Dynamical response to a stationary tidal field

TL;DR

This paper shows that slowly rotating compact bodies experience a dynamical internal response to gravitomagnetic tidal fields, with interior variables varying over the rotation period, while exterior geometry remains stationary.

Contribution

It reveals the dynamical internal response of rotating bodies to gravitomagnetic tides, a phenomenon not reflected in the exterior spacetime at first order in rotation.

Findings

Interior fluid and metric vary over the rotation period due to gravitomagnetic tides.

Exterior geometry remains stationary despite internal dynamics.

The response is specific to gravitomagnetic components, not gravitoelectric ones.

Abstract

We demonstrate that a slowly rotating compact body subjected to a stationary tidal field undergoes a dynamical response, in which the fluid variables and the interior metric vary on the time scale of the rotation period. This dynamical response requires the tidal field to have a gravitomagnetic component generated by external mass currents; the response to a gravitoelectric tidal field is stationary. We confirm that in a calculation carried out to first order in the body's rotation, the exterior geometry bears no trace of this internal dynamics; it remains stationary in spite of the time-dependent interior.