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.

arXiv comment10 pages

References in corpus (40)

• f(R) Theories Of Gravity
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Can modified gravity explain accelerated cosmic expansion?
• Dilatonic Black Holes in Higher Curvature String Gravity
• 1/R gravity and Scalar-Tensor Gravity
• Black hole hair in generalized scalar-tensor gravity
• Black holes in scalar-tensor gravity
• Limit to General Relativity in f(R) theories of gravity
• Black Holes in f(R) theories
• Matter instability in modified gravity
• de Sitter black hole with a conformally coupled scalar field in four dimensions
• Non-perturbative and self-consistent models of neutron stars in R-squared gravity
• Black Holes and Scalar Fields
• Kerr Black Holes are Not Unique to General Relativity
• The existence of relativistic stars in f(R) gravity
• Relativistic stars in f(R) and scalar-tensor theories
• Spherically symmetric spacetimes in f(R) gravity theories
• Relativistic stars in f(R) gravity
• Viable Singularity-Free f(R) Gravity Without a Cosmological Constant
• Stealth Scalar Field Overflying a 2+1 Black Hole
• Static Solutions for 4th order gravity
• Spherically symmetric false vacuum: no-go theorems and global structure
• New no-scalar-hair theorem for black-holes
• ${\mathcal{R}}^2$ inflation from scale invariant supergravity and anomaly free superstrings with fluxes
• Spherically symmetric black holes in $f(R)$ gravity: Is geometric scalar hair supported ?
• Stellar configurations in f(R) theories of gravity
• Reconstructing the inflationary $f(R)$ from observations
• Brans-Dicke Theory with $Λ{\ensuremath >} 0$: Black Holes and Large Scale Structures
• Black holes cannot support conformal scalar hair
• Static and spherically symmetric black holes in $f(R)$ theories
• Jordan frame no-hair for spherical scalar-tensor black holes
• A Rotating Charged Black Hole Solution in f(R) Gravity
• Thermodynamics of topological black holes in $R^2$ gravity
• Comparing scalar-tensor gravity and f(R)-gravity in the Newtonian limit
• Comments on "Solar System constraints to general f(R) gravity"
• Constraining Newtonian stellar configurations in f(R) theories of gravity
• Radiating Kerr-Newman black hole in $f(R)$ gravity
• Scale-invariant rotating black holes in quadratic 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