Black Hole Solutions in $R^2$ Gravity

Abstract

We find static spherically symmetric solutions of scale invariant $R^2$ gravity. The latter has been shown to be equivalent to General Relativity with a positive cosmological constant and a scalar mode. Therefore, one expects that solutions of the $R^2$ theory will be identical to that of Einstein theory. Indeed, we find that the solutions of $R^2$ gravity are in one-to-one correspondence with solutions of General Relativity in the case of non-vanishing Ricci scalar. However, scalar-flat $R=0$ solutions are global minima of the $R^2$ action and they cannot in general be mapped to solutions of the Einstein theory. As we will discuss, the $R=0$ solutions arise in Einstein gravity as solutions in the tensionless, strong coupling limit $M_P\to 0$. As a further result, there is no corresponding Birkhoff theorem and the Schwarzschild black hole is by no means unique in this framework. In fact, $R^2$ gravity has a rich structure of vacuum static spherically symmetric solutions partially uncovered here. We also find charged static spherically symmetric backgrounds coupled to a $U(1)$ field. Finally, we provide the entropy and energy formulas for the $R^2$ theory and we find that entropy and energy vanish for scalar-flat backgrounds.

19 pages, revised version with additional references

References in corpus (21)

• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Black Hole Thermodynamics and Negative Entropy in deSitter and Anti-deSitter Einstein-Gauss-Bonnet gravity
• Gravitational Energy in Quadratic Curvature Gravities
• Superconformal generalizations of the Starobinsky model
• Starobinsky-like Inflationary Models as Avatars of No-Scale Supergravity
• Black Holes in Higher-Derivative Gravity
• On the Starobinsky Model of Inflation from Supergravity
• Shortcuts to high symmetry solutions in gravitational theories
• The Imaginary Starobinsky Model
• Static Solutions for 4th order gravity
• On the Supersymmetric Completion of $R+R^2$ Gravity and Cosmology
• Inflation in scale-invariant theories of gravity
• Inflation in no-scale supergravity
• The Imaginary Starobinsky Model and Higher Curvature Corrections
• Minimal $R+R^2$ Supergravity Models of Inflation Coupled to Matter
• Starobinsky-Like Inflation in Dilaton-Brane Cosmology
• Black Holes in Higher Dimensional Gravity Theory with Quadratic in Curvature Corrections
• Vacuum structure in a chiral R+R^n modification of pure supergravity
• The Gauss-Bonnet Coupling Constant in Classically Scale-Invariant Gravity
• Inflation in $R^2$ supergravity with non-minimal superpotentials
• Higher Curvature Supergravity, Supersymmetry Breaking and Inflation

Cited by in corpus (3)

• ${\mathcal{R}}^2$ Supergravity
• Aspects of Conformal Supergravity
• Path Integrals in Quadratic Gravity