Some exact relativistic star solutions in <i>f</i>(<i>R</i>) gravity

Abstract We present a covariant description of non-vacuum static spherically symmetric spacetimes in f ( R ) gravity applying the (1+1+2) covariant formalism. The propagation equations are then used to derive a covariant and dimensionless form of the Tolman–Oppenheimer–Volkoff equations. We then give a solution strategy to these equations and obtain some new exact solutions for the particular case <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>R</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> <mml:mi>α</mml:mi> <mml:msup> <mml:mi>R</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , which have the correct thermodynamic properties for standard matter.