Maximal Acceleration Is Nonrotating

TL;DR

This paper investigates special congruences of worldlines in stationary axisymmetric spacetimes, defining locally extremal acceleration conditions and deriving explicit formulas, with applications to Kerr-Newman and astrophysical objects.

Contribution

It introduces the concept of Nonrotating Acceleration Worldlines (NAW) and related congruences, providing explicit formulas and analyzing their properties in various gravitational fields.

Findings

Formulas for SCALE properties in Kerr-Newman spacetime

SCAM is counter-rotating in weak-field limit

Applications to stars and Solar System gravitational fields

Abstract

In a stationary axisymmetric spacetime, the angular velocity of a stationary observer that Fermi-Walker transports its acceleration vector is also the angular velocity that locally extremizes the magnitude of the acceleration of such an observer, and conversely if the spacetime is also symmetric under reversing both t and phi together. Thus a congruence of Nonrotating Acceleration Worldlines (NAW) is equivalent to a Stationary Congruence Accelerating Locally Extremely (SCALE). These congruences are defined completely locally, unlike the case of Zero Angular Momentum Observers (ZAMOs), which requires knowledge around a symmetry axis. The SCALE subcase of a Stationary Congruence Accelerating Maximally (SCAM) is made up of stationary worldlines that may be considered to be locally most nearly at rest in a stationary axisymmetric gravitational field. Formulas for the angular velocity and other properties of the SCALEs are given explicitly on a generalization of an equatorial plane, infinitesimally near a symmetry axis, and in a slowly rotating gravitational field, including the weak-field limit, where the SCAM is shown to be counter-rotating relative to infinity. These formulas are evaluated in particular detail for the Kerr-Newman metric. Various other congruences are also defined, such as a Stationary Congruence Rotating at Minimum (SCRAM), and Stationary Worldlines Accelerating Radially Maximally (SWARM), both of which coincide with a SCAM on an equatorial plane of reflection symmetry. Applications are also made to the gravitational fields of maximally rotating stars, the Sun, and the Solar System.