The gravitational wave of the scalar-tensor theory.
S. W. Kim · 1998
this paper, we derive the gravitational wave equations in Einstein-Cartan(EC) manifold with torsion and scalar field. The fundamental variables of this theory are the tetrad, spin connection, and scalar field, as we will see later. The scalar field is the reciprocal value of the gravitational constant like the usual Brans-Dicke theory. In this manifold, three wave equations for each variable are derived according to the linearized theory. The first one is similar to the gravitational wave equation of general relativity(GR) which is the tensor wave equation. The second one is the same as electromagnetic wave equation. It is just the vector wave equation such as the electromagnetic wave equation generated by the dipole moment. The last one is the scalar wave equation. The spin in the electromagnetic field causes the magnetic dipole moment that couples with the electromagnetic field. Thus we can ask a question if the spin in EC theory causes the gravitational dipole moment that couples with the antisymmetric part of the Ricci tensor. In the last part of this paper, the possibility of the existence of the gravitational dipole moment is checked.