Matter Lagrangian of particles and fluids
Abstract
We consider a model where particles are described as localized concentrations of energy, with fixed rest mass and structure, which are not significantly affected by their selfinduced gravitational field. We show that the volume average of the onshell matter Lagrangian L_{m} describing such particles, in the proper frame, is equal to the volume average of the trace T of the energymomentum tensor in the same frame, independently of the particle's structure and constitution. Since both L_{m} and T are scalars, and thus independent of the reference frame, this result is also applicable to collections of moving particles and, in particular, to those which can be described by a perfect fluid. Our results are expected to be particularly relevant in the case of modified theories of gravity with nonminimal coupling to matter where the matter Lagrangian appears explicitly in the equations of motion of the gravitational and matter fields, such as f (R ,L_{m}) and f (R ,T ) gravity. In particular, they indicate that, in this context, f (R ,L_{m}) theories may be regarded as a subclass of f (R ,T ) gravity.
 Publication:

Physical Review D
 Pub Date:
 March 2018
 DOI:
 10.1103/PhysRevD.97.064019
 arXiv:
 arXiv:1802.03961
 Bibcode:
 2018PhRvD..97f4019A
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 5 pages, no figures, matches published version