The matter Lagrangian of an ideal fluid

Abstract

We show that the matter Lagrangian of an ideal fluid equals (up to a sign -depending on its definition and on the chosen signature of the metric) the total energy density of the fluid, i.e. rest energy density plus internal energy density.

arXiv comment5 pages, accepted for publication in: International Journal of Geometric Methods in Modern Physics (IJGMMP)

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• f(R,L_m) gravity
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• Generalized curvature-matter couplings in modified gravity
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• The first variation of the matter energy-momentum tensor with respect to the metric, and its implications on modified gravity theories
• Effects of the matter Lagrangian degeneracy in $f(Q,T)$ gravity
• Anisotropic Tolman V Solutions by Decoupling Approach in $f(R,T^2)$ Gravity
• Late-Time Anisotropy Sourced by a 2-Form Field Non-Minimally Coupled to Cold Dark Matter
• Tunneling to Holographic Traversable Wormholes
• Gravitational Collapse via Wheeler-DeWitt Equation
• Gravitation with modified fluid Lagrangian: Variational principle and an early dark energy model
• Probing Strong Field $f(R)$ Gravity and Ultra-Dense Matter with the Structure and Thermal Evolution of Neutron Stars
• Cosmologies in $f(R,{\mathcal{L}}_m)$ theory with non-minimal coupling between geometry and matter
• Black hole spectra from Vaz's quantum gravitational collapse
• The matter Lagrangian of a non-perfect fluid
• Relations between Newtonian and relativistic cosmology