Infinitely degenerate exact Ricci-flat solutions in f(R) gravity

Abstract

We obtain an infinite number of exact static, Ricci-flat spherically symmetric vacuum solutions for a class of f(R) theories of gravity. We analytically derive two exact vacuum black-hole solutions for the same class of f(R) theories. The two black-hole solutions have the event-horizon at the same point; however, their asymptotic features are different. Our results suggest that no-hair theorem may not hold for generic modified gravity theories. We discuss the implications of our work to distinguish modified gravity theories from general relativity in gravitational wave detections.

arXiv commentv2: 15 pages, 1 figure, changed title, added an appendix, accepted in Classical and Quantum Gravity

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• Beyond Schwarzschild-de Sitter spacetimes: II. An exact non-Schwarzschild metric in pure $R^2$ gravity and new anomalous properties of $R^2$ spacetimes
• Black Holes with Electric and Magnetic Charges in $F(R)$ Gravity
• Beyond Schwarzschild-de Sitter spacetimes: III. A perturbative vacuum with non-constant scalar curvature in $R+R^2$ gravity
• Nonstatic Reissner-Nordström metric in the perturbative $f(R)$ theory: Embedding in the background of the FLRW cosmology, uniqueness of solutions, the TOV equation
• Birkhoff's Theorem and Uniqueness: A Peek Beyond General Relativity
• Non-triviality of asymptotically flat Buchdahl-inspired metrics in pure $R^2$ gravity
• Primordial Black Holes: A Review of Formation and Evolution