Analog gravity from field theory normal modes?

Details Analog gravity from field theory normal modes? Analog gravity from field theory normal modes?

2001-04-02

arxiv.org/abs/gr-qc/0104001v1

Class.Quant.Grav. 18 (2001) 3595-3610

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Revtex 4 (beta 5); 12 pages in single-column format

Scientific paper

10.1088/0264-9381/18/17/313

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.)

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