41 research outputs found
Topological Appearance of Event Horizon: What Is the Topology of the Event Horizon That We Can See?
The topology of the event horizon (TOEH) is usually believed to be a sphere.
Nevertheless, some numerical simulations of gravitational collapse with a
toroidal event horizon or the collision of event horizons are reported.
Considering the indifferentiability of the event horizon (EH), we see that such
non-trivial TOEHs are caused by the set of endpoints (the crease set) of the
EH. The two-dimensional (one-dimensional) crease set is related to the toroidal
EH (the coalescence of the EH). Furthermore, examining the stability of the
structure of the endpoints, it becomes clear that the spherical TOEH is
unstable under linear perturbation. On the other hand, a discussion based on
catastrophe theory reveals that the TOEH with handles is stable and generic.
Also, the relation between the TOEH and the hoop conjecture is discussed. It is
shown that the Kastor-Traschen solution is regarded as a good example of the
hoop conjecture by the discussion of its TOEH. We further conjecture that a
non-trivial TOEH can be smoothed out by rough observation in its mass scale.Comment: 53 pages, revtex, Published in Prog. Theo. Phys. vol.99, 13 figure
Slow-roll Extended Quintessence
We derive the slow-roll conditions for a non-minimally coupled scalar field
(extended quintessence) during the radiation/matter dominated era extending our
previous results for thawing quintessence. We find that the ratio
becomes constant but negative, in sharp contrast to the
ratio for the minimally coupled scalar field. We also find that the functional
form of the equation of state of the scalar field asymptotically approaches
that of the minimally coupled thawing quintessence.Comment: 11 pages, 4 figures, references added, to appear in Phys. Rev.
Four Dimensional Quantum Topology Changes of Spacetimes
We investigate topology changing processes in the WKB approximation of four
dimensional quantum cosmology with a negative cosmological constant. As
Riemannian manifolds which describe quantum tunnelings of spacetime we consider
constant negative curvature solutions of the Einstein equation i.e. hyperbolic
geometries. Using four dimensional polytopes, we can explicitly construct
hyperbolic manifolds with topologically non-trivial boundaries which describe
topology changes. These instanton-like solutions are constructed out of
8-cell's, 16-cell's or 24-cell's and have several points at infinity called
cusps. The hyperbolic manifolds are non-compact because of the cusps but have
finite volumes. Then we evaluate topology change amplitudes in the WKB
approximation in terms of the volumes of these manifolds. We find that the more
complicated are the topology changes, the more likely are suppressed.Comment: 26 pages, revtex, 13 figures. The calculation of volume and
grammatical errors are correcte