Regular Black Holes: Towards a New Paradigm of Gravitational Collapse

Description

Black holes are one of the most fascinating predictions of general relativity. They are the natural product of the complete gravitational collapse of matter and today we have a body of observational evidence supporting the existence of black holes in the Universe. However, general relativity predicts that at the center of black holes there are spacetime singularities, where predictability is lost and standard physics breaks down. It is widely believed that spacetime singularities are a symptom of the limitations of general relativity and must be solved within a theory of quantum gravity. Since we do not have yet any mature and reliable candidate for a quantum gravity theory, researchers have studied toy-models of singularity-free black holes and of singularity-free gravitational collapses in order to explore possible implications of the yet unknown theory of quantum gravity. This book reviews all main models of regular black holes and non-singular gravitational collapses proposed in the literature, and discuss the theoretical and observational implications of these scenarios. Preface Contents Contributors 1 Regular Rotating Black Holes and Solitons with the de Sitter/Phantom Interiors 1.1 Introduction 1.2 Geometry 1.2.1 Metric and Spacetime Symmetry 1.2.2 Horizons and Ergoregions 1.3 Interiors of Regular Rotating Black Holes and Spinning Solitons 1.3.1 Stress-Energy Tensor 1.3.2 Two Types of Regular Interiors 1.3.3 Light Rings 1.4 Observational Signatures 1.4.1 Identification of RRBH by its Shadow 1.4.2 Primordial RRBHs and G-Lumps as Dark Matter Candidates 1.5 Conclusions References 2 Regular Black Holes Sourced by Nonlinear Electrodynamics 2.1 Introduction 2.2 Static Spherically Symmetric Space-Times. Regularity and Asymptotic Conditions 2.3 L(f) NED Coupled to General Relativity. FP Duality 2.3.1 Field Equations 2.3.2 FP Duality 2.4 Regular Black Holes with L = L(f) 2.4.1 Magnetic, Electric and Dyonic Solutions 2.4.2 Regularity and no-go Theorems 2.4.3 Causality and Unitarity 2.4.4 Light Propagation and the Effective Metric 2.4.5 Dynamic Stability 2.4.6 Examples 2.5 NED with More General Lagrangians 2.5.1 Systems with L = L(f,h) 2.5.2 Systems with L = L(f, J) 2.6 Conclusion References 3 How Strings Can Explain Regular Black Holes 3.1 Introduction 3.1.1 Three Facts About Evaporating Black Holes 3.2 Can One Probe Length Scales Smaller than sqrtα? 3.2.1 How to Derive a Consistent ``Particle-Black Hole'' Metric 3.3 What T-duality can tell us About Black Holes 3.3.1 How to Implement T-duality Effects 3.4 A Short Guide to Black Holes in Noncommutative Geometry 3.5 Conclusions References 4 Regular Black Holes from Higher-Derivative Effective Delta Sources 4.1 Introduction 4.2 Higher-Derivative Gravity Models 4.3 Higher-Derivative Gravity in the Newtonian Limit 4.3.1 Linearized Higher-Derivative Gravity 4.3.2 Field Equations in the Newtonian Limit 4.3.3 Effective Delta Sources 4.4 Properties of the Effective Sources and Newtonian Potentials 4.4.1 Regularity and Higher-Order Regularity of the Effective Sources 4.4.2 Regularity of Newtonian-Limit Solutions 4.4.3 Curvature Invariants in the Newtonian Limit 4.5 Selected Examples 4.5.1 Fourth-Derivative Gravity 4.5.2 Polynomial Higher-Derivative Gravity 4.5.3 Nonlocal Gravity 4.6 Regular Black Holes from Effective Delta Sources 4.6.1 General Properties of A(r) and B(r) 4.6.2 Curvature Regularity of the Solutions 4.6.3 Example of Regular Black Hole: The Case of Nonlocal Form Factor 