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arXiv · 0908.3333

A new framework for studying spherically symmetric static solutions in f(R) gravity

Anne Marie Nzioki·Sante Carloni·Rituparno Goswami·Peter K. S. Dunsby
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Abstract

We develop a new covariant formalism to treat spherically symmetric spacetimes in metric} f(R) theories of gravity. Using this formalism we derive the general equations for a static and spherically symmetric metric in a general f(R)-gravity. These equations are used to determine the conditions for which the Schwarzschild metric is the only vacuum solution with vanishing Ricci scalar. We also show that our general framework provides a clear way of showing that the Schwarzschild solution is not a unique static spherically symmetric solution, providing some incite on how the current form of Birkhoff's theorem breaks down for these theories.

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Anne Marie Nzioki, Sante Carloni, Rituparno Goswami, Peter K. S. Dunsby. 2010-02-10. A new framework for studying spherically symmetric static solutions in f(R) gravity. https://doi.org/10.1103/physrevd.81.084028

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