Tolman IV solution in the Randall-Sundrum Braneworld
AbstractIn the context of the Randall-Sundrum braneworld, the minimal geometric deformation ap-proach(MGD) is usedto generateanexact analyticinteriorsolutionto four-dimensionaleﬀectiveEinstein’s ﬁeld equations for a spherically symmetric compact distribution. This solution rep-resents the braneworld version of the well known Tolman IV solution in General Relativity. Byusing this analytic solution, an exhaustive analysis of the braneworld eﬀects on realistic stellarinteriors is developed, ﬁnding strong evidences in favor of the hypothesis that compactness isreduced due to bulk eﬀects on stellar conﬁgurations. 1 Introduction In recent years there has been great interest in ﬁnding alternative theories to General Relativity(GR) [1, 2], mainly due to the inability of the latter to explain satisfactorily some fundamental issuesassociated with the gravitational interaction, such as the dark matter problem, the dark energyproblem, as well as the impossibility to reconcile GR with the Standard Model of particle physics.Extra-dimensional theories, which are mostly inspired by String/M-theory, are among the theoriesthat lead to gravity beyond GR. One of these extra-dimensional theories is the Braneworld (BW)proposed by Randall and Sundrum (RS) [3] which has been largely studied and which explains oneof the fundamental problems of Physics, i.e. the hierarchy problem (see also the ADD model [4]and [5]). Because of this, its study and impact on GR is fully justiﬁed and is of great importance[6].Even though we have a covariant approach that is useful to study many fundamental aspectsof the theory of RS BW [7], we are still far from fully understanding its impact on gravity, mainlydue to the lack of the complete ﬁve-dimensional solution (bulk plus brane), which could helpsto explain certain key issues that remain unresolved, such as the existence of black holes in RSBW [8]-[11] and the bulk eﬀects on stellar conﬁgurations [12]. Since the complete ﬁve-dimensional