Black Holes, Wormholes, and the Disappearance of Global Charge

TL;DR

This paper investigates how wormholes can violate global charge conservation during black hole formation and evaporation, showing that all global charge is lost before matter reaches the singularity, affecting Hawking radiation.

Contribution

It provides a model-independent analysis demonstrating that wormholes lead to the disappearance of global charges in black hole processes.

Findings

Global charges are extinguished before matter reaches the singularity.

Hawking radiation contains no global charge due to wormhole effects.

Charge violation is significant at high energy densities inside black holes.

Abstract

One of the paradoxes associated with the theory of the formation and subsequent Hawking evaporation of a black hole is the disappearance of conserved global charges. It has long been known that metric fluctuations at short distances (wormholes) violate global-charge conservation; if global charges are apparently conserved at ordinary energies, it is only because wormhole-induced global-charge-violating terms in the low-energy effective Lagrangian are suppressed by large mass denominators. However, such suppressed interactions can become important at the high energy densities inside a collapsing star. We analyze this effect for a simple model of the black-hole singularity. (Our analysis is totally independent of any detailed theory of wormhole dynamics; in particular it does not depend on the wormhole theory of the vanishing of the cosmological constant.) We find that in general all charge is extinguished before the infalling matter crosses the singularity. No global charge appears in the outgoing Hawking radiation because it has all gone down the wormholes.