Schwarzschild solution from a Raychaudhuri-Huygens relation
Abstract
Null-congruences encode the causal structure of spacetime, describing a phase space of radiation channels, whose expansion scalar θ satisfies the Raychaudhuri equation. In spherical symmetry, the expansion scalar of wave fronts of area A=4πr2 satisfies θ= A′/A = 2/r. About a mass M, this carries an encoding area AE = λφℓp2 = λRg r ≤ A in a UV-IR consistent coupling ℓp2= Gℏ/c3 to its Compton phase φ= (mc/ℏ)r ∝ 1/ℏ. Here, λ= 8π is fixed by the Newtonian limit at large distances and the saturation limit AE=A at horizon about M based on the non-local extension of the equivalence principle in Rindler spacetime, without using the Einstein equations. In spherical symmetry, this recovers the Schwarzschild metric from a geometric embedding of p=AE/A, which is directly observable in gravitational lensing. The result shows a non-thermal origin of the scaling dimension of two of gravitational phase space, previously derived based on the second law of thermodynamics by Bekenstein (1973), with possible implications for cosmological spacetime.
Related
- Root-of-unity limit of the An−1 lens elliptic gamma function solution of the star-star relation
- Landau Levels of Landau-Raychaudhuri Equation and Wheeler-DeWitt Crystals.
- Reconstruction of f(Q) Gravity from Geodesic Congruence Dynamics: Raychaudhuri Equation
- Scale-Invariant Non-Collapse from Raychaudhuri Comparison
- Raychaudhuri-Ehlers Kinematics on Quantum State-Space: Caustics and Extrinsic Quantum Geometry
BibTeX
@misc{putten2026schwarzschild,
title = {{Schwarzschild solution from a Raychaudhuri-Huygens relation}},
author = {Maurice H. P. M. van Putten},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19171},
eprint = {2609.19171},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19171},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Schwarzschild solution from a Raychaudhuri-Huygens relation
AU - Maurice H. P. M. van Putten
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.19171
UR - https://arxiv.org/abs/2609.19171
AB - Null-congruences encode the causal structure of spacetime, describing a phase space of radiation channels, whose expansion scalar θ satisfies the Raychaudhuri equation. In spherical symmetry, the expansion scalar of wave fronts of area A=4πr^2 satisfies θ= A^′/A = 2/r. About a mass M, this carries an encoding area A_E = λφℓ_p^2 = λR_g r ≤ A in a UV-IR consistent coupling ℓ_p^2= Gℏ/c^3 to its Compton phase φ= (mc/ℏ)r ∝ 1/ℏ. Here, λ= 8π is fixed by the Newtonian limit at large distances and the saturation limit A_E=A at horizon about M based on the non-local extension of the equivalence principle in Rindler spacetime, without using the Einstein equations. In spherical symmetry, this recovers the Schwarzschild metric from a geometric embedding of p=A_E/A, which is directly observable in gravitational lensing. The result shows a non-thermal origin of the scaling dimension of two of gravitational phase space, previously derived based on the second law of thermodynamics by Bekenstein (1973), with possible implications for cosmological spacetime.
ER -