2016
DOI: 10.1140/epjc/s10052-016-4164-z
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Generation of spherically symmetric metrics in f(R) gravity

Abstract: In D-dimensional spherically symmetric f (R) gravity there are three unknown functions to be determined from the fourth order differential equations. It is shown that the system remarkably may be integrated to relate two functions through the third one to provide a reduction to second order equations accompanied with a large class of potential solutions. The third function, which acts as the generator of the process, isWe recall that our generating function has been employed as a scalar field with an accompany… Show more

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Cited by 43 publications
(35 citation statements)
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“…The surface energy density, the pressure, and the external tension/pressure are given by Eqs. (38), (39), and (40), respectively. The shell also presents the dipole layer distribution with a non-zero strength given by Eq.…”
Section: Different Curvature Scalars R 1 and Rmentioning
confidence: 99%
See 1 more Smart Citation
“…The surface energy density, the pressure, and the external tension/pressure are given by Eqs. (38), (39), and (40), respectively. The shell also presents the dipole layer distribution with a non-zero strength given by Eq.…”
Section: Different Curvature Scalars R 1 and Rmentioning
confidence: 99%
“…These results were recently extended to any quadratic theory Lagrangian [33]. Within F(R) gravity, several studies have been performed in recent years such as static and spherically symmetric black holes [26,27,[34][35][36][37][38][39], traversable wormholes [40][41][42][43][44][45] and pure double layer bubbles [46].…”
Section: Introductionmentioning
confidence: 99%
“…where r > 0 is the radial coordinate, 0 ≤ θ ≤ π, and 0 ≤ ϕ < 2π are the angular coordinates. This class of static spacetimes in F (R) theories includes (in the metric formalism) several well known exact solutions, among them those with constant curvature scalar R, corresponding to vacuum [18,19] and to a Maxwell field in 3+1 dimensions [19] (for other metrics of this form, see also [20]). For the construction of wormholes, we use the thin-shell formalism in F (R) gravity.…”
Section: Wormhole Constructionmentioning
confidence: 99%
“…This theory can provide a unified picture of both inflation in the early Universe and the accelerated expansion at later times. It is also of interest the study of compact objects within F (R) gravity; in particular, static and spherically symmetric black hole solutions [18][19][20] and traversable wormholes [21,22] were investigated in recent years. The junction conditions have been extended to F (R) gravity in the last decade [23,24]; these conditions are more demanding in non-linear F (R) theories than in General Relativity, because they always require continuity of the trace of the second fundamental form at the shell and, except in the case of quadratic F (R), the continuity of the curvature scalar R. In quadratic F (R), the Ricci scalar can be discontinuous at the matching hypersurface and, as a consequence, the shell will have, besides the standard energy-momentum tensor, an external energy flux vector, an external scalar tension (or pressure), and another energy-momentum contribution resembling classical dipole distributions [25,26], which can be interpreted as a gravitational double layer.…”
Section: Introductionmentioning
confidence: 99%
“…With the Weyl's canonical coordinates, the static solutions for axially symmetric black holes in vacuum have been acquired [44]. Furthermore, d-dimensional static spherically symmetric black holes have been obtained using the generator method [45]. For more references on the static spherically symmetric black holes, we refer to [23, and references therein.…”
mentioning
confidence: 99%