TSV-Hawking Radiation: Unified Derivation – From Khronon Action to Anisotropic Power Spectrum v1

Abstract:

This paper provides a first-principles derivation of the modification that the Multipolar Time Hypothesis (TSV) induces on Hawking radiation. Moving beyond conceptual foundations, the work introduces a matter-khronon coupling Lagrangian $\mathcal{L}_{coupling} = -(\chi/2)(u^\mu \partial_\mu \Phi)^2$ as the unique dimension-4 operator coupling a scalar field to the preferred local time direction.

Key Technical Contributions:

1. Lagrangian Formulation: Derivation of the effective metric and the modified dispersion relation $k_\mu k^\mu + \chi(u^\mu k_\mu)^2 = 0$.

2. Anisotropic Mode Density: Proof that the density of quantum vacuum modes follows the flux density function $f(\theta,\beta)$, emerging as a theorem from solid-angle transformation.

3. Bogoliubov Transformation: Calculation of modified coefficients and greybody factors within the TSV framework.

4. Falsifiable Predictions: Prediction of an anisotropic angular power spectrum of Hawking radiation, offering a potential resolution to the black hole information paradox.

Files included:

• PDF: The complete formatted article with all derivations and figures.

• LaTeX (.tex): The source code of the manuscript for full transparency of the mathematical proofs and easier verification by the scientific community.