We investigate the interior Einstein’s equations in case of a static, axially symmetric, perfect fluid source. present particular line element that is specially suitable for investigation this type gravitational fields. Assuming deviation from spherically symmetry small, we linearize corresponding and field find several classes vacuum solutions. some approximate solutions by imposing appropriat...

Recently it has shown that Einstein’s field equations can be rewritten into a form of the first law of thermodynamics both at event horizon of static spherically symmetric black holes and apparent horizon of Friedmann-Robertson-Walker (FRW) universe, which indicates intrinsic thermodynamic properties of spacetime horizon. In the present paper we deal with the socalled f(R) gravity, whose action...