Takao Koikawa

The electrically charged BTZ black hole with self (anti-self) dual Maxwell field

Abstract The Einstein-Maxwell equations with a negative cosmological constant Λ in 2 + 1 spacetime dimensions discussed by Banados, Teitelboim and Zanelli are solved by assuming a self (anti-self) dual equation E r = ±B^ , which is imposed on the orthonormal basis components of the electric field E r and the magnetic field B^. This solution describes an electrically charged extreme black hole with mass, angular momentum and electric charge Q e. Although the coordinate components of the electric field Er and the magnetic field B have singularities on the horizon at r = ( 4πGQ e 2 |Λ| ) 1 2 , the spacetime has the same value of constant negative curvature R = 6Λ of Banados et al.

2+1 dimensional charged black hole with (anti-)self dual Maxwell fields

Abstract We discuss the exact electrically charged BTZ black hole solutions to the Einstein-Maxwell equations with a negative cosmological constant in 2+1 spacetime dimensions assuming a (anti-)self dual condition between the electromagnetic fields. In a coordinate condition there appears a logarithmic divergence in the angular momentum at spatial infinity. We show how it is to be regularized by taking the contribution from the boundary into account. We show another coordinate condition which leads to a finite angular momentum though it brings about a peculiar spacetime topology.

An Infinite Number of Stationary Soliton Solutions to the Five-Dimensional Vacuum Einstein Equation

We obtain an infinite number of soliton solutions to the five-dimensional stationary Einstein equation with axial symmetry by using the inverse scattering method. We start with the five-dimensional Minkowski space as a seed metric to obtain these solutions. The solutions are characterized by two soliton numbers and a constant appearing in the normalization factor which is related to a coordinate condition. We show that the (2,0)-soliton solution is identical to the Myers-Perry solution with one angular momentum variable by imposing a condition on the relation between parameters. We also show that the (2,2)-soliton solution is different from the black ring solution discovered by Emparan and Reall, although one component of the two metrics can be identical.

Magnetic solutions to 2 + 1 dimensional gravity with dilaton field

Abstract We show a general method to solve 2 + 1 dimensional dilatonic Maxwell-Einstein equation with a positive or negative cosmological constant. All the physical solutions are listed with assumptions that they are static, rotationally symmetric, and has a nonzero magnetic field and a nonzero dilaton field. On the contrary to the magnetic solution without a dilaton field, some of the present solutions with a dilaton field possess a horizon.

Soliton Equations Extracted from the Noncommutative Zero-Curvature Equation

We investigate the equation where the commutation relation in 2-dimensional zero-curvature equation composed of the algebra-valued potentials is replaced by the Moyal bracket and the algebra-valued potentials are replaced by the non-algebra-valued ones with two more new variables. We call the 4-dimensional equation the noncommutative zero-curvature equation. We show that various soliton equations are derived by the dimensional reduction of the equation.

Discrete and continuous Bogomolny equations through the deformed algebra

Abstract We show that there exists one-parameter algebra connecting the discrete and continuous Bogomolny equations. The algebra is the deformation of the extended conformal algebra. This shows that the deformed algebra plays a role of the link between the matrix valued model and the model with one more space dimension higher.

An Infinite Number of Static Soliton Solutions to the 5D Einstein-Maxwell Equations with a Dilaton Field

We study the 5D static Einstein-Maxwell equations with a dilaton field. We develop an infinite number of solutions using a soliton technique. We study the rod structure of a two-soliton solution and show that a 5D dilatonic black ring and black hole solutions are included. Subject Index: 450, 451

An Infinite Number of Static Soliton Solutions to the 5D Einstein-Maxwell Equations

The soliton technique is applied to the 5D static Einstein-Maxwell equations, and an infinite number of solutions are explicitly obtained. We study the rod structure of 2-soliton solutions and we show that the 5D Reissner-Nordstrom solution and the 5D Majumdar-Papapetrou solution are included as the 2-soliton solutions.

Equivalence of the Weyl vacuum and normally ordered vacuum in the Moyal quantization

We study features of the vacuum of the harmonic oscillator in the Moyal quantization. Two vacua are defined, one with the normal ordering and the other with Weyl ordering. Their equivalence up to an overall constant factor is shown by using a differential equation satisfied by the normally ordered vacuum.

Soliton Formulation Using Moyal Algebra

It is well known that the soliton equations can be expressed as a zero-curvature equation emerging as a compatibility condition of the scattering problem equation and the time evolution equation in the inverse scattering problem. The potentials are sl(N,C) valued. Many of the familiar soliton equations fall into the N = 2 category. In this paper we consider a formulation of the soliton equation by using the Moyal algebra 1) which is identical to su(N) algebra for some value of parameter it contains. 2) 4) In order to realize this, we replace the commutation relation in the zero-curvature equation by the Moyal algebra. This introduces two new variables into the equations. We assume that the potentials are expanded in powers of ep, where the variable p is one of the newly introduced variables. Specification of the expansion determines the type of soliton equation. Substituting the potentials into the zerocurvature equation, we obtain various soliton equations. Taking out coefficients at each order of the power of ep in the zero-curvature equation, we obtain soliton equations on a lattice, one of which is the well-known Toda lattice equation. In general, the equations thus obtained include one parameter originating from the Moyal algebra. It is interesting to note that the parameter of the Moyal bracket has the physical meaning in the soliton equation as the spacing between particles on the lattice. 5) We then naturally obtain the continuous correspondence of the discrete soliton equations by taking the limit in which this parameter vanishes. We first recapitulate the notation of the Moyal algebra following Strachan. 6) Define the star product by