Macroscopic Effects of the Quantum Trace Anomaly

TL;DR

This paper explores how the quantum trace anomaly influences macroscopic gravitational effects by introducing auxiliary scalar fields that encode global geometric and quantum information, affecting the stress tensor near horizons.

Contribution

It provides a local auxiliary field framework to describe the quantum trace anomaly's macroscopic effects in various spacetimes, linking boundary conditions to horizon behavior.

Findings

Auxiliary scalar fields encode global geometric information.

The stress tensor near horizons is determined by a few classical order parameters.

Qualitative global approximations to the quantum stress tensor are achieved.

Abstract

The low energy effective action of gravity in any even dimension generally acquires non-local terms associated with the trace anomaly, generated by the quantum fluctuations of massless fields. The local auxiliary field description of this effective action in four dimensions requires two additional scalar fields, not contained in classical general relativity, which remain relevant at macroscopic distance scales. The auxiliary scalar fields depend upon boundary conditions for their complete specification, and therefore carry global information about the geometry and macroscopic quantum state of the gravitational field. The scalar potentials also provide coordinate invariant order parameters describing the conformal behavior and divergences of the stress tensor on event horizons. We compute the stress tensor due to the anomaly in terms of its auxiliary scalar potentials in a number of concrete examples, including the Rindler wedge, the Schwarzschild geometry, and de Sitter spacetime. In all of these cases, a small number of classical order parameters completely determine the divergent behaviors allowed on the horizon, and yield qualitatively correct global approximations to the renormalized expectation value of the quantum stress tensor.