On the Resolution of the Time-Like Singularities in Reissner-Nordstrom and Negative-Mass Schwarzschild

TL;DR

This paper demonstrates that certain classical time-like singularities in Reissner-Nordstrom and negative-mass Schwarzschild spacetimes can be resolved through scalar wave analysis, revealing unique evolution and transmission properties.

Contribution

It shows classical resolution of time-like singularities via scalar waves and generalizes the results to higher dimensions, introducing new insights into singularity behavior.

Findings

Reissner-Nordstrom singularity acts as a 'beam splitter' with 25% transmission.

Scalar wave evolution can be uniquely defined across certain singularities.

Negative-mass Schwarzschild singularity is fully reflecting, indicating different resolution mechanisms.

Abstract

Certain time-like singularities are shown to be resolved already in classical General Relativity once one passes from particle probes to scalar waves. The time evolution can be defined uniquely and some general conditions for that are formulated. The Reissner-Nordstrom singularity allows for communication through the singularity and can be termed "beam splitter" since the transmission probability of a suitably prepared high energy wave packet is 25%. The high frequency dependence of the cross section is w^{-4/3}. However, smooth geometries arbitrarily close to the singular one require a finite amount of negative energy matter. The negative-mass Schwarzschild has a qualitatively different resolution interpreted to be fully reflecting. These 4d results are similar to the 2d black hole and are generalized to an arbitrary dimension d>4.