The Cauchy problem for metric-affine f(R)-gravity in presence of perfect-fluid matter

TL;DR

This paper investigates the initial value problem for metric-affine f(R)-gravity with torsion and perfect-fluid matter, establishing conditions for well-posedness and analyzing conservation laws in different frames.

Contribution

It extends the analysis of the Cauchy problem to metric-affine f(R)-gravity with torsion, highlighting the importance of conformal invariance of the stress-energy tensor.

Findings

The Cauchy problem is well-posed under specific conditions.

Conservation laws are crucial for the problem's formulation.

The stress-energy tensor's form is preserved under conformal transformations.

Abstract

The Cauchy problem for metric-affine f(R)-gravity `a la Palatini and with torsion, in presence of perfect fluid matter acting as source, is discussed following the well-known Bruhat prescriptions for General Relativity. The problem results well-formulated and well-posed when the perfect-fluid form of the stress-energy tensor is preserved under conformal transformations. The key role of conservation laws in Jordan and in Einstein frame is also discussed.