ACKNOWLEDGEMENTS This work would not have been possible without the help of a lot of people. I would like to thank my family and friends for their encouragement, my collaborators David Mota and Robert Scherrer for their hard work and my office mate Simon West for innumerable delightful lunches. Most of all I would like to thank my supervisor, John Barrow, for his constant support, his guidance ...

The theory of f(R)-gravity is one the theories modified Einstein gravity. vacuum solution, on other hand, field equation solution for black hole geometry. We establish here an asymptotically flat rotating in f(R)-gravity. This essentially leads to Kerr hole. exhibits change fundamental properties and its It particularly shows that radii marginally stable bound orbits event horizon increase comp...

In the context of modified gravity, we point out how the Palatini version of these theories is singled out as a very special case corresponding to the unique fixed point of a transformation involving a special conformal rescaling of the metric. This mathematical peculiarity signals deeply rooted problems which make the theory unphysical. PACS: 04.50+h, 04.20.Cv, 04.20.Fy, 04.90.+e.

Near the horizon of a black brane in Anti-de Sitter (AdS) space and near the AdS boundary, the long-wavelength fluctuations of the metric exhibit hydrodynamic behaviour. The gauge-gravity duality then relates the boundary hydrodynamics for generalized gravity to that of gauge theories with large finite values of ’t Hooft coupling. We discuss, for this framework, the hydrodynamics of the shear m...

In this proceeding, we review modified theories of gravity with a curvature-matter coupling between an arbitrary function the scalar curvature and Lagrangian density matter. This explicit nonminimal induces non-vanishing covariant derivative energy-momentum tensor, that implies non-geodesic motion consequently leads to appearance extra force. Here, explore physical cosmological implications non...