The Effect of Negative-Energy Shells on the Schwarzschild Black Hole

TL;DR

This paper constructs and corrects Penrose diagrams for Schwarzschild spacetimes with matter shells, demonstrating that negative-energy shells can connect causally separated regions, revealing new insights into black hole horizon dynamics.

Contribution

It provides corrected Penrose diagrams for shells in Schwarzschild spacetime and explores the causal effects of negative-energy shells on black hole horizons.

Findings

Negative-energy shells cause horizon shifts that enable causal contact between exterior regions.

Successive shells with opposite energies can connect separate Schwarzschild regions causally.

The diagrammatic techniques clarify the impact of matter shells on black hole causal structure.

Abstract

We construct Penrose diagrams for Schwarzschild spacetimes joined by massless shells of matter, in the process correcting minor flaws in the similar diagrams drawn by Dray and 't Hooft, and confirming their result that such shells generate a horizon shift. We then consider shells with negative energy density, showing that the horizon shift in this case allows for travel between the heretofore causally separated exterior regions of the Schwarzschild geometry. These drawing techniques are then used to investigate the properties of successive shells, joining multiple Schwarzschild regions. Again, the presence of negative-energy shells leads to a causal connection between the exterior regions, even in (some) cases with two successive shells of equal but opposite total energy.