4.7 Concluding Remarks References 5 Black Holes in Asymptotically Safe Gravity and Beyond 5.1 Invitation: Black Holes, Quantum Scale Symmetry and Probes of Quantum Gravity 5.2 A Heuristic Argument for Singularity Resolution from Quantum Scale Symmetry 5.3 Constructing Asymptotic-Safety Inspired Spacetimes 5.3.1 Renormalization-Group Improvement and the Decoupling Mechanism 5.3.2 Scale Dependence of Gravitational Couplings 5.3.3 Scale Identification for Gravitational Solutions 5.4 Spherically Symmetric Black Holes 5.4.1 Construction of Asymptotic-Safety Inspired Black Holes 5.4.2 Singularity-Resolution 5.4.3 Spacetime Structure 5.4.4 Thermodynamics 5.5 Spinning Asymptotic-Safety Inspired Black Holes 5.5.1 Universal and Non-universal Aspects of RG Improvement 5.5.2 The Line Element for the Locally Renormalization-Group Improved Kerr Spacetime 5.5.3 Spacetime Structure and Symmetries 5.5.4 Horizonless Spacetimes 5.6 Formation of Asymptotic-Safety Inspired Black Holes 5.6.1 Spacetime Structure of Gravitational Collapse 5.6.2 Formation of Black Holes in High-Energy Scattering 5.7 Towards Observational Constraints 5.7.1 The Scale of Quantum Gravity 5.7.2 Constraints from Electromagnetic Signatures 5.7.3 Towards Constraints from Gravitational-Wave Signatures 5.8 Generalization Beyond Asymptotic Safety: The Principled-Parameterized Approach to Black Holes 5.9 Summary, Challenges and Open Questions References 6 Regular Black Holes in Palatini Gravity 6.1 Introduction to Metric-Affine Gravity and Resolution of Space-Time Singularities 6.2 Gravitational Models 6.2.1 f(mathcalR) Gravity 6.2.2 Quadratic Gravity 6.2.3 Eddington-Inspired Born-Infeld Gravity 6.2.4 The Ricci-Based Gravity Family 6.2.5 Einstein Frame and the Mapping Method 6.3 Spherically Symmetric Black Hole Solutions 6.3.1 A Case-Sample on the Direct Attack to Solve the Palatini Equations 6.3.2 Other Spherically Symmetric Solutions 6.3.3 Mapping-Generated Solutions 6.4 Regularity Criteria 6.4.1 Curvature Divergences 6.4.2 Geodesic Completeness and Mechanisms for Its Restoration 6.4.3 The Non-equivalence Between Geodesic Completeness and Curvature Divergences 6.4.4 Tidal Forces and Congruences of Geodesics 6.4.5 Completeness of Accelerated Paths 6.4.6 Further Tests? 6.5 Closing Thoughts References 7 Regular Black Holes from Loop Quantum Gravity 7.1 Introduction 7.2 The Schwarzschild Interior 7.2.1 The Framework 7.2.2 Singularity Resolution, Causal Structure and Curvature Bounds 7.2.3 Summary of LQG Investigations 7.3 The Schwarzschild Exterior 7.3.1 The Underlying Framework 7.3.2 Quantum Corrected, Near Horizon Geometry 7.3.3 Asymptotic Properties of the Effective Geometry 7.4 Quantum Geometric Effects in Gravitational Collapse: Illustrations 7.4.1 Dust Field Collapse Models 7.4.2 Quantum Geometric Effects in the Critical Phenomena 7.5 Black Hole Evaporation 7.5.1 Setting the Stage 7.5.2 Black Hole Evaporation in LQG 7.6 Discussion References 8 Gravitational Vacuum Condensate Stars 8.1 The Issue of the Final State of Gravitational Collapse 8.2 What's the (Quantum) Matter with Black Holes? 