Takeshi Shirafuji

Energy of General Spherically Symmetric Solution in the Tetrad Theory of Gravitation.

We find the most general spherically symmetric solution in a special class of the tetrad theory of gravitation. The tetrad gives the Schwarzschild metric. The energy is calculated using both the superpotential method and the Euclidean continuation method. We find that unless the time-space components of the tetrad go to zero faster than 1/ rr at infinity, the two methods give different results and that these results differ from the gravitational mass of the central gravitating body. This fact implies that the time-space components of the tetrad describing an isolated spherical body must vanish faster than 1/ rr at infinity.

Mass and Spin of Exact Solutions of the Poincaré Gauge Theory

Recently, in the framework of the Poincare gauge theory (PGT), I) the question of the total energy and spin of an isolated system has been discussed in some detail, assuming that the spacetime around the system is asymptotically flat. 2 ) In the present paper we would like to relax the assumption of asymptotic flatness, and asymptotical· ly only require a spacetime of constant curvature, because exact solutions of the PGT typically approach a de Sitter space for increasing radial coordinate r.3) The underlying spacetime of the PGT is a Riemann-Cartan spacetime with torsion and curvatures:

REISSNER–NORDSTRÖM SPACE–TIME IN THE TETRAD THEORY OF GRAVITATION

We give two classes of spherically symmetric exact solutions of the coupled gravitational and electromagnetic fields with charged source in the tetrad theory of gravitation. The first solution depends on an arbitrary function H(R,t). The second solution depends on a constant parameter η. These solutions reproduce the same metric, i.e. the Reissner–Nordstrom metric. If the arbitrary function which characterizes the first solution and the arbitrary constant of the second solution are set to be zero, then the two exact solutions will coincide with each other. We then calculate the energy content associated with these analytic solutions using the superpotential method. In particular, we examine whether these solutions meet the condition, which Moller required for a consistent energy–momentum complex, namely, we check whether the total four-momentum of an isolated system behaves as a four-vector under Lorentz transformations. It is then found that the arbitrary function should decrease faster than for R → ∞. It is also shown that the second exact solution meets the Mollers condition.

Equivalence Principle in the New General Relativity

We study the problem of whether the active gravitational mass of an isolated system is equal to the total energy in the tetrad theory of gravitation. The superpotential is derived using the gravitational Lagrangian which is invariant under parity operation, and applied to an exact spherically symmetric solution. Its associated energy is found equal to the gravitational mass. The field equation in vacuum is also solved at far distances under the assumption of spherical symmetry. Using the most general expression for parallel vector fields with spherical symmetry, we find that the equality between the gravitational mass and the energy is always true if the parameters of the theory

The Canonical formulation of N=2 supergravity in terms of the Ashtekar variable

a_1

Supersymmetry algebra in N=1 chiral supergravity

,

Construction of N = 2 chiral supergravity compatible with the reality condition

a_2

Minimal off-shell version ofN=1chiral supergravity

and

Torsion Field Equation and Spinor Source

a_3

Higher Derivative Gravity in Generalized Covariant Derivative Formalism

satisfy the condition,