Cosmological Lorentzian Wormholes via Noether symmetry approach

TL;DR

This paper uses Noether symmetry to find exact solutions in scalar-tensor gravity theories that describe cosmological Lorentzian wormholes, which satisfy energy conditions and differ from Euclidean wormholes.

Contribution

It introduces a Noether symmetry approach to derive exact Lorentzian wormhole solutions in various scalar-tensor theories of gravity.

Findings

Solutions describe cosmological Lorentzian wormholes.

Wormholes satisfy the weak energy condition.

Scale factors are consistent across different theories.

Abstract

Noether symmetry has been invoked to explore the forms of a couple of coupling parameters and the potential appearing in a general scalar-tensor theory of gravity in the background of Robertson-Walker space-time. Exact solutions of Einstein's field equations in the familiar Brans-Dicke, Induced gravity and a General non-minimally coupled scalar-tensor theories of gravity have been found using the conserved current and the energy equation, after being expressed in a set of new variables. Noticeably, the form of the scale factors remains unaltered in all the three cases and represents cosmological Lorentzian wormholes, analogous to the Euclidean ones. While classical Euclidean wormholes requires an imaginary scalar field, the Lorentzian wormhole do not, and the solutions satisfy the weak energy condition.