Soluções esfericamente simétricas na gravitação de Starobinsky-Podolsky

Abstract

Extensions of General Relativity have received increasing attention over the last few decades due to motivations coming from high-energy physics, astrophysics, and cosmology. The non-renormalizability of Einstein’s gravitation and the search for a coherent quantum theory of gravity drove the rising of higher-derivative gravity during the 1960s. Today, robust observational data indicate that modified gravity theories are possible candidates in describing evolution of the Universe. In this dissertation, the model called Starobinsky-Podolsky gravitation is explored, which includes higher-order corrections of the curvature invariants. Here, the Einstein-Hilbert action is supplemented by a quadratic correction of the Ricci scalar R plus a derivative contraction term of R. After a review of Einstein’s gravitation and an exposition about Schwarzschild black holes, the proposed gravitation is explored. The field equations of Starobinsky-Podolsky gravity are deduced and then spherically symmetric solutions are studied. Its Newtonian limit is developed and analyzed. Finally, an analysis of the black holes solutions is made, in particular, under which conditions only Schwarzschild black holes can occur.