Kinematics and Dynamics of $f(R)$ Theories of Gravity

Details Kinematics and Dynamics of $f(R)$ Theories of Gravity Kinematics and Dynamics of $f(R)$ Theories of Gravity

1995-11-02

arxiv.org/abs/gr-qc/9511010v1

Gen.Rel.Grav. 28 (1996) 193-205

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, latex, to appear in GRG

Scientific paper

10.1007/BF02105423

We generalise the equations governing relativistic fluid dynamics given by Ehlers and Ellis for general relativity, and by Maartens and Taylor for quadratic theories, to generalised $f(R)$ theories of gravity. In view of the usefulness of this alternative framework to general relativity, its generalisation can be of potential importance for deriving analogous results to those obtained in general relativity. We generalise, as an example, the results of Maartens and Taylor to show that within the framework of general $f(R)$ theories, a perfect fluid spacetime with vanishing vorticity, shear and acceleration is Friedmann--Lema\^{\i}tre--Robertson--Walker only if the fluid has in addition a barotropic equation of state. It then follows that the Ehlers--Geren--Sachs theorem and its ``almost'' extension also hold for $f(R)$ theories of gravity.

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