PREPRINT
34686ECB-1887-44BE-99CD-96198A31F950

# Junction conditions in perfect fluid gravitational theory

M. Z. Bhatti, Z. Yousaf, M. Yousaf
arXiv:2207.05965

Submitted on 13 July 2022

## Abstract

This manuscript aims to establish the gravitational junction conditions(JCs) for the gravity. In this gravitational theory, $f$ is an arbitrary function of Gauss-Bonnet invariant $\mathcal{G}$ and the trace of the energy-momentum tensor ${T}_{\mu \nu }$ 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 $\mathcal{G}$ 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 $\mathrm{\Sigma }$, 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 $\mathrm{\Sigma }$ 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 $\mathrm{\Sigma }$ 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 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.

## Preprint

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