116 research outputs found
Causality violation and singularities
We show that singularities necessarily occur when a boundary of causality
violating set exists in a space-time under the physically suitable assumptions
except the global causality condition in the Hawking-Penrose singularity
theorems. Instead of the global causality condition, we impose some
restrictions on the causality violating sets to show the occurrence of
singularities.Comment: 11 pages, latex, 2 eps figure
Existence, Regularity, and Properties of Generalized Apparent Horizons
We prove a conjecture of Tom Ilmanen's and Hubert Bray's regarding the
existence of the outermost generalized apparent horizon in an initial data set
and that it is outer area minimizing.Comment: 16 pages, thoroughly revised, no major changes, to appear in Comm.
Math. Phy
Dimensionality, topology, energy, the cosmological constant, and signature change
Using the concept of real tunneling configurations (classical signature
change) and nucleation energy, we explore the consequences of an alternative
minimization procedure for the Euclidean action in multiple-dimensional quantum
cosmology. In both standard Hartle-Hawking type as well as Coleman type
wormhole-based approaches, it is suggested that the action should be minimized
among configurations of equal energy. In a simplified model, allowing for
arbitrary products of spheres as Euclidean solutions, the favoured space-time
dimension is 4, the global topology of spacelike slices being (hence predicting a universe of Kantowski-Sachs type). There is,
however, some freedom for a Kaluza-Klein scenario, in which case the observed
spacelike slices are . In this case, the internal space is a product
of two-spheres, and the total space-time dimension is 6, 8, 10 or 12.Comment: 34 pages, LaTeX, no figure
Trapped surfaces, horizons and exact solutions in higher dimensions
A very simple criterion to ascertain if (D-2)-surfaces are trapped in
arbitrary D-dimensional Lorentzian manifolds is given. The result is purely
geometric, independent of the particular gravitational theory, of any field
equations or of any other conditions. Many physical applications arise, a few
shown here: a definition of general horizon, which reduces to the standard one
in black holes/rings and other known cases; the classification of solutions
with a (D-2)-dimensional abelian group of motions and the invariance of the
trapping under simple dimensional reductions of the
Kaluza-Klein/string/M-theory type. Finally, a stronger result involving closed
trapped surfaces is presented. It provides in particular a simple sufficient
condition for their absence.Comment: 7 pages, no figures, final version to appear in Class. Quantum Gra
Black holes, cosmological singularities and change of signature
There exists a widespread belief that signature type change could be used to
avoid spacetime singularities. We show that signature change cannot be utilised
to this end unless the Einstein equation is abandoned at the suface of
signature type change. We also discuss how to solve the initial value problem
and show to which extent smooth and discontinuous signature changing solutions
are equivalent.Comment: 14pages, Latex, no figur
The limit space of a Cauchy sequence of globally hyperbolic spacetimes
In this second paper, I construct a limit space of a Cauchy sequence of
globally hyperbolic spacetimes. In the second section, I work gradually towards
a construction of the limit space. I prove the limit space is unique up to
isometry. I als show that, in general, the limit space has quite complicated
causal behaviour. This work prepares the final paper in which I shall study in
more detail properties of the limit space and the moduli space of (compact)
globally hyperbolic spacetimes (cobordisms). As a fait divers, I give in this
paper a suitable definition of dimension of a Lorentz space in agreement with
the one given by Gromov in the Riemannian case.Comment: 31 pages, 5 figures, submitted to Classical and Quantum gravity,
seriously improved presentatio
The region with trapped surfaces in spherical symmetry, its core, and their boundaries
We consider the region in spacetime containing future-trapped
closed surfaces and its boundary \B, and derive some of their general
properties. We then concentrate on the case of spherical symmetry, but the
methods we use are general and applicable to other situations. We argue that
closed trapped surfaces have a non-local property, "clairvoyance", which is
inherited by \B. We prove that \B is not a marginally trapped tube in
general, and that it can have portions in regions whose whole past is flat. For
asymptotically flat black holes, we identify a general past barrier, well
inside the event horizon, to the location of \B under physically reasonable
conditions. We also define the core of the trapped region as that
part of which is indispensable to sustain closed trapped
surfaces. We prove that the unique spherically symmetric dynamical horizon is
the boundary of such a core, and we argue that this may serve to single it out.
To illustrate the results, some explicit examples are discussed, namely
Robertson-Walker geometries and the imploding Vaidya spacetime.Comment: 70 pages, 14 figures. Figure 6 has been replaced, and corrected.
Minor changes around Propositions 10.3 and 10.4, and some typos correcte
Cosmological perturbations and classical change of signature
Cosmological perturbations on a manifold admitting signature change are
studied. The background solution consists in a Friedmann-Lemaitre-Robertson-
Walker (FLRW) Universe filled by a constant scalar field playing the role of a
cosmological constant. It is shown that no regular solution exist satisfying
the junction conditions at the surface of change. The comparison with similar
studies in quantum cosmology is made.Comment: 35 pages, latex, 2 figures available at [email protected], to
appear in Physical Review
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