The Cauchy problem for metric-affine f(R)-gravity in presence of a Klein-Gordon scalar field

TL;DR

This paper investigates the initial value problem in metric-affine f(R)-gravity with a Klein-Gordon scalar field, establishing conditions for well-posedness and extending previous analyses with different sources.

Contribution

It provides the first comprehensive analysis of the Cauchy problem for metric-affine f(R)-gravity with a Klein-Gordon scalar field, identifying key conditions for well-posedness.

Findings

Sufficient conditions for well-posedness are formulated.

Completes the analysis of the Cauchy problem for various matter sources.

Extends previous work to include Klein-Gordon scalar fields.

Abstract

We study the initial value formulation of metric-affine f(R)-gravity in presence of a Klein-Gordon scalar field acting as source of the field equations. Sufficient conditions for the well-posedness of the Cauchy problem are formulated. This result completes the analysis of the same problem already considered for other sources.