Finite-Depth Null Capture and Mass-History Sensitivity in Vaidya Spacetime
Abstract
We formulate a finite-depth endpoint map for past-directed null rays in dynamical black-hole spacetimes, retaining an unresolved label when no terminal is reached before a prescribed optical depth. For regular transverse terminal hits, common-flow, transversality, and separation hypotheses make the regular decision sets open and the endpoint label locally constant. In Schwarzschild spacetime, the resulting finite-depth capture circle converges to the standard critical circle as exp[−L/(3M)] when the cutoff is measured in static-observer optical depth. We then apply the construction to ingoing Vaidya spacetime. Two C4 accretion profiles that coincide on a neighborhood of the observation event, and therefore have identical local mass and metric jets there, nevertheless produce distinct finite-depth critical angles. For the baseline protocol, Δhistα45=0.0819062ε−0.0231767ε2+O(ε3). A backward adjoint gives an explicit causal kernel representing the first-order response to the mass history. The kernel is broad, peaks away from the photon-sphere dwell region, and changes between finite backgrounds even where their instantaneous masses agree. The quadratic coefficient is independently confirmed by centered nonlinear solutions and Richardson extrapolation. These results separate instability-controlled cutoff convergence from globally transported mass-history sensitivity.
Related
- Scalar fields in the background of a linear Vaidya spacetime
- Curved momentum space and finite Landau spectrum in κ-Minkowski spacetime
- Finite quantum gravity in locally conformally flat spacetime through covariant spectral regularization
- Circular acceleration in Minkowski spacetime: thermality versus finite size
- Electronic-Structure Control of Nuclear Excitation by Electron Capture in Finite-Density 229Th
BibTeX
@misc{palamara2026finitedepth,
title = {{Finite-Depth Null Capture and Mass-History Sensitivity in Vaidya Spacetime}},
author = {Jorge Luis Palamara and Jorge R. Palamara},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41922},
eprint = {2610.41922},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41922},
}
RIS
TY - UNPB
TI - Finite-Depth Null Capture and Mass-History Sensitivity in Vaidya Spacetime
AU - Jorge Luis Palamara
AU - Jorge R. Palamara
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41922
UR - https://arxiv.org/abs/2610.41922
AB - We formulate a finite-depth endpoint map for past-directed null rays in dynamical black-hole spacetimes, retaining an unresolved label when no terminal is reached before a prescribed optical depth. For regular transverse terminal hits, common-flow, transversality, and separation hypotheses make the regular decision sets open and the endpoint label locally constant. In Schwarzschild spacetime, the resulting finite-depth capture circle converges to the standard critical circle as exp[−L/(3M)] when the cutoff is measured in static-observer optical depth. We then apply the construction to ingoing Vaidya spacetime. Two C^4 accretion profiles that coincide on a neighborhood of the observation event, and therefore have identical local mass and metric jets there, nevertheless produce distinct finite-depth critical angles. For the baseline protocol, Δ_histα_45=0.0819062ε−0.0231767ε^2+O(ε^3). A backward adjoint gives an explicit causal kernel representing the first-order response to the mass history. The kernel is broad, peaks away from the photon-sphere dwell region, and changes between finite backgrounds even where their instantaneous masses agree. The quadratic coefficient is independently confirmed by centered nonlinear solutions and Richardson extrapolation. These results separate instability-controlled cutoff convergence from globally transported mass-history sensitivity.
ER -