Violation of unitarity by Hawking radiation does not violate energy-momentum conservation

TL;DR

This paper challenges the belief that non-unitary Hawking radiation violates energy-momentum conservation by showing that high Hamiltonian degeneracy allows local non-unitary evolution without such violations, especially in gravitational systems.

Contribution

It demonstrates that the Banks-Susskind-Peskin argument relies on an assumption not valid for systems with many degrees of freedom, and explicitly constructs energy-momentum conserving Lindblad operators for non-unitary Hawking radiation.

Findings

High degeneracy of the Hamiltonian permits local non-unitary evolution without energy-momentum violation.

Energy-momentum is conserved in a broad class of non-unitary systems with gravity.

Explicit Lindblad operators for non-unitary Hawking radiation are constructed and shown to conserve energy-momentum.

Abstract

An argument by Banks, Susskind and Peskin (BSP), according to which violation of unitarity would violate either locality or energy-momentum conservation, is widely believed to be a strong argument against non-unitarity of Hawking radiation. We find that the whole BSP argument rests on the crucial assumption that the Hamiltonian is not highly degenerate, and point out that this assumption is not satisfied for systems with many degrees of freedom. Using Lindblad equation, we show that high degeneracy of the Hamiltonian allows local non-unitary evolution without violating energy-momentum conservation. Moreover, since energy-momentum is the source of gravity, we argue that energy-momentum is necessarily conserved for a large class of non-unitary systems with gravity. Finally, we explicitly calculate the Lindblad operators for non-unitary Hawking radiation and show that they conserve energy-momentum.