A no-hair theorem for spherically symmetric black holes in $R^2$ gravity

Abstract

In a recent paper Cañate (CQG, {\bf 35}, 025018 (2018)) proved a no hair theorem to static and spherically symmetric or stationary axisymmetric black holes in general $f(R)$ gravity. The theorem applies for isolated asymptotically flat or asymptotically de Sitter black holes and also in the case when vacuum is replaced by a minimally coupled source having a traceless energy momentum tensor. This theorem excludes the case of pure quadratic gravity, $f(R)=R^2$. In this paper we use the scalar tensor representation of general $f(R)$ theory to show that there are no hairy black hole in pure $R^2$ gravity. The result is limited to spherically symmetric black holes but does not assume asymptotic flatness or de-Sitter asymptotics as in most of the no-hair theorems encountered in the literature. We include an example of a static and spherically symmetric black hole in $R^2$ gravity with a conformally coupled scalar field having a Higgs-type quartic potential.

10 pages

References in corpus (13)

• Limit to General Relativity in f(R) theories of gravity
• Matter instability in modified gravity
• Kerr Black Holes are Not Unique to General Relativity
• The existence of relativistic stars in f(R) gravity
• Spherically symmetric spacetimes in f(R) gravity theories
• Static Solutions for 4th order gravity
• Stellar configurations in f(R) theories of gravity
• Reconstructing the inflationary $f(R)$ from observations
• Jordan frame no-hair for spherical scalar-tensor black holes
• Thermodynamics of topological black holes in $R^2$ gravity
• Comments on "Solar System constraints to general f(R) gravity"
• Constraining Newtonian stellar configurations in f(R) theories of gravity
• Creation of the universe with a stealth scalar field

Cited by in corpus (24)

• Anisotropic compact stars in $f(R)$ gravity
• Novel Black-Hole Solutions in Einstein-Scalar-Gauss-Bonnet Theories with a Cosmological Constant
• Spherically symmetric black holes with electric and magnetic charge in extended gravity: Physical properties, causal structure, and stability analysis in Einstein's and Jordan's frames
• Large and Ultra-compact Gauss-Bonnet Black Holes with a Self-interacting Scalar Field
• Non-trivial black hole solutions in $f(R)$ gravitational theory
• On the Existence of Solutions with a Horizon in Pure Scalar-Gauss-Bonnet Theories
• Neutron stars in $f(R)$ gravity and scalar-tensor theories
• Spherical inhomogeneous solutions of Einstein and scalar-tensor gravity: a map of the land
• Anisotropic compact stars in higher-order curvature theory
• $f(\mathsf{R})$ Gravity Wormholes sourced by a Phantom Scalar Field
• Thermodynamic topology of topological black hole in $F(R)$-ModMax gravity's rainbow
• Quasinormal modes and their anomalous behavior for black holes in $f(R)$ gravity
• Analytic charged BHs in $f(\mathcal{R})$ gravity
• Analytic Electrically Charged Black Holes in $F(R)$-ModMax Theory
• Transforming singular black holes into regular black holes sourced by nonlinear electrodynamics
• Wyman's "other" scalar field solution, Sultana's generalization, and their Brans-Dicke and $R^2$ relatives
• Black Holes with Electric and Magnetic Charges in $F(R)$ Gravity
• A note on the linear stability of black holes in quadratic gravity
• Energy Conditions in Gauss-Bonnet Gravity
• Gravitational analog of the canonical acoustic black hole in Einstein-scalar-Gauss-Bonnet theory
• An innovative black hole solution and thermodynamic properties in higher-order curvature gravity with a scalar field
• Black holes with scalar hair: Extending from and beyond the Schwarzschild solution
• Exact Black Hole Solutions with a Conformally Coupled Scalar Field and Dynamic Ricci Curvature in $f(R)$ Gravity Theories
• On instabilities of stationary scalar field configurations supported by reflecting compact stars