Rotation Curves of Spiral Galaxies and Large Scale Structure of Universe under Generalized Einstein Action

We consider an addition of the term which is a square of the scalar curvature to the Einstein-Hilbert action. Under this generalized action, we attempt to explain i) the flat rotation curves observed in spiral galaxies, which is usually attributed to the existence of dark matter, and ii) the contradicting observations of uniform cosmic microwave background and non-uniform galaxy distributions against redshift. For the former, we attain the flatness of velocities, although the magnitudes remain about half of the observations. For the latter, we obtain a solution with oscillating Hubble parameter under uniform mass distributions. This solution leads to several peaks of galaxy number counts as a function of redshift with the first peak corresponding to the Great Wall.Comment: 16 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

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

Quantum creation of an Inhomogeneous universe

In this paper we study a class of inhomogeneous cosmological models which is a modified version of what is usually called the Lema\^itre-Tolman model. We assume that we have a space with 2-dimensional locally homogeneous spacelike surfaces. In addition we assume they are compact. Classically we investigate both homogeneous and inhomogeneous spacetimes which this model describe. For instance one is a quotient of the AdS$_4$ space which resembles the BTZ black hole in AdS$_3$. Due to the complexity of the model we indicate a simpler model which can be quantized easily. This model still has the feature that it is in general inhomogeneous. How this model could describe a spontaneous creation of a universe through a tunneling event is emphasized.Comment: 21 pages, 5 ps figures, REVTeX, new subsection include

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

Generalized Einstein Theory on Solar and Galactic Scales

We study a generalized Einstein theory with the following two criteria:{\it i}) on the solar scale, it must be consistent with the classical tests of general relativity, {\it ii}) on the galactic scale, the gravitational potential is a sum of Newtonian and Yukawa potentials so that it may explain the flat rotation curves of spiral galaxies. Under these criteria, we find that such a generalized Einstein action must include at least one scalar field and one vector field as well as the quadratic term of the scalar curvature.Comment: 13 pages, Latex, SLAC-PUB-596