Lemaître–Tolman–Bondi dust solutions in f (R) gravity

Abstract

We derive a class of non-static inhomogeneous dust solutions in gravity described by the Lemaître–Tolman–Bondi (LTB) metric. The field equations are fully integrated for all parameter subcases and compared with analogous subcases of LTB dust solutions of GR. Since the solutions do not admit regular symmetry centres, we have two possibilities: (i) a spherical dust cloud with angle deficit acting as the source of a vacuum Schwarzschild-like solution associated with a global monopole, or (ii) fully regular dust wormholes without angle deficit, whose rest frames are homeomorphic to the Schwarzschild–Kruskal manifold or to a 3d torus. The compatibility between the LTB metric and generic ansatzes furnishes an ‘inverse procedure’ to generate LTB solutions whose sources are found from the geometry. While the resulting fluids may have an elusive physical interpretation, they can be used as exact non-perturbative toy models in theoretical and cosmological applications of theories.