On the visibility of singularities in general relativity and modified gravity theories

Abstract We investigate the global causal structure of end state a spherically symmetric marginally bound Lemaitre–Tolman–Bondi (LTB) (Lemaitre 1933 Ann. Soc. Sci. Brux. A 53 51, Tolman 1934 Proc. Natl Acad. USA 20 169–76, Bondi 1947 Mon. Not. Astron. 107 410) collapsing cloud (which is well studied in general relativity) framework modified gravity having generalized Lagrangian R + α 2 action. Here R Ricci scalar, and $\alpha \geqslant 0$?> ⩾ 0 constant. By fixing functional form metric components LTB spacetime, using up available degree freedom, we realize that matching surface interior exterior are different for values α . This change can alter property first central singularity. depict this by showing numerical example. Additionally, globally naked singularity to have physical relevance, congruence null geodesics should escape from such be visible an asymptotic observer infinite time. For happen, nodal point. here give heuristic method show point considering above class theory gravity, which relativity particular case.