Junction conditions in perfect fluid f(G, T) gravitational theory

M. Z. Bhatti, Z. Yousaf, M. Yousaf

Submitted on 13 July 2022


This manuscript aims to establish the gravitational junction conditions(JCs) for the f(G, T) gravity. In this gravitational theory, f is an arbitrary function of Gauss-Bonnet invariant G and the trace of the energy-momentum tensor Tμν i.e., T. We start by introducing this gravity theory in its usual geometrical representation and posteriorly obtain a dynamically equivalent scalar-tensor demonstration on which the arbitrary dependence on the generic function f in both G and T is exchanged by two scalar fields and scalar potential. We then derive the JCs for matching between two different space-times across a separation hyper-surface Σ, assuming the matter sector to be described by an isotropic perfect fluid configuration. We take the general approach assuming the possibility of a thin-shell arising at Σ between the two space-times. However, our results establish that, for the distribution formalism to be well-defined, thin-shells are not allowed to emerge in the general version of this theory. We thus obtain instead a complete set of JCs for a smooth matching at Σ under the same conditions. The same results are then obtained in the scalar-tensor representation of the theory, thus emphasizing the equivalence between these two representations. Our results significantly constrain the possibility of developing models for alternative compact structures supported by thin-shells in f(G, T) gravity, e.g. gravastars and thin-shell wormholes, but provide a suitable framework for the search of models presenting a smooth matching at their surface, from which perfect fluid stars are possible examples.


Comment: 27 pages, 1 figure, version submitted for publication

Subjects: General Relativity and Quantum Cosmology; Astrophysics - Cosmology and Nongalactic Astrophysics; High Energy Physics - Phenomenology; High Energy Physics - Theory