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 self-induced gravitational field. We show that the volume average of the on-shell matter Lagrangian ${\mathcal{L}}_m$ describing such particles, in the proper frame, is equal to the volume average of the trace $T$ of the energy-momentum tensor in the same frame, independently of the particle's structure and constitution. Since both ${\mathcal{L}}_m$ 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 $f(R,{\mathcal{L}}_m)$ and $f(R,T)$ gravity. In particular, they indicate that, in this context, $f(R,{\mathcal{L}}_m)$ theories may be regarded as a subclass of $f(R,T)$ gravity.

5 pages, no figures, matches published version

References in corpus (5)

• f(R,T) gravity
• f(R,L_m) gravity
• New derivation of the Lagrangian of a perfect fluid with a barotropic equation of state
• p-brane dynamics in (N+1)-dimensional FRW universes: a unified framework
• Localized D-dimensional global k-defects

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• Hydrostatic equilibrium configurations of neutron stars in a non-minimal geometry-matter coupling theory of gravity
• Probing gravity at sub-femtometer scales through the pressure distribution inside the proton
• Distance-duality in theories with a nonminimal coupling to gravity
• Analytical external spherical solutions in entangled relativity
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• Palatini $f(\mathcal{R},{\mathcal{L}}_m,{\mathcal{R}}_{\mu \nu }{T}^{\mu \nu })$ gravity and its Born-Infeld semblance
• Domain walls and other defects in Eddington-inspired Born-Infeld gravity