The matter Lagrangian and the energy-momentum tensor in modified gravity with nonminimal coupling between matter and geometry

Journal Article · Mon Feb 15 00:00:00 EST 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.044021· OSTI ID:21409308

Harko, T ^[1]

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1. Department of Physics and Center for Theoretical and Computational Physics, University of Hong Kong, Pok Fu Lam Road (Hong Kong)

We show that in modified f(R) type gravity models with nonminimal coupling between matter and geometry, both the matter Lagrangian and the energy-momentum tensor are completely and uniquely determined by the form of the coupling. This result is obtained by using the variational formulation for the derivation of the equations of motion in the modified gravity models with geometry-matter coupling, and the Newtonian limit for a fluid obeying a barotropic equation of state. The corresponding energy-momentum tensor of the matter in modified gravity models with nonminimal coupling is more general than the usual general-relativistic energy-momentum tensor for perfect fluids, and it contains a supplementary, equation of state dependent term, which could be related to the elastic stresses in the body, or to other forms of internal energy. Therefore, the extra force induced by the coupling between matter and geometry never vanishes as a consequence of the thermodynamic properties of the system, or for a specific choice of the matter Lagrangian, and it is nonzero in the case of a fluid of dust particles.

• OSTI ID: 21409308
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 4; Other Information: DOI: 10.1103/PhysRevD.81.044021; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COUPLING
ENERGY-MOMENTUM TENSOR
EQUATIONS OF MOTION
EQUATIONS OF STATE
FLUIDS
GRAVITATION
IDEAL FLOW
LAGRANGIAN FUNCTION
MATTER
NONLUMINOUS MATTER
RELATIVISTIC RANGE
STRESSES
THERMODYNAMIC PROPERTIES
VARIATIONAL METHODS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
ENERGY RANGE
EQUATIONS
FLUID FLOW
FUNCTIONS
INCOMPRESSIBLE FLOW
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
STEADY FLOW
TENSORS