Scalar-tensor representation of $f(R)$ gravity and Birkhoff's theorem

Abstract

Birkhoff's theorem is discussed in the frame of f(R) gravity by using its scalar-tensor representation. Modified gravity has become very popular at recent times as it is able to reproduce the unification of inflation and late-time acceleration with no need of a dark energy component or an inflaton field. Here, another aspect of modified f(R) gravity is studied, specifically the range of validity of Birkhoff's theorem, compared with another alternative to General Relativity, the well known Brans-Dicke theory. As a novelty, here both theories are studied by using a conformal transformation and writing the actions in the Einstein frame, where spherically symmetric solutions are studied by using perturbation techniques. The differences between both theories are analyzed as well as the validity of the theorem within the Jordan and Einstein frames, where interesting results are obtained.

8 pages. Version to be published in Annalen der Physik

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• Black Holes in f(R) theories
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• Physical non-equivalence of the Jordan and Einstein frames
• Initial and final de Sitter universes from modified $f(R)$ gravity
• The Jebsen-Birkhoff theorem in alternative gravity
• Stability of f(R) black holes
• Modified f(R) gravity from scalar-tensor theory and inhomogeneous EoS dark energy
• Comparing scalar-tensor gravity and f(R)-gravity in the Newtonian limit

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• Jeans Analysis of Bok globules in $f(R)$ gravity
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