an ``almost G_2 manifold,'' for which the associative
3-form is closed but not co-closed. We obtain explicit classes of non-singular
metrics of almost special holonomy, associated with the near Gromov-Hausdorff
limits of families of complete non-singular G_2 and Spin(7) metrics.Comment: Latex, 26 page
- …