Eguchi-Hanson like space-times in F(R) gravity

Abstract

We consider a model of $F(R)$ gravity in which exponential and power corrections to Einstein-$\Lambda$ gravity are included. We show that this model has 4-dimensional Eguchi-Hanson type instanton solutions in Euclidean space. We then seek solutions to the five dimensional equations for which space-time contains a hypersurface corresponding to the Eguchi-Hanson space. We obtain analytic solutions of the $F(R)$ gravitational field equations, and by assuming certain relationships between the model parameters and integration constants, find several classes of exact solutions. Finally, we investigate the asymptotic behavior of the solutions and compute the second derivative of the $F(R)$ function with respect to the Ricci scalar to confirm Dolgov-Kawasaki stability.

Latex, 20 pages, 6 figures

References in corpus (31)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• Cosmological viability of f(R)-gravity as an ideal fluid and its compatibility with a matter dominated phase
• Friedmann Equations of FRW Universe in Scalar-tensor Gravity, f(R) Gravity and First Law of Thermodynamics
• Future of the universe in modified gravitational theories: Approaching to the finite-time future singularity
• Dark energy and dark matter as curvature effects
• Phantom scalar dark energy as modified gravity: understanding the origin of the Big Rip singularity
• The future evolution and finite-time singularities in $F(R)$-gravity unifying the inflation and cosmic acceleration
• A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function
• Matter instability in modified gravity
• Non-singular exponential gravity: a simple theory for early- and late-time accelerated expansion
• A f(R) gravity without cosmological constant
• Inflation and late-time cosmic acceleration in non-minimal Maxwell-$F(R)$ gravity and the generation of large-scale magnetic fields
• Analysis of Rotation Curves in the framework of R^n gravity
• f(R) gravity theories in Palatini formalism: cosmological dynamics and observational constraints
• A viability criterion for modified gravity with an extra force
• The phase space view of f(R) gravity
• The behavior of $f(R)$ gravity in the solar system, galaxies and clusters
• Can higher curvature corrections cure the singularity problem in f(R) gravity?
• Inflation from R^2 gravity: a new approach using nonlinear electrodynamics
• Kaluza-Klein Multi-Black Holes in Five-Dimensional Einstein-Maxwell Theory
• Taub-NUT/Bolt Black Holes in Gauss-Bonnet-Maxwell Gravity
• Black Holes on Eguchi-Hanson Space in Five-Dimensional Einstein-Maxwell Theory
• Taub-NUT Black Holes in Third order Lovelock Gravity
• Accelerating universe in $f(\mathcal{R})$ brane gravity
• Accelerated expansion in modified gravity with a Yukawa-like term
• An oscillating Universe from the linearized R^{2} theory of gravity
• A spherically symmetric and stationary universe from a weak modification of general relativity
• A non-geodesic motion in the R^-1 theory of gravity tuned with observations

Cited by in corpus (19)

• Phase transition and thermodynamic geometry of Einstein-Maxwell-dilaton black holes
• Charged Black Hole Solutions in Gauss-Bonnet-Massive Gravity
• Thermodynamical Structure of AdS Black Holes in Massive Gravity with Stringy Gauge-Gravity Corrections
• The instabilities and (anti)-evaporation of Schwarzschild-de Sitter black holes in modified gravity
• Phase transition of charged black holes in massive gravity through new methods
• Asymptotically Lifshitz black hole solutions in F(R) gravity
• Neutron stars in Einstein-$\Lambda$ gravity: the cosmological constant effects
• Magnetic brane solutions of Lovelock gravity with nonlinear electrodynamics
• Topological Origin of Holographic Principle: Application to wormholes
• Thermodynamics of $f(R)$ Gravity with Disformal Transformation
• Axial anomaly in nonlinear conformal electrodynamics
• Thermal stability of a special class of black hole solutions in F(R) gravity
• Isotropic universe with almost scale-invariant fourth-order gravity
• Higher-curvature generalization of Eguchi-Hanson spaces
• Exact Solutions to Einstein-Maxwell theory on Eguchi-Hanson Space
• Study of cylindrically symmetric solutions in metric f(R) gravity with constant R
• Self duality in unconventional conformal supersymmetry
• Thermodynamics, Phase Transitions, and Geodesic Structure of F(R)-Phantom Banados-Teitelboim-Zanelli (BTZ) Black Holes
• Nonconformally Ricci-flat instantons in Conformal Gravity with and without nonlinear matter fields