Role of gravity in the pair creation induced by electric fields

TL;DR

This paper investigates how gravity influences pair creation caused by electric fields in an expanding universe, emphasizing the importance of proper adiabatic renormalization for energy conservation.

Contribution

It highlights the necessity of a specific adiabatic renormalization scheme in curved spacetime to ensure consistent energy-momentum conservation during pair production.

Findings

In Minkowski space, two renormalization schemes are equivalent.

In curved spacetime, only the scheme with a gravitational hierarchy is consistent.

Gravity affects the renormalization process and energy conservation in pair creation.

Abstract

We analyze the pair production induced by homogenous, time-dependent electric fields in an expanding space-time background. We point out that, in obtaining the semiclassical Maxwell equations, two distinct notions of adiabatic renormalization are possible. In Minkowski space the two recipes turn out to be equivalent. However, in the presence of gravity only the recipe requiring an adiabatic hierarchy between the gravitational and the gauge field is consistent with the conservation of the energy-momentum tensor.