Spinning gyroscope in an acoustic black hole: precession effects and observational aspects

Chandrachur Chakraborty,Parthasarathi Majumdar

doi:10.1140/epjc/s10052-020-8060-1

Abstract

The exact precession frequency of a freely-precessing test gyroscope is derived for a 2+1 dimensional rotating acoustic black hole analogue spacetime, without making the somewhat unrealistic assumption that the gyroscope is static. We show that, as a consequence, the gyroscope crosses the acoustic ergosphere of the black hole with a finite precession frequency, provided its angular velocity lies within a particular range determined by the stipulation that the Killing vector is timelike over the ergoregion. Specializing to the ‘Draining Sink’ acoustic black hole, the precession frequency is shown to diverge near the acoustic horizon, instead of the vicinity of the ergosphere. In the limit of an infinitesimally small rotation of the acoustic black hole, the gyroscope still precesses with a finite frequency, thus confirming a behaviour analogous to geodetic precession in a physical non-rotating spacetime like a Schwarzschild black hole. Possible experimental approaches to detect acoustic spin precession and measure the consequent precession frequency, are discussed.

Highlights

The direct observation of such precession effects is extremely challenging technically, if not outright impossible, in strong-gravity astrophysical phenomena
We have derived the exact spin precession frequency in the (2 + 1)D stationary and axisymmetric spacetime. From this general formulation, we have shown that the spin precession frequency becomes arbitrarily large as it approaches to the horizon
We have shown that a test spin attached with the zero angular momentum observer (ZAMO) can reach close to the horizon of the draining sink geometry without facing any major problem, i.e., its precession frequency remains finite

Summary

Introduction

The direct observation of such precession effects is extremely challenging technically, if not outright impossible, in strong-gravity astrophysical phenomena. Where K is the timelike Killing vector field appropriate to stationarity of the spacetime In this special situation, it is known that the gyroscope precession frequency coincides with the vorticity field associated with the Killing congruence, i.e., the gyro rotates relative to a corotating frame with an angular velocity. We can construct a new Killing vector from a linear combination, with constant coefficients, of ∂0 and ∂φ With this motivation, we consider here the precession of the spin of gyroscopes attached to stationary observers, whose velocity vectors are proportional to the Killing vectors K = ∂0 + ∂φ [9].

Application to the ‘Draining Sink’ acoustic black hole

At the boundary of ergoregion

Geodetic precession in the ‘non-rotating’ acoustic analogue black hole

Observational prospects

Conclusions and discussions