Canonical Theory of 2+1 Gravity

Recently 2+1 dimensional gravity theory, especially ${\rm AdS_3}$ has been studied extensively. It was shown to be equivalent to the 2+1 Chern-Simon theory and has been investigated to understand the black hole thermodynamics, i.e. Hawking temperature and others. The purpose of this report is to investigate the canonical formalism of the original 2+1 Einstein gravity theory instead of the Chern-Simon theory. For the spherically symmetric space-time, local conserved quantities(local mass and angular momentum) are introduced and using them canonical quantum theory is defined. Constraints are imposed on state vectors and solved analytically. The strategy to obtain the solution is followed by our previous work.Comment: 6 pages, talk given at LLWI-2000: From Particles to Universe, Alberta, 20-26 February 200

Analytic Solutions of The Wheeler-DeWitt Equation in Spherically Symmetric Space-time

We study the quantum theory of the Einstein-Maxwell action with a cosmological term in the spherically symmetric space-time, and explored quantum black hole solutions in Reissner-Nordstrom-de Sitter geometry. We succeeded to obtain analytic solutions to satisfy both the energy and momentum constraints.Comment: LaTeX file, 15 page

Rotating Black Hole Entropy from Two Different Viewpoints

Using the brick-wall method, we study the entropy of Kerr-Newman black hole from two different viewpoints, a rest observer at infinity and zero angular momentum observer near horizon. We investigate this with scalar field in the canonical quantization approach. An observer at infinity can take one of the two possible frequency ranges; one is with positive frequencies only and the other is with the whole range including negative frequencies. On the other hand, a zero angular momentum observer near horizon can take positive frequencies only. For the observer at infinity the superradiant modes appear in either choice of the frequency ranges and the two results coincide. For the zero angular momentum observer superradiant modes do not appear due to absence of ergoregion. The resulting entropies from the two viewpoints turn out to be the same.Comment: LaTeX 18 pages, 2 figures, Minor modifications in section 3(ZAMO

Classical and Quantum Solutions and the Problem of Time in R2R^2 Cosmology

We have studied various classical solutions in $R^2$ cosmology. Especially we have obtained general classical solutions in pure $R^2$\ cosmology. Even in the quantum theory, we can solve the Wheeler-DeWitt equation in pure $R^2$\ cosmology exactly. Comparing these classical and quantum solutions in $R^2$\ cosmology, we have studied the problem of time in general relativity.Comment: 17 pages, latex, no figure, one reference is correcte

de Broglie-Bohm Interpretation for the Wave Function of Quantum Black Holes

We study the quantum theory of the spherically symmetric black holes. The theory yields the wave function inside the apparent horizon, where the role of time and space coordinates is interchanged. The de Broglie-Bohm interpretation is applied to the wave function and then the trajectory picture on the minisuperspace is introduced in the quantum as well as the semi-classical region. Around the horizon large quantum fluctuations on the trajectories of metrics $U$ and $V$ appear in our model, where the metrics are functions of time variable $T$ and are expressed as $ds^2=-{\alpha^2}/U dT^2 + U dR^2 + V d\Omega^2$. On the trajectories, the classical relation $U=-V^{1/2}+2Gm$ holds, and the event horizon U=0 corresponds to the classical apparent horizon on $V=2Gm$. In order to investigate the quantum fluctuation near the horizon, we study a null ray on the dBB trajectory and compare it with the one in the classical black hole geometry.Comment: 20 pages, Latex, 7 Postscript figure

Scalar field dynamics in warped AdS_3 black hole background

We study the normal modes of a scalar field in the background of a warped AdS_3 black hole which arises in topologically massive gravity. We discuss the normal mode spectrum using the brick wall boundary condition. In addition, we investigate the possibility of a more general boundary condition for the scalar field.Comment: 7 pages, one figure, revtex4, refs. added and minor modifications in tex

On the Perturbative Solutions of Bohmian Quantum Gravity

In this paper we have solved the Bohmian equations of quantum gravity, perturbatively. Solutions up to second order are derived explicitly, but in principle the method can be used in any order. Some consequences of the solution are disscused.Comment: 14 Pages, RevTeX. To appear in Phys. Rev.

Normal mode analysis for scalar fields in BTZ black hole background

We analyze the possibility of inequivalent boundary conditions for a scalar field propagating in the BTZ black hole space-time. We find that for certain ranges of the black hole parameters, the Klein-Gordon operator admits a one-parameter family of self-adjoint extensions. For this range, the BTZ space-time is not quantum mechanically complete. We suggest a physically motivated method for determining the spectra of the Klein-Gordon operator.Comment: 6 pages, no figure, late

Canonical entropy of three-dimensional BTZ black hole

Recently, Hawking radiation of the black hole has been studied using the tunnel effect method. It is found that the radiation spectrum of the black hole is not a strictly pure thermal spectrum. How does the departure from pure thermal spectrum affect the entropy? This is a very interesting problem. In this paper, we calculate the partition function by energy spectrum obtained from tunnel effect. Using the partition function, we compute the black hole entropy and derive the expression of the black hole entropy after considering the radiation. And we derive the entropy of charged black hole. In our calculation, we consider not only the correction to the black hole entropy due to fluctuation of energy but also the effect of the change of the black hole charges on entropy. There is no other hypothesis. Our result is more reasonable.According to the fact that the black hole entropy is not divergent, we obtain the lower limit of Banados-Teitelboim-Zanelli black hole energy. That is, the least energy of Banados-Teitelboim-Zanelli black hole, which satisfies the stationary condition in thermodynamics.Comment: 10 page

Entropy of the Schwarzschild black hole to all orders in the Planck length

Considering corrections to all orders in the Planck length on the quantum state density from a generalized uncertainty principle (GUP), we calculate the statistical entropy of the scalar field on the background of the Schwarzschild black hole without any cutoff. We obtain the entropy of the massive scalar field proportional to the horizon area.Comment: 13 pages, 1 figure; Minor typos corrected, one reference added; Accepted for publication in Phys. Lett.