New Horizons in Effective Field Theory?

TL;DR

This paper investigates a general scalar-tensor effective field theory with multiple propagation cones, demonstrating that stationary black hole horizons remain null with respect to the metric, preserving the fundamental concept of Killing horizons despite complex wave propagation.

Contribution

It proves that stationary black hole horizons are null in the metric and that all propagation cones touch the horizon, supporting the continued relevance of Killing horizons in complex theories.

Findings

Black hole horizons are null with respect to the metric.

All propagation cones touch the horizon.

Killing horizon concept remains valid in complex theories.

Abstract

We consider the most general parity symmetric effective scalar tensor theory in four dimensions containing terms up to fourth derivative order in the Lagrangian. It has been shown [H.S. Reall, Phys. Rev. D 103 (2021), 084027] that this theory has three polarizations generically goverened by different (nested) propagation cones, neither of which in general coincides with the lightcone as defined by the metric. Consequently, the notion of black hole horizon must be defined relative to the widest propagation cone, and not with respect to the metric. We provide two theorems stating that, nevertheless, the horizon of a \emph{stationary} black hole is null with respect to the metric, and that, in fact, all three propagation cones touch on the horizon. The conditions in these theorems allow for rotating black holes. Our theorems thereby suggest that the notion of Killing horizon, central in most discussions of black hole thermodynamics, retains its fundamental status, and that certain thermodynamic paradoxes associated with multiple propagation cones are evaded.