Static spherically symmetric perfect fluid solutions inf(R)theories of gravity

Abstract

Static spherically symmetric perfect fluid solutions are studied in metric f (R) theories of gravity. We show that pressure and density do not uniquely determine f (R) ie. given a matter distribution and an equation state, one cannot determine the functional form of f (R). However, we also show that matching the outside Schwarzschild-de Sitter-metric to the metric inside the mass distribution leads to additional constraints that severely limit the allowed fluid configurations.

Good and bad tetrads inf(T)gravity

“…Excluding the first case we can see what happens when T = T 0 = constant. The remaining two independent field equations becomes 20) where f 0 = f (T 0 ) and f T0 = f ′ (T 0 ) are constants. We can find conditions when the universe is accelerating in this case analysing the acceleration condition a > 0.…”

Axially symmetric solutions in f ( R )-gravity

“…The authors have reconstructed the form of some f (R)-models, discussing their physical relevance. In [8], the same authors have discussed static spherically symmetric solutions, in presence of perfect fluid matter, adopting the metric formalism. They have shown that a given matter distribution is not capable of globally determining the functional form of f (R).…”

Relativistic stars inf(R)gravity, and absence thereof

“…This motivates us to study relativistic stars in the context of f (R) gravity. Spherically symmetric stars in f (R) gravity have been investigated so far in [27,28,29,30]. (We confine ourselves to a metric theory of f (R) gravity.…”