Gravitational Decoupling in Higher Order Theories

Abstract

Gravitational decoupling via the Minimal Geometric Deformation (MGD) approach has been used extensively in General Relativity (GR), mainly as a simple method for generating exact anisotropic solutions from perfect fluid seed solutions. Recently this method has also been used to generate exact spherically symmetric solutions of the Einstein-scalar system from the Schwarzschild vacuum metric. This was then used to investigate the effect of scalar fields on the Schwarzschild black hole solution. We show that this method can be extended to higher order theories. In particular, we consider fourth order Einstein–Weyl gravity, and in this case by using the Schwarzschild metric as a seed solution to the associated vacuum field equations, we apply the MGD method to generate a solution to the Einstein–Weyl scalar theory representing a hairy black hole solution. This solution is expressed in terms of a series using the Homotopy Analysis Method (HAM).

An anisotropic extension of Heintzmann IIa solution with vanishing complexity factor

“…[32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]). Even this framework has been used widely in several scenarios such as 2 + 1 space-times [50][51][52][53][54][55], higher dimensions [56,57], asymptotically (A-)dS space-times [58], for axially symmetric systems and rotating black holes [59], hairy black holes [60][61][62], Cosmology [63,64], solutions in the background of Reissner-Nordström space-time [65][66][67], modified gravity theories [68][69][70][71][72][73][74][75][76][77][78], as well in braneworld gravity [79][80]…”

Energy exchange between relativistic fluids: the polytropic case

“…We see that the effects are greater for the innermost layers, and are always proportional to K and 1/n. The same total effective pressure (73) is displayed in Figs. 2 and 3, now showing the effects of polytropes on stellar spheres explicitly.…”

Isotropization and Complexity of Decoupled Solutions in Self-interacting Brans-Dicke Gravity

“…Recently, Contreras and Fuenmayor [39] analyzed the stability of static spheres via gravitational cracking in the background of decoupling. Sultana [40] showed the applicability of decoupling through MGD in higher order theories as well.…”