About this guide: This step-by-step walkthrough develops the complete theory of singularity-free black holes in temporal geometry. Each chapter builds on the previous one, with detailed mathematical derivations and physical explanations.
Chapter 1: Foundation
Setting up the temporal geometry framework, defining the lapse function Φ, and establishing the fundamental equations that govern spacetime in this formulation.
Chapter 2: The Spherical Solution
Deriving the spherically symmetric solution in temporal geometry and showing its equivalence to the Schwarzschild metric in the exterior region.
Chapter 3: Dynamics and the Lapse Field
Understanding how the lapse field Φ evolves dynamically, the role of energy flux, and the connection to gravitational collapse.
Chapter 4: Replacing the Central Singularity
The crucial step: showing how energy conservation and quantum considerations naturally replace the singularity with a quantum core.
Chapter 5: Dynamics of the Absorbing Core
Analyzing how matter and energy interact with the quantum core, including absorption, processing, and eventual re-emission.
Chapter 6: Verifying the Singularity is Gone
Mathematical proof that the solution is singularity-free, checking curvature invariants, energy conditions, and geodesic completeness.
Chapter 7: What Was Enforced vs Chosen
Distinguishing between fundamental requirements (energy conservation, quantum mechanics) and specific choices in constructing the solution.
Chapter 8: Predictions and Testability
Observable consequences of singularity-free black holes, potential experimental signatures, and connections to current observations.
Chapter 9: Final Summary
Synthesis of the complete theory, implications for quantum gravity, the information paradox, and future research directions.