Analog gravity from field theory normal modes?

TL;DR

This paper shows that linearizing field theories around non-trivial backgrounds naturally produces an effective curved spacetime geometry, which can simulate aspects of general relativity and suggests gravity as an emergent phenomenon.

Contribution

It demonstrates that effective Lorentzian geometries emerge from linearized field theories, linking classical and quantum aspects to gravity's emergence.

Findings

Linearization yields a unique effective metric for scalar fields.

Quantization introduces terms resembling Einstein-Hilbert action.

Effective geometry is robust and analogous to emergent hydrodynamics.

Abstract

We demonstrate that the emergence of a curved spacetime ``effective Lorentzian geometry'' is a common and generic result of linearizing a field theory around some non-trivial background. This investigation is motivated by considering the large number of ``analog models'' of general relativity that have recently been developed based on condensed matter physics, and asking whether there is something more fundamental going on. Indeed, linearization of a classical field theory (a field theoretic ``normal mode analysis'') results in fluctuations whose propagation is governed by a Lorentzian-signature curved spacetime ``effective metric''. For a single scalar field, this procedure results in a unique effective metric, which is quite sufficient for simulating kinematic aspects of general relativity (up to and including Hawking radiation). Quantizing the linearized fluctuations, the one-loop effective action contains a term proportional to the Einstein--Hilbert action, suggesting that while classical physics is responsible for generating an ``effective geometry'', quantum physics can be argued to induce an ``effective dynamics''. The situation is strongly reminiscent of Sakharov's ``induced gravity'' scenario, and suggests that Einstein gravity is an emergent low-energy long-distance phenomenon that is insensitive to the details of the high-energy short-distance physics. (We mean this in the same sense that hydrodynamics is a long-distance emergent phenomenon, many of whose predictions are insensitive to the short-distance cutoff implicit in molecular dynamics.)