Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-05-22
Lect.NotesPhys.718:115-163,2007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Chapter contributed to "Quantum Simulations via Analogues: From Phase Transitions to Black Holes", based on the COSLAB Dresden
Scientific paper
10.1007/3-540-70859-6_6
Analogue spacetimes are powerful models for probing the fundamental physical aspects of geometry - while one is most typically interested in ultimately reproducing the pseudo-Riemannian geometries of interest in general relativity and cosmology, analogue models can also provide useful physical probes of more general geometries such as pseudo-Finsler spacetimes. In this chapter we shall see how a 2-component Bose-Einstein condensate can be used to model a specific class of pseudo-Finsler geometries, and after suitable tuning of parameters, both bi-metric pseudo-Riemannian geometries and standard single metric pseudo-Riemannian geometries, while independently allowing the quasi-particle excitations to exhibit a "mass". Furthermore, when extrapolated to extremely high energy the quasi-particles eventually leave the phononic regime and begin to act like free bosons. Thus this analogue spacetime exhibits an analogue of the "Lorentz violation" that is now commonly believed to occur at or near the Planck scale defined by the interplay between quantum physics and gravitational physics. In the 2-component Bose-Einstein analogue spacetime we will show that the mass generating mechanism for the quasi-particles is related to the size of the Lorentz violations. This relates the "mass hierarchy" to the so-called "naturalness problem". In short the analogue spacetime based on 2-component Bose-Einstein condensates exhibits a very rich mathematical and physical structure that can be used to investigate many issues of interest to the high-energy physics, cosmology, and general relativity communities.
Liberati Stefano
Visser Matt
Weinfurtner Silke
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