Solving higher curvature gravity theories

Abstract

Solving field equations in the context of higher curvature gravity theories is a formidable task. However, in many situations, e.g., in the context of f (R) theories, the higher curvature gravity action can be written as an EinsteinHilbert action plus a scalar field action. We show that not only the action but the field equations derived from the action are also equivalent, provided the spacetime is regular. We also demonstrate that such an equivalence continues to hold even when the gravitational field equations are projected on a lower-dimensional hypersurface. We have further addressed explicit examples in which the solutions for Einstein-Hilbert and a scalar field system lead to solutions of the equivalent higher curvature theory. The same, but on the lowerdimensional hypersurface, has been illustrated in the reverse order as well. We conclude with a brief discussion on this technique of solving higher curvature field equations.

Cosmological implications of a shift symmetric Galileon field

“…Thus given a suitable scale factor describing evolution of our universe we can use the Friedmann equations to determine the structure of the potential. In a recent work using the reconstruction method the authors have tried to demonstrate the structure of the functions G 2 , G 3 in weakly broken Galileon theories for either a bouncing or cyclic cosmology, here we apply it to the late time acceleration [47,53].…”

Complexity growth rates for AdS black holes in massive gravity and f(R) gravity

“…The other solutions and thermodynamical qualities for f (R) gravity black holes have also been investigated in Refs. [56][57][58][59][60][61][62][63][64][65]. The authors of [32] conjectured that only the stationary black holes in gravity theories without higher derivative terms of curvature can saturate Eq.…”

Anisotropic solutions by gravitational decoupling

“…Indeed, this simple and systematic method could be conveniently exploited in a large number of relevant cases, such as the Einstein-Maxwell [20] and Einstein-Klein-Gordon system [21][22][23][24], for higher derivative gravity [25][26][27], f (R)-theories of gravity [28][29][30][31][32][33][34], Hořava-aether gravity [35,36], polytropic spheres [37][38][39], among many others. In this respect, the simplest practical application of the MGD-decoupling consists in extending known isotropic and physically acceptable interior solutions for spherically symmetric self-gravitating systems into the anisotropic domain, at the same time preserving physical acceptability, which represents a highly non-trivial problem [40] (for obtaining anisotropic solutions in a generic way, see for instance Refs.…”