Hamilton-Jacobi equation and the breaking of the WKB approximation

TL;DR

This paper introduces a straightforward method for analyzing the Hamilton-Jacobi equation in four-dimensional curved spacetimes, identifying conditions that cause the breakdown of the WKB approximation and exploring implications for black holes and cosmic censorship.

Contribution

A new simple geometrical approach to determine when the WKB approximation fails in curved spacetimes, linking it to black hole physics and cosmic censorship.

Findings

Identified geometric conditions causing WKB failure

Linked WKB breakdown to extreme black holes

Discussed implications for cosmic Censorship hypothesis

Abstract

A simple method to deal with four dimensional Hamilton-Jacobi equation for null hypersurfaces is introduced. This method allows to find simple geometrical conditions which give rise to the failure of the WKB approximation on curved spacetimes. The relation between such failure, extreme blackholes and the Cosmic Censor hypothesis is briefly discussed.