arXiv subjects

Shintaro Sawayama

Publications and source records attributed to Shintaro Sawayama.

9 recordsLinked to original sources

arXiv2011

Black Hole evaporation in semi-classical approach

As well as known, the black hole evaporation problem is famous problem. Because the S.W.Hawking found the black holes emit light at the future null infinity as a thermal radiation \cite{H}, we think that the black holes may be vanish. However, to prove this problem, we should solve field equation, i.e. forth order partial differential equations \cite{Ford}\cite{BD}. However, we can find a method to solve this equation, and we could prove that the black holes finally vanish. To solve this problem we use dynamical horizons equation in the Vaidya spacetime.

physics.gen-ph↗

arXiv2009

Solving the Wheeler-DeWitt of Small Universe

We can solve the Wheeler-DeWitt equation of the small universe enough to metric becomes diagonal and take a Gaussian normal coordinate. Our previous works are concerning to this paper. In this paper, we only write how to solve the Wheeler-DeWitt equation of such universe. Our motivation is simple, that is to solve the Wheeler-DeWitt equation. Even if the Wheeler-DeWitt equation is solved, quantum gravity does not complete yet. However, this work may be one of the first step to quantum gravity.

gr-qc↗

arXiv2009

Problem of the time and static restriction in quantum gravity

The problem of the time is one of the open issues in the quantum gravity. This problem is particular problem in the canonical quantum gravity. Even in the loop gravity the problem of the time remain. Our work is concerning to the problem of the time. The Wheeler-DeWitt itself contains time evolution part, but which part is the time evolution part is open issue. However, we can create a method that seems to solve this problem that is up-to-down method created in the previous works. We can derive equation relating to the time and static restriction in this paper. As a example we treat the problem of the time of the Friedmann universe. And we derive the static restriction in quantum gravity.

gr-qc↗

arXiv2008

Quantization of enlarged Bianchi I universe

We can solve the Wheeler-DeWitt equation of the enlarged Bianchi I as inhomogeneous type universe with static restriction which had been derived by previous paper. We consider the commutation relation between the static restriction and the Hamiltonian constraint. And we can simplify the usual 3+1 Hamiltonian constraint of the enlarged Biancki I type universe, and we finally show the state's form is the exponential. And we find that the states of the quantum gravity are entangled. Our paper based on the previous work of ours that we call up-to-down method which was aimed to simplify the Wheeler-DeWitt equation.

gr-qc↗

arXiv2008

A new way to solve Wheeler-DeWitt equation including black hole universe

One of the unsolved issues in the quantum gravity comes from the Wheeler-DeWitt equation, which is second order functional derivative equation. In this paper, we introduce a new method to solve the Wheeler-DeWitt equation. Usually one treats the state functional of the space of 3-dimensional metrics, which do not contain timelike metrics. However we can expand this state to the state which has support on the space of spacetime metrics with using additional constraint which requires the recovery of 4-dimensional quantum gravity. Enlarging the support of the state functional of the spacetime metrics, we can simply solve the usual Wheeler-DeWitt equation with the additional constraint. Using this method we can solve some unsolved problems, such as the quantization of the black hole.

gr-qc↗

arXiv2007

Quantization of the metric diagonal spacetime with Gaussian normal coordinates

In the analysis of the Wheeler-DeWitt equation, we have simplified the Hamiltonian constraint of the Wheeler-DeWitt equation using the coordinate transformation. The coordinate is choose such that metric becomes diagonal and as Gaussian normal coordinate. Or we treat small universe so that the metric become diagonal and universe is covered by Gaussian normal coordinates. We have solved the Wheeler-DeWitt equation of such universes. Such that universe contains Biancki I type universe or the black hole universe.

gr-qc↗

arXiv2006

Quantization of static inhomogeneous spacetime

In this paper we can solve a Wheeler-DeWitt equation of the some inhomogeneous spacetime models as a local solution. From the previous study of up-to-down method we derived the static restriction relating the problem of the time. Although static restriction does not commute with the general Hamiltonian constraint, the Hamiltonian constraint of some mini-superspace models commute with static restriction. We can quantize such inhomogeneous models. With obtained result we can success to simplify the general local Hamiltonian constraint.

gr-qc↗

arXiv2006

One Local Solution of the Wheeler-DeWitt equation

We can obtain one solution of the Hamiltonian constraint equation in the local sense. The form of the state is suggested from the up-to-down method in our previous work. The up-to-down method works for different way in treating the general metrics. In the mini-superspace approach there appears additional constraint in the 4-dimensional quantum gravity Hilbert space. However, in the general treatment of the metrics this method works as only solving technique.

gr-qc↗

arXiv2006

Dynamical horizon of evaporating black hole in Vaidya spacetime

We consider how the mass of the black hole decreases by the Hawking radiation in the Vaidya spacetime, using the concept of dynamical horizon equation, proposed by Ashtekar and Krishnan. Using the formula for the change of the dynamical horizon, we derive an equation for the mass incorporating the Hawking radiation. It is shown that final state is the Minkowski spacetime in our particular model.

gr-qc↗