Gravitational Waves in Conformal Gravity Theory

Abstract

We have studied in this thesis the evolution of the gravitational waves in the framework of a scalar tensor theory. We have reviewed the emission of the gravitational waves according to the general theory of relativity. Recalling that the scalar tensor theory is a conformal theory while the general relativity is not. We explored the emission of the gravitational waves in the Brans-Dicke theory which is an example of a tensor theory. It is a rival theory to general relativity and a agrees with it for some limiting cases. A particular solution of the wave equation is found that is similar to the quantum telegraph equation that is shown recently to govern the behavior of matter wave. A wave equation with massless particle is found to transform to a wave with massive particle that has a quantum signature. This may help provide some clues to quantum gravity. Quantum geometrical quantities for the conformal scalar theory are calculated. These can be considered as quantum corrections to the classical gravitational values. These can be applied to study the evolution of black holes in the frame of conformal theory. The conformal factor is found to represent the vacuum field that is coupled to matter field. We see that a theory that is not conformally invariant reveals the effect of the vacuum on the interaction with other fields present in the universe. Because of the vacuum field the wave equation transforms to the telegraph equation whereas the Klein Gordon equation transforms to the quantum telegraph equation.