Non-Riemannian effective spacetime effects on Hawking radiation in superfluids

TL;DR

This paper explores how non-Riemannian geometries, including torsion, affect Hawking radiation in superfluid helium-3 and helium-4, revealing conditions under which Hawking radiation is supported or suppressed.

Contribution

It extends the effective spacetime description of Hawking radiation in superfluids to include non-Riemannian geometries with torsion, providing new insights into superfluid effective metrics.

Findings

Non-Riemannian geometry can influence Hawking radiation in superfluids.

Rotational superfluid vortices with torsion do not support Hawking radiation.

Topological solitons in fermionic superfluids can exhibit Hawking radiation in teleparallel spacetime.

Abstract

Riemannian effective spacetime description of Hawking radiation in $^{3}He-A$ superfluids is extended to non-Riemannian effective spacetime. An example is given of non-Riemannian effective geometry of the rotational motion of the superfluid vacuum around the vortex where the effective spacetime Cartan torsion can be associated to the Hawking giving rise to a physical interpretation of effective torsion recently introduced in the literature in the form of an acoustic torsion in superfluid $^{4}He$ (PRD-70(2004),064004). Curvature and torsion singularities of this $^{3}He-A$ fermionic superfluid are investigated. This Lense-Thirring effective metric, representing the superfluid vacuum in rotational motion, is shown not support Hawking radiation when the isotropic $^{4}He$ is restored at far distances from the vortex axis. Hawking radiation can be expressed also in topological solitons (moving domain walls) in fermionic superfluids in non-Riemannian (teleparallel) $(1+1)$ dimensional effective spacetime. A teleparallel solution is proposed where the quasiparticle speed is determined from the teleparallel geometry.