Masaru Siino

Disappearance of Black Hole Criticality in Semiclassical General Relativity

We investigate the quantum effects on the so-called critical phenomena in black hole formation. Quantum effects of a scalar field are treated semiclassically via a trace anomaly method. It is found that the demand of regularity at the origin implies the disappearance of the echo. It is also found that semiclassical equations of motion do not admit continuously self-similar solutions. The quantum effects would change the critical solution from a discretely self-similar one to a solution without critical phenomena.

Gravitational Collapse in Painlevé-Gullstrand Coordinates

We construct an exact solution for the spherical gravitational collapse in asingle coordinate patch. To describe the dynamics of collapse, we use ageneralized form of the Painleve-Gullstrand coordinates in the Schwarzschildspacetime. The time coordinate of the form is the proper time of a free-fallingobserver so that we can describe the collapsing star not only outside but alsoinside the event horizon in a single coordinate patch. We show the bothsolutions corresponding to the gravitational collapse from infinity and from afinite radius.

Slow-roll Extended Quintessence

We derive the slow-roll conditions for a nonminimally coupled scalar field (extended quintessence) during the radiation/matter dominated era extending our previous results for thawing quintessence. We find that the ratio {phi}e/3H{phi} 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.

TOPOLOGICAL CLASSIFICATION OF BLACK HOLES: GENERIC MAXWELL SET AND CREASE SET OF A HORIZON

The crease set of an event horizon or a Cauchy horizon is an important object which determines the qualitative properties of the horizon. In particular, it determines the possible topologies of the spatial sections of the horizon. By Fermats principle in geometric optics, we relate the crease set and the Maxwell set of a smooth function in the context of singularity theory. We thereby give a classification of generic topological structures of the Maxwell sets and the generic topologies of the spatial section of the horizon.

Thurston's geometrization conjecture and cosmological models

We investigate a class of spatially compact inhomogeneous spacetimes. Motivated by Thurstons geometrization conjecture, we give a formulation for constructing spatially compact composite spacetimes as solutions for the Einstein equations. Such composite spacetimes are built from the spatially compact locally homogeneous vacuum spacetimes which have two commuting local Killing vector fields and are homeomorphic to torus bundles over the circle by gluing them through a timelike hypersurface admitting a homogeneous spatial torus spanned by the commuting local Killing vector fields. We also assume that the matter which will arise from the gluing is compressed on the boundary, i.e. we take the thin-shell approximation. By solving the junction conditions, we can see dynamical behaviour of the connected (composite) spacetime. The Teichmuller deformation of the torus can also be obtained. We apply our formalism to a concrete model. The relation to the torus sum of 3-manifolds and the difficulty of this problem are also discussed.

Topology Change of Black Holes

The topological structure of the event horizon has been investigated in terms of the Morse theory. The elementary process of topological evolution can be understood as a handle attachment. It has been found that there are certain constraints on the nature of black hole topological evolution: (i) There are n kinds of handle attachments in (n+1)-dimensional black hole space-times. (ii) Handles are further classified as either of black or white type, and only black handles appear in real black hole space-times. (iii) The spatial section of an exterior of the black hole region is always connected. As a corollary, it is shown that the formation of a black hole with an S**(n-2) x S**1 horizon from that with an S**(n-1) horizon must be non-axisymmetric in asymptotically flat space-times.

HEAD-ON COLLISION AND MERGING ENTROPY OF BLACK HOLES: RECONSIDERATION OF HAWKING'S INEQUALITY

We evaluate the amount of energy that can be converted into gravitational radiation in head-on collision of black holes. We estimate it by the area theorem of black hole horizon incorporating merging entropy of colliding black holes from a viewpoint of black hole thermodynamics. Then we obtain an upper bound of energy ratio of the gravitational radiation which is smaller than the upper bound originally derived by Hawking. The fact that this estimation is not inconsistent with the results of both numerical investigations in low- and high-energy head-on collision implies that thermodynamics of coalescing black holes requires the contribution of the merging entropy.

Point particles as defects in (2+1)-dimensional quantum gravity

The authors have shown explicit examples of topology change of the universe by quantum tunnelling in the (2+1)-dimensional quantum gravity. They show that mass points can be created in pairs as spacetime defects in the course of the topology changing processes.

Teichmüller parameters for a multiple BTZ black hole spacetime

We investigate the Teichmuller parameters for a Euclidean multiple BTZ black hole spacetime. To induce a complex structure in the asymptotic boundary of such a spacetime, we consider the limit in which two black holes are at a large distance from each other. In this limit, we can approximately determine the period matrix ij (i.e., the Teichmuller parameters) for the spacetime boundary by using a pinching param- eter. The Teichmuller parameters are essential in describing the partition function for the boundary conformal field theory (CFT). We provide an interpretation of the partition function for the genus two extremal boundary CFT proposed by Gaiotto and Yin that it is relevant to double BTZ black hole spacetime.

Limit structure of future null infinity tangent—topology of the event horizon and gravitational wave tail

We investigated the relation between the behaviour of gravitational waves at late time and the limit structure of future null infinity tangent which will determine the topology of the event horizon far in the future. In the present paper, we mainly consider a spacetime with two black holes. Although in most cases, the black holes coalesce and the event horizon is topologically a single sphere far in the future, there are several possibilities that the black holes never coalesce and such exact solutions as examples. In our formulation, the tangent vector of future null infinity is, under conformal embedding, related to the number of black holes far in the future through the Poincare–Hopf theorem. Under the conformal embedding, the topology of the event horizon far in the future will be affected by the geometrical structure of the future null infinity. In this paper, we relate the behaviour of Weyl curvature to this limit behaviour of the generator vector of the future null infinity. We show if Weyl curvature decays sufficiently slowly at late time in the neighbourhood of future null infinity, two black holes never coalesce.