On the fate of singularities and horizons in higher derivative gravity

Abstract

We study static spherically symmetric solutions of high derivative gravity theories, with 4, 6, 8 and even 10 derivatives. Except for isolated points in the space of theories with more than 4 derivatives, only solutions that are nonsingular near the origin are found. But these solutions cannot smooth out the Schwarzschild singularity without the appearance of a second horizon. This conundrum, and the possibility of singularities at finite r, leads us to study numerical solutions of theories truncated at four derivatives. Rather than two horizons we are led to the suggestion that the original horizon is replaced by a rapid nonsingular transition from weak to strong gravity. We also consider this possibility for the de Sitter horizon.

15 pages, 3 figures, improvements and references added, to appear in PRD

References in corpus (2)

• The family of regular interiors for non-rotating black holes with $T_0^0=T_1^1$
• A weak instability in an expanding universe?

Cited by in corpus (52)

• Spherically Symmetric Solutions in Higher-Derivative Gravity
• Quadratic Gravity
• Not quite a black hole
• Metastability in Quadratic Gravity
• A QCD analogy for quantum gravity
• Regular black holes without mass inflation instability
• On Newtonian singularities in higher derivative gravity models
• Towards a Non-singular Paradigm of Black Hole Physics
• Dimensional Transmutation in Gravity and Cosmology
• Black holes and other exact spherical solutions in Quadratic Gravity
• Effective delta sources and regularity in higher-derivative and ghost-free gravity
• Gravity a la Born-Infeld
• High-Energy Scatterings in Infinite-Derivative Field Theory and Ghost-Free Gravity
• Weak-field limit and regular solutions in polynomial higher-derivative gravities
• What can the quantum liquid say on the brane black hole, the entropy of extremal black hole and the vacuum energy?
• Action principle selection of regular black holes
• Instability of spherically-symmetric black holes in Quadratic Gravity
• Formation and evaporation of quantum black holes from the decoupling mechanism in quantum gravity
• Ultra-Planckian scattering from a QFT for gravity
• Charged black holes in Einsteinian cubic gravity and nonuniqueness
• Not quite black holes at LIGO
• Probing Quadratic Gravity with the Event Horizon Telescope
• Anatomy of a thermal black hole mimicker
• Not quite black holes as dark matter
• Horizonless ultracompact objects and dark matter in quadratic gravity
• Suppression of spacetime singularities in quantum gravity
• Sectional Curvature Bounds in Gravity: Regularisation of the Schwarzschild Singularity
• Classical limit of quantum gravity in an accelerating universe
• 2-2-holes simplified
• A Unified Spectral Approach for Quasinormal Modes of Lee-Wick Black Holes
• On effective models of regular black holes inspired by higher-derivative and nonlocal gravity
• Scale-invariance at the core of quantum black holes
• Visions in Quantum Gravity
• Can black holes have Euclidean cores?
• Toward regular black holes in sixth-derivative gravity
• Geometric obstruction of black holes
• Lectures in Quantum Gravity
• Regular black holes from higher-derivative effective delta sources
• Dark sector production and baryogenesis from not quite black holes
• Dust collapse and horizon formation in Quadratic Gravity
• High-energy properties of the graviton scattering in quadratic gravity
• On thermodynamics of compact objects
• The fate of horizons under quantum corrections
• Structural stability of spherical horizons
• Probing light scalars with not quite black holes
• Black holes and other exact solutions in six-derivative gravity
• Ultraviolet Finiteness or Asymptotic Safety in Higher Derivative Gravitational Theories
• Singularity and differentiability at the origin of static and spherically symmetric black holes
• Birkhoff's Theorem and Uniqueness: A Peek Beyond General Relativity
• Neglected solutions in quadratic gravity
• Axion dark matter with not quite black hole domination
• Charting GLOBs in Asymptotically Safe Gravity