Structure scalars and an extension to LTB metric

Abstract

The main goal of this paper is to present the Lemaître–Tolman–Bondi (LTB) spacetime for the radiating case by extending the study of [L. Herrera, A. Di Prisco, J. Ospino and J. Carot, Phys. Rev. D 82 (2010) 024021] in [Formula: see text] theory, where [Formula: see text] is the Ricci scalar and [Formula: see text] is the energy–momentum tensor trace. We will start with some fundamental equations, such as the kinematical variables, mass function introduced by Misner and Sharp, the Weyl tensor under the influence of the [Formula: see text] modified Bianchi identities. We have also considered the evolution of the modified constraint equation. Later on, we have analyzed LTB in terms of modified structure scalars emerging from the orthogonal splitting of the Riemann tensor, and the transport equation in [Formula: see text] gravity theory. We will also discuss a case in order to generalize LTB metric.