Generation of spherically symmetric metrics in $f\left(R\right)$ gravity

Abstract

In $D-$dimensional spherically symmetric $f\left(R\right)$ gravity there are three unknown functions to be determined from the fourth order differential equations. It is shown that the system remarkably integrates to relate two functions through the third one to provide reduction to second order equations accompanied with a large class of potential solutions. The third function which acts as the generator of the process is $F\left(R\right)=\frac{df\left(R\right)}{dR}.$ We recall that our generating function has been employed as a scalar field with an accompanying self-interacting potential previously which is entirely different from our approach. Reduction of $f\left(R\right)$ theory into system of equations seems to be efficient enough to generate a solution corresponding to each generating function. As particular examples, besides known ones, we obtain new black hole solutions in any dimension $D$. We further extend our analysis to cover non-zero energy-momentum tensors. Global monopole and Maxwell sources are given as examples.

8 pages, no figure, revised version accepted for publication in EPJC

References in corpus (21)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Conditions for the cosmological viability of f(R) dark energy models
• Wormhole geometries in f(R) modified theories of gravity
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Spherically symmetric solutions of modified field equations in f(R) theories of gravity
• The Cosmology of f(R) Gravity in the Metric Variational Approach
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• Matter instability in modified gravity
• Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion
• Spherical symmetry in $f(R)$-gravity
• Collapsing spherical stars in f(R) gravity
• Cylindrical solutions in metric f(R) gravity
• Spherically symmetric spacetimes in f(R) gravity theories
• Reconstructing the inflationary $f(R)$ from observations
• $f(R)$ gravity theories in the Palatini Formalism constrained from strong lensing
• Thermodynamics of topological black holes in $R^2$ gravity
• Cosmological tests of modified gravity: constraints on $F(R)$ theories from the galaxy clustering ratio
• Black holes and gravitational waves in three-dimensional f(R) gravity

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