Geometric structure of spherically symmetric spacetime in massive gravity theory

Abstract

Recent observations suggest that the universe is expanding with acceleration. General relativity theory is supposed to be a theory to describe this phenomenon. However, without introducing exotic matter such as dark energy, it cannot explain this phenomenon. One possibility to explain this phenomenon is a modification of general relativity which is usually called modified gravity theory. Massive gravity theory is one of the modifications in which the massless spin-2 graviton acquires masses in contrast to usual general relativity corresponding to massless graviton. A model that can explain acceleration of the expanding universe is presented by de Rham, Gabadadze, and Tolley and is called dRGT massive gravity theory. Even though this massive gravity theory can explain the expanding universe with acceleration, it must reduce to the usual explanation of local gravity scale such as the solar system. In order to study consequences of massive gravity at local gravity scale, the aim of this research is therefore to study spacetime geometry by using the spherically symmetric solutions in this theory. By using these solutions, one can find particle trajectories by analyzing the effective potential. From the data of Mercury\'s orbit, we found that the trajectory of Mercury obtained by massive gravity theory is same as the result predicted from GR. It implies that the dRGT massive gravity theory can reduce to GR at the local gravity scale.