Late-time behavior of scalar field modes for a collapsing null shell spacetime and for the Unruh state in Schwarzschild spacetime
Phys. Rev. D 112, 045013 – Published 27 August, 2025
DOI: https://doi.org/10.1103/xty8-mxl3
Abstract
The behaviors of the spherically symmetric modes for a massless minimally coupled scalar field are investigated for the Unruh state for Schwarzschild spacetime and the in vacuum state for a spacetime in which a null shell collapses to form a Schwarzschild black hole. In both cases, there are two different sets of solutions to the mode equation that make up the state. For both spacetimes, one set of modes oscillates forever with no damping of the oscillations and the other set approaches zero at late times. The difference between a mode that oscillates forever in the null-shell spacetime and the corresponding mode for the Unruh state at late times vanishes as a power law in time. The modes that approach zero at late times also vanish as a power law in time. In all cases, the power-law damping is preceded by a period of oscillations that appear to be due to quasinormal modes.
