Eur. Phys. J. C (2019) 79: 674
https://doi.org/10.1140/epjc/s10052-019-7195-4

Letter

The trace of the trace of the energy–momentum tensor-dependent Einstein’s field equations

¹ Departamento de Física, ITA-Instituto Tecnológico de Aeronáutica, São José dos Campos, São Paulo, 12228-900, Brazil
² Dipartimento di Fisica, UNINA-Università degli Studi di Napoli “Federico II”, 80126, Naples, Italy

^* e-mail: moraes.phrs@gmail.com

Received: 9 July 2019
Accepted: 1 August 2019
Published online: 13 August 2019

Abstract

The f(R, T) gravity field equations depend generically on both the Ricci scalar R and trace of the energy–momentum tensor T. Within the assumption of perfect fluids, the theory carries an arbitrariness regarding the choice of the matter lagrangian density , not uniquely defined. Such an arbitrariness can be evaded by working with the trace of the theory field equations. From such an equation, one can obtain a form for , which does not carry the arbitrariness. The obtained form for shows that the f(R, T) gravity is unimodular. A new version of the theory is, therefore, presented and forthcoming applications are expected.