Colliding plane wave solution in F(R)=R^{N} gravity

Abstract

We identify a region of F (R) = R N gravity without external sources which is isometric to the spacetime of colliding plane waves (CPW). From the derived curvature sources, N (N > 1) measures the strength (i.e. the charge) of the source. The analogy renders construction and collision of plane waves in F (R) = R N gravity possible, as in the Einstein-Maxwell (EM) theory, simply because R = 0. A plane wave in this type of gravity is equivalent to a Weyl curvature plus an electromagnetic energy-momentum-like term (i.e. 'source without source'). For N = 1 we recover naturally the plane waves (and their collision) in Einstein's theory. Our aim is to find the effect of an expanding universe by virtue of F (R) = R N on the colliding gravitational plane waves of Einstein.

Asymptotically Lifshitz black hole solutions in F(R) gravity

“…Charged spherically symmetric black hole solutions have been obtained in Refs. [10,31] and creation of the electric charge and cosmological constant from pure gravity, simultaneously, have been extracted in [11].…”