Dynamical Wormhole Solutions in Rastall Theory

TL;DR

This paper explores dynamical wormhole solutions within Rastall's theory, demonstrating that modifications to the energy-momentum tensor can allow for configurations that respect energy conditions near the throat, unlike in general relativity.

Contribution

It introduces analytical solutions for dynamical wormholes in Rastall theory that can satisfy energy conditions, contrasting with the violations typically seen in GR static wormholes.

Findings

Existence of solutions respecting WEC near the wormhole throat

Analytical solutions with constant redshift function and specific equations of state

Modification of matter source allows energy condition compliance in dynamical wormholes

Abstract

Wormhole configurations in Einstein's general theory of relativity (GR) require exotic matter sources violating the weak energy condition (WEC). Rastall's theory is a generalization of GR in its matter source considering a nonconserved energy-momentum (EM) tensor. Hence, on one hand, the nature of this generalization of the matter source of field equations and, on the other hand, the possibility of respecting energy conditions for dynamical wormholes in contrast to static ones motivates us to study the possibility of the existence of wormhole configurations respecting energy conditions or minimizing the violations of them in Rastall's modified theory. We derive general analytical solutions considering a constant redshift function and a particular equation of state for energy density and pressure profiles. We show that because of the modification in the EM source of the field equations, there exist solutions respecting the WEC in the vicinity of the wormhole's throat for specified values of the parameters. Some particular solutions are discussed in detail.