arXiv subjects

Akio Hosoya

Publications and source records attributed to Akio Hosoya.

28 records · Page 2Linked to original sources

arXiv2002

Naked Singularity and Thunderbolt

We consider quantum theoretical effects of the sudden change of the boundary conditions which mimics the occurrence of naked singularities. For a simple demonstration, we study a massless scalar field in $(1 + 1)$-dimensional Minkowski spacetime with finite spatial interval. We calculate the vacuum expectation value of the energy-momentum tensor and explicitly show that singular wave or {\em thunderbolt} appears along the Cauchy horizon. The thunderbolt possibly destroys the Cauchy horizon if its backreaction on the geometry is taken into account, leading to quantum restoration of the global hyperbolicity. The result of the present work may also apply to the situation that a closed string freely oscillating is traveling to a brane and changes itself to an open string pinned-down by the ends satisfying the Dirichlet boundary conditions on the brane.

gr-qc↗

arXiv1999

Who's Afraid of Naked Singularities?

To probe naked spacetime singularities with waves rather than with particles we study the well-posedness of initial value problems for test scalar fields with finite energy so that the natural function space of initial data is the Sobolev space. In the case of static and conformally static spacetimes we examine the essential self-adjointness of the time translation operator in the wave equation defined in the Hilbert space. For some spacetimes the classical singularity becomes regular if probed with waves while stronger classical singularities remain singular. If the spacetime is regular when probed with waves we may say that the spacetime is `globally hyperbolic.'

gr-qc↗

arXiv1997

Hamiltonians for Compact Homogeneous Universes

We briefly show how we can obtain Hamiltonians for spatially compact locally homogeneous vacuum spacetimes. The dynamical variables are categorized into the curvature parameters and the Teichmüller parameters. While the Teichmüller parameters usually parameterise the covering group of the spatial sections, we utilise another suitable parameterization where the universal cover metric carries all the dynamical variables and with this we reduce the Hamiltonians. For our models, all dynamical variables possess their clear geometrical meaning, in contrast to the conventional open models.}

gr-qc↗

arXiv1997

Renormalization Group Approach to Einstein Equation in Cosmology

The renormalization group method has been adapted to the analysis of the long-time behavior of non-linear partial differential equation and has demonstrated its power in the study of critical phenomena of gravitational collapse. In the present work we apply the renormalization group to the Einstein equation in cosmology and carry out detailed analysis of renormalization group flow in the vicinity of the scale invariant fixed point in the spherically symmetric and inhomogeneous dust filled universe model.

gr-qc↗

arXiv1997

Hamiltonian structures for compact homogeneous universes

Hamiltonian structures for spatially compact locally homogeneous vacuum universes are investigated, provided that the set of dynamical variables contains the \Teich parameters, parameterizing the purely global geometry. One of the key ingredients of our arguments is a suitable mathematical expression for quotient manifolds, where the universal cover metric carries all the degrees of freedom of geometrical variations, i.e., the covering group is fixed. We discuss general problems concerned with the use of this expression in the context of general relativity, and demonstrate the reduction of the Hamiltonians for some examples. For our models, all the dynamical degrees of freedom in Hamiltonian view are unambiguously interpretable as geometrical deformations, in contrast to the conventional open models.

gr-qc↗

arXiv1996

Black Hole Radiation inside Apparent Horizon in Quantum Gravity

We study a black hole radiation inside the apparent horizon in quantum gravity. First we perform a canonical quantization for spherically symmetric geometry where one of the spatial coordinates is dealt as the time variable since we would like to consider the interior region of a black hole. Next this rather general formalism is applied for a specific model where the ingoing Vaidya metric is used as a simple model of an evaporating black hole. Following Tomimatsu's idea, we will solve analytically the Wheeler-DeWitt equation in the vicinity of the apparent horizon and see that mass-loss rate of a black hole by thermal radiation is equal to the result obtained by Hawking in his semiclassical treatment. The present formalism may have a wide application in quantum gravity inside the horizon of a black hole such as mass inflation and strong cosmic censorship etc.

gr-qc↗

arXiv1996

Dynamics of compact homogeneous universes

A complete description of dynamics of compact locally homogeneous universes is given, which, in particular, includes explicit calculations of Teichmüller deformations and careful counting of dynamical degrees of freedom. We regard each of the universes as a simply connected four dimensional spacetime with identifications by the action of a discrete subgroup of the isometry group. We then reduce the identifications defined by the spacetime isometries to ones in a homogeneous section, and find a condition that such spatial identifications must satisfy. This is essential for explicit construction of compact homogenoeus universes. Some examples are demonstrated for Bianchi II, VI${}_0$, VII${}_0$, and I universal covers.

gr-qc↗

arXiv1996

Black Hole Singularity and Generalized Quantum Affine Parameter

We study a behavior of quantum generalized affine parameter (QGAP), which has been recently proposed by one of the present authors, near the singularity and the event horizon in three and four spacetime dimensions in terms of a minisuperspace model of quantum gravity. It is shown that the QGAP is infinite to the singularity while it remains finite to the event horizon. This fact indicates a possible interpretation that the singularity is wiped out in quantum gravity in this particular model of black hole.

gr-qc↗

arXiv1995

Anderson Localization in the Sky and Cosmological Magnetic Field

We discuss the Anderson localization of electromagnetic fields in the fluctuating plasma induced by the gravitational density perturbation before the recombination time of the Universe. Randomly distributed localized coherent electromagnetic fields emerge in the thermal equilibrium before the recombination time. We argue that the localized coherent electric fields eventually produce cosmological magnetic fields after the decoupling time.

gr-qc↗

arXiv1994

Compact Homogeneous Universes

A thorough classification of the topologies of compact homogeneous universes is given except for the hyperbolic spaces, and their global degrees of freedom are completely worked out. To obtain compact universes, spatial points are identified by discrete subgroups of the isometry group of the generalized Thurston geometries, which are related to the Bianchi and the Kantowski-Sachs-Nariai universes. Corresponding to this procedure their total degrees of freedom are shown to be categorised into those of the universal covering space and the Teichmüller parameters. The former are given by constructing homogeneous metrics on simply connected manifold. The Teichmüller spaces are also given by explicitly constructing expressions for the discrete subgroups of the isometry group.

gr-qc↗