Spherically symmetric solutions of modified field equations in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>theories of gravity

Spherically symmetric static empty space solutions are studied in $f(R)$ theories of gravity. We reduce the set of modified Einstein's equations to a single equation and show how one can construct exact solutions in different $f(R)$ models. In particular, we show that for a large class models, including e.g. the $f(R)=R\ensuremath{-}{\ensuremath{\mu}}^{4}/R$ model, the Schwarzschild-de Sitter metric is an exact solution of the field equations. The significance of these solutions is discussed in light of solar system constraints on $f(R)$ theories of gravity.

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