# Evaporating black-holes, wormholes, and vacuum polarisation: must they always conserve charge?

## TL;DR

This paper explores how topologically complex spacetimes can violate global charge conservation in electromagnetism, proposing gauge freedoms in D and H fields to address charge transfer in black hole evaporation and wormholes.

## Contribution

It introduces a gauge freedom in electromagnetic excitation fields D and H, challenging the standard charge conservation assumptions in non-trivial topologies.

## Key findings

- Charge conservation can be violated in non-trivial topologies due to mathematical assumptions.
- Gauge freedom in D and H fields allows alternative interpretations of charge transfer.
- Proposes a new perspective on charge passing through wormholes without necessarily increasing wormhole charge.

## Abstract

A careful examination of the fundamentals of electromagnetic theory shows that due to the underlying mathematical assumptions required for Stokes' Theorem, global charge conservation cannot be guaranteed in topologically non-trivial spacetimes. However, in order to break the charge conservation mechanism we must also allow the electromagnetic excitation fields D, H to possess a gauge freedom, just as the electromagnetic scalar and vector potentials phi and A do. This has implications for the treatment of electromagnetism in spacetimes where black holes both form and then evaporate, as well as extending the possibilities for treating vacuum polarisation. Using this gauge freedom of D, H we also propose an alternative to the accepted notion that a charge passing through a wormhole necessarily leads to an additional (effective) charge on the wormhole's mouth.