Infinite number of soliton solutions to 5-dimensional vacuum Einstein equation

We give an infinite number of exact solutions to the 5-dimensional static Einstein equation with axial symmetry by using the inverse scattering method. The solutions are characterized by two integers representing the soliton numbers. The first non trivial example of these solutions is the static black ring solution found recently.Comment: 13 page

Role of the imaginary part in the Moyal quantization

We show that the imaginary part of the $\star$-genvalue equation in the Moyal quantization reveals the symmetries of the Hamiltonian by which we obtain the conserved quantities. Applying to the Toda lattice equation, we derive conserved quantities which are used as the independent variables of Wigner function.Comment: 5 page

Equivalence of Weyl Vacuum and Normal Ordered Vacuum in the Moyal Quantization

We study the 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 the Weyl ordering. Their equivalence is shown by using a differential equation satisfied by the normal ordered vacuum.Comment: 8 page

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.Comment: 18 page

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

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.Comment: 8 pages, no figs, Late

Discrete and Continuous Bogomolny Equations through the Deformed Algebra

We connect the discrete and continuous Bogomolny equations. There exists one-parameter algebra relating two equations which is the deformation of the extended conformal algebra. This shows that the deformed algebra plays the role of the link between the matrix valued model and the model with one more space dimension higher.Comment: 12 page

Moyal Quantization for Constrained System

We study the Moyal quantization for the constrained system. One of the purposes is to give a proper definition of the Wigner-Weyl(WW) correspondence, which connects the Weyl symbols with the corresponding quantum operators. A Hamiltonian in terms of the Weyl symbols becomes different from the classical Hamiltonian for the constrained system, which is related to the fact that the naively constructed WW correspondence is not one-to-one any more. In the Moyal quantization a geometrical meaning of the constraints is clear. In our proposal, the 2nd class constraints are incorporated into the definition of the WW correspondence by limiting the phasespace to the hypersurface. Even though we assume the canonical commutation relations in the formulation, the Moyal brackets between the Weyl symbols yield the same results as those for the constrained system derived by using the Dirac bracket formulation.Comment: 25 page