New solutions of the Ermakov-Pinney equation in curved space-time

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.

20 pages, 10 figures. The presentation has been improved

References in corpus (3)

• Off-critical parafermions and the winding angle distribution of the O($n$) model
• Bicharacteristics and Fourier integral operators in Kasner spacetime
• The Method of Comparison Equations for Schwarzschild Black Holes

Cited by in corpus (1)

• Einstein, Planck and Vera Rubin: relevant encounters between the Cosmological and the Quantum Worlds