Black Holes

  1. Anatomy of a Black Hole
    1. The Central Singularity
      1. Definition and Properties
        1. Point of Infinite Density
          1. Zero Volume
            1. Infinite Curvature
            2. Mathematical Description
              1. Coordinate Singularities vs. Physical Singularities
                1. Kretschmann Scalar
                2. Physics Breakdown
                  1. Limits of General Relativity
                    1. Need for Quantum Gravity
                      1. Planck Scale Physics
                      2. Cosmic Censorship
                        1. Weak Cosmic Censorship Hypothesis
                          1. Strong Cosmic Censorship Hypothesis
                            1. Implications for Observability
                          2. The Event Horizon
                            1. Fundamental Properties
                              1. Point of No Return
                                1. Null Surface
                                  1. One-Way Membrane
                                  2. Schwarzschild Radius
                                    1. Mathematical Definition
                                      1. Calculation Methods
                                        1. Scaling with Mass
                                        2. Causal Structure
                                          1. Causal Disconnection
                                            1. Information Barriers
                                              1. Light Cones and Causality
                                              2. Horizon Dynamics
                                                1. Area Increase Theorem
                                                  1. Horizon Generators
                                                    1. Surface Gravity
                                                  2. Structure of Rotating Black Holes
                                                    1. Kerr Geometry
                                                      1. Kerr Metric
                                                        1. Ring Singularity
                                                          1. Coordinate Systems
                                                          2. The Ergosphere
                                                            1. Definition and Boundaries
                                                              1. Static Limit Surface
                                                                1. Spacetime Dragging
                                                                  1. Penrose Process
                                                                    1. Energy Extraction Mechanisms
                                                                    2. Multiple Horizons
                                                                      1. Outer Event Horizon
                                                                        1. Inner Cauchy Horizon
                                                                          1. Horizon Structure
                                                                          2. Rotational Effects
                                                                            1. Frame-Dragging
                                                                              1. Preferred Direction of Rotation
                                                                            2. Photon Dynamics
                                                                              1. Photon Sphere
                                                                                1. Unstable Circular Orbits
                                                                                  1. Critical Radius
                                                                                    1. Observational Significance
                                                                                    2. Light Ray Behavior
                                                                                      1. Null Geodesics
                                                                                        1. Deflection Angles
                                                                                          1. Critical Impact Parameters
                                                                                          2. Innermost Stable Circular Orbit
                                                                                            1. Definition for Photons
                                                                                              1. Comparison with Massive Particles

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                                                                                          2. The Theoretical Framework: General Relativity

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                                                                                          4. Formation Mechanisms