Spherically symmetric brane spacetime with bulk $$f(\mathcal {R})$$ f ( R ) gravity

Abstract

Introducing f (R) term in the five-dimensional bulk action we derive effective Einstein's equation on the brane using Gauss-Codazzi equation. This effective equation is then solved for different conditions on dark radiation and dark pressure to obtain various spherically symmetric solutions. Some of these static spherically symmetric solutions correspond to black hole solutions, with parameters induced from the bulk. Specially, the dark pressure and dark radiation terms (electric part of Weyl curvature) affect the brane spherically symmetric solutions significantly. We have solved for one parameter group of conformal motions where the dark radiation and dark pressure terms are exactly obtained exploiting the corresponding Lie symmetry. Various thermodynamic features of these spherically symmetric space-times are studied, showing existence of second order phase transition. This phenomenon has its origin in the higher curvature term with f (R) gravity in the bulk.

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.…”

Silhouette of M87*: A new window to peek into the world of hidden dimensions

“…To understand how the gravitational dynamics on the brane is modified in a quantitative manner, the higher dimensional gravitational field equations are expressed in terms of the four dimensional quantities [29][30][31][32][33][34]. Black hole solutions associated with such effective gravitational field equations [30,31,35,36] often inherit a tidal charge from the extra dimensions which unlike GR can also be negative.…”

Constraining some Horndeski gravity theories

“…[22]), which are viable alternatives to the dark energy, such constraints can be found in [23][24][25]. A further subclass of Horndeski theories, known as f (R) gravity was introduced in [26] and latter has been used extensively in cosmological (see [27,28] for a review) and extra dimensional scenarios [29][30][31]. We refer our reader to [32][33][34] for discussions on the solar system physics and Newtonian limits of f (R) gravity.…”