8.3 The Proposed Solution: Gravitational Condensate Stars 8.3.1 Background and Motivations for the First Gravastar Model 8.3.2 The First Gravastar Model 8.3.3 The Lanczos–Israel Conditions at the r1 and r2 Boundaries 8.3.4 Thermodynamic Stability 8.4 The Schwarzschild Constant barρ Interior Solution Revisited: Evading the Buchdahl Bound and Determination of C 8.4.1 Redshift Modified Boundary Conditions on a Null Hypersurface 8.4.2 The `First Law' for Spherically Symmetric Gravastars 8.5 Slowly Rotating Gravastars: Junction Conditions and Moment of Inertia 8.6 Macroscopic Effects of the Quantum Conformal Anomaly 8.6.1 The Two Dimensional Conformal Anomaly and Stress Tensor 8.6.2 The Conformal Anomaly Effective Action and Stress Tensor in Four Dimensions 8.6.3 The Stress Tensor of the Conformal Anomaly on the Schwarzschild and de Sitter Horizons 8.6.4 Determination of ε and ell for a Gravastar 8.7 The EFT of Gravity, and Dynamical Vacuum Energy References 9 Singularity-Free Gravitational Collapse: From Regular Black Holes to Horizonless Objects 9.1 Singularity Regularization in Effective Geometries 9.1.1 General Relativity: Singularity Theorems and Geodesic Incompleteness 9.1.2 Beyond General Relativity: Deforming Black Holes into Geodesically Complete Spacetimes 9.2 Geodesically Complete Alternatives to Static Black Holes 9.2.1 Regularization in Simply Connected Topologies 9.2.2 Regularization in Non-simply Connected Topologies 9.2.3 Comment on ``Mixed'' Geometries 9.3 Dynamical Geometries 9.3.1 Dynamical Regularization in Simply Connected Topologies 9.3.2 Dynamical Regularization in Non-simply Connected Topologies 9.3.3 Dynamical Regularization in ``Mixed'' Cases 9.4 Discussion and Wrap-up References 10 Stability Properties of Regular Black Holes 10.1 Introduction 10.2 Spherically Symmetric Spacetimes: A Primer 10.3 Regular Black Holes 10.3.1 de Sitter Cores 10.3.2 Examples of Regular Black Hole Geometries 10.3.3 Hawking Effect and Final State 10.4 The Elementary Mechanics of Mass-Inflation 10.4.1 Colliding Mass-Shells and DTR-Relations 10.4.2 Dynamical Models of Mass Inflation 10.4.3 Mass-Inflation Instability and Singularities of Spacetime 10.5 Mass-Inflation for Regular Black Holes 10.5.1 The Ori-Model—General Setup and Dynamics 10.5.2 The Ori-Model on Static Backgrounds 10.5.3 The Ori-Model Including Hawking Radiation 10.6 Conclusions References 11 Regular Rotating Black Holes 11.1 A Glance at Classical Rotating Black Holes 11.2 Kerr-like Rotating Black Holes 11.3 Regularity in Kerr-like Rotating Black Holes 11.4 Violation of the Energy Conditions 11.5 Extensions Beyond r=0 11.6 Maximal Extensions, Null Horizons and Global Structure 11.7 Causality 11.8 Thermodynamics 11.9 Obtaining Regular Rotating Black Hole Models 11.9.1 Generalized Newman-Janis Algorithms 11.10 Phenomenology 11.10.1 Shadows 11.11 Summary References 12 Semi-classical Dust Collapse and Regular Black Holes 12.1 Introduction 12.2 Interior: Gravitational Collapse 12.2.1 Regularity and Scaling 12.2.2 Trapped Surfaces, Singularities and Energy Conditions 12.2.3 Semi-classical Collapse 12.3 Exterior: Regular Black Holes 12.3.1 Regular Black Holes in Non-linear Electrodynamics 12.4 Matching 12.4.1 Spherical Time-Like Matching 12.4.2 Interior Geometry: Collapse 12.4.3 Exterior Geometry: Regular Black Holes 12.5 Dust Collapse 12.5.1 Homogeneous Dust 12.5.2 Schwarzschild in Lemaìtre Coordinates 12.5.3 Semi-classical Homogeneous Dust 12.5.4 NLED Black Holes in Lemaitre Coordinates 12.5.5 Final Fates 12.5.6 Trapped Surfaces 12.5.7 Example: Collapse and Bounce in LQG 12.5.8 Example: Collapse to the Hayward Black Hole 12.6 Conclusions References 13 Gravitational Collapse with Torsion and Universe in a Black Hole 13.1 Torsion and Regular Black Holes 13.2 Einstein–Cartan Gravity 13.3 Gravitational Collapse of a Homogeneous Sphere 13.4 Spinless Dustlike Sphere 13.5 Spin-fluid Sphere 13.6 Nonsingular Bounce and Formation of a New Universe 13.7 Particle Production 13.8 Inflation and Oscillations References