A post-Newtonian Gravitational Collapse Model from Linearized Gravity

TL;DR

This paper develops a gravity-based collapse model derived from linearized gravity, extending the Diási-Penrose model to include gravitomagnetic effects and their influence on rotational degrees of freedom.

Contribution

It introduces a novel collapse mechanism based on linearized gravity that accounts for both gravitoelectric and gravitomagnetic effects, expanding existing models.

Findings

Recovers the Diási-Penrose collapse model for positional degrees of freedom.

Identifies additional collapse effects for rotational degrees of freedom.

Shows that gravitomagnetic effects induce new collapse mechanisms.

Abstract

We introduce a general gravity-related collapse mechanism based on linearized gravity. Starting from the weak-field limit of general relativity, gravitoelectromagnetism suggests an effective coupling between the gravitoelectric potential and the mass density distribution. At the same time, it provides a similar relation for the gravitomagnetic vector potential and the mass current. Following a hybrid (classical-quantum) dynamics approach, these couplings lead to a master equation whose non-unitary part is determined by the underlying mass distribution and currents. When the gravitoelectric potential coupling is considered, the well-known Di\'osi-Penrose collapse model acting on positional degrees of freedom is recovered. However, upon including the gravitomagnetic vector potential, additional collapse mechanisms emerge for rotational degrees of freedom as well as for mixed mass-rotation contributions.