New solutions of the Ermakov-Pinney equation in curved space-time
General Relativity and Quantum Cosmology
2020-07-01 v2 High Energy Physics - Theory
Abstract
An Ermakov-Pinney-like equation associated with the scalar wave equation in curved space-time is here studied. The example of Schwarzschild space-time considered in the present work shows that this equation can be viewed more as a model equation, with interesting applications in black hole physics. Other applications studied involve cosmological space-times (de Sitter) and pulse of plane gravitational waves. In all these cases the evolution of the Ermakov-Pinney field seems to be consistent with a rapid blow-up, unlike the Schwarzschild case where spatially damped oscillations are allowed. Eventually, the phase function is also evaluated in many of the above space-time models.
Keywords
Cite
@article{arxiv.1912.01869,
title = {New solutions of the Ermakov-Pinney equation in curved space-time},
author = {Donato Bini and Giampiero Esposito},
journal= {arXiv preprint arXiv:1912.01869},
year = {2020}
}
Comments
20 pages, 10 figures. The presentation has been improved