arXiv subjects

K. Shigemoto

Publications and source records attributed to K. Shigemoto.

11 recordsLinked to original sources

arXiv2008

Normal Modes and No Zero Mode Theorem of Scalar Fields in BTZ Black Hole Spacetime

Eigenfunctions for normal modes of scalar fields in BTZ black hole spacetime are studied. Orthonormal relations among them are derived. Quantization for scalar fields is done and particle number, energy and angular momentum are expressed by the creation and annihilation operators. Allowed physical normal mode region is studied on the basis of the no zero mode theorem. Its implication to the statistical mechanics is also studied.

gr-qc↗

arXiv2007

Solution Independent Analysis of Black Hole Entropy in Brick Wall Model

Using the brick wall regularization of 't Hooft, the entropy of non-extreme and extreme black holes is investigated in a general static, spherically symmetric spacetime. We classify the singularity in the entropy by introducing a {\it new} index $δ$ with respect to the brick wall cut-off $ε$. The leading contribution to entropy for non-extreme case $(δ\neq 0)$ is shown to satisfy the area law with quadratic divergence with respect to the invariant cut-off $ε_{\rm inv}$ while the extreme case $(δ=0)$ exhibits logarithmic divergence or constant value with respect to $ε$. The general formula is applied to Reissner-Nordström, dilaton and brane-world black holes and we obtain consistent results.

gr-qc↗

arXiv2005

Scalar Field Contribution to Rotating Black Hole Entropy

Scalar field contribution to entropy is studied in arbitrary D dimensional one parameter rotating spacetime by semiclassical method. By introducing the zenithal angle dependent cutoff parameter, the generalized area law is derived. The non-rotating limit can be taken smoothly and it yields known results. The derived area law is then applied to the Banados-Teitelboim-Zanelli (BTZ) black hole in (2+1) dimension and the Kerr-Newman black hole in (3+1) dimension. The generalized area law is reconfirmed by the Euclidean path integral method for the quantized scalar field. The scalar field mass contribution is discussed briefly.

gr-qc↗

arXiv2003

Weber-Fechner's Law and Demand Function

We apply the Weber-Fechner's law, which represents the relation between the magnitude of physical stimulus and the magnitude of psychological sense in human being, to the utility function. We conclude that the utility function of n-types of goods is of separable type u(x_1,x_2,..., x_n)=u_1(x_1)+u_2(x_2)+... +u_n(x_n), which give the relation of the demand function in the form p_i=d u_i/d x_i. The explicit quantitative form of each utility function, which is suggested by the Weber-Fechner's law, becomes u_i(x_i)=A_i \log (x_i/x^{(0)}_i). Then we obtain each demand function in the familiar form p_i=A_i/x_i.

physics.gen-ph↗

arXiv2002

Conservation of Energy in Black Holes and in Cosmology

We first review the various definition of the total energy in the gravitational system. The naive definition has some defects, and we review how to modify the definition of the total energy. Then we explicitly demonstrate how to calculate the total energy of the system. Our example is the total energy of a black hole in the expanding closed de Sitter universe in (2+1) dimension. In general, we find that the contribution to the total energy comes only from the singularity. Then we can calculate the total energy by evaluating the contribution around the singularity.

gr-qc↗

arXiv2001

Star-Triangle Relation of the Chiral Potts Model Revisited

We give the simple proof of the star-triangle relation of the chiral Potts model. We also give the constructive way to understand the star-triangle relation of the chiral Potts model, which may give the hint to give the new integrable models.

cond-mat.stat-mech↗

arXiv2000

The Scenario for the Astrophysics with Scalar Field and the Cosmological Constant

In order to give the standard scenario of the astrophysics, we study the Einstein theory with minimally coupled scalar field and the cosmological term by considering the scalar field as a candidate of the dark matter. We obtained the exact solution in the cosmological scale and the approximate gravitational potential in the galactic or solar scale. We find that the scalar field plays the role of the dark matter in some sense in the cosmological scale but it does not play the role of the dark matter in the galactic or solar scale within our approximation.

gr-qc↗

arXiv1999

The Structure of the Bazhanov-Baxter Model and a New Solution of the Tetrahedron Equation

We clarify the structure of the Bazhanov-Baxter model of the 3-dim N-state integrable model. There are two essential points, i) the cubic symmetries, and ii) the spherical trigonometry parametrization, to understand the structure of this model. We propose two approaches to find a candidate as a solution of the tetrahedron equation, and we find a new solution.

solv-int↗

arXiv1995

Classical and Quantum Solutions and the Problem of Time in $R^2$ 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.

gr-qc↗

arXiv1995

On Solutions of Tetrahedron Equations based on Korepanov Mechanism

We have examined solutions of tetrahedron equations from the elliptic free fermion model by using Korepanov mechanism based on tetrahedral Zamolodchikov algebras. As a byproduct, we have found a new integrable 2-dim. lattice model. We have also studied the relation between tetrahedral Zamolodchikov algebras and tetrahedron equations.

hep-th↗

arXiv1992

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.

hep-ph↗