A variational approach to homogeneous scalar fields in General Relativity

TL;DR

This paper introduces a variational method to establish the existence of homogeneous scalar field solutions in General Relativity, employing a modified Euler--Maupertuis principle and approximation techniques.

Contribution

It presents a novel variational approach for proving the existence of scalar field solutions in a gravitational context, extending previous methods with new approximation techniques.

Findings

Existence of solutions between prescribed configurations.

Solutions obtained as limits of approximating variational problems.

Application of Rabinowitz's techniques to gravitational scalar fields.

Abstract

A result of existence of homogeneous scalar field solutions between prescribed configurations is given, using a modified version of Euler--Maupertuis least action variational principle. Solutions are obtained as limit of approximating variational problems, solved using techniques introduced by Rabinowitz.