On the Kerr metric in a synchronous reference frame

TL;DR

This paper explores the Kerr metric within a synchronous reference frame derived from proper time and initial conditions, leading to a new coordinate system that retains key singularity properties of the original metric.

Contribution

It introduces a novel synchronous coordinate system for the Kerr metric, analogous to the Lemaitre metric, with singularities confined to the physical ring singularity.

Findings

The singularities are limited to the physical Kerr singularity.

The coordinate transformation preserves the interpretation of initial conditions at large distances.

The new frame offers insights into the structure of the Kerr spacetime.

Abstract

The Kerr metric is considered in a synchronous frame of reference obtained by using proper time and initial conditions for particles that freely move along a certain set of trajectories as coordinates. Modifying these coordinates in a certain way (keeping their interpretation as initial values at large distances), we still have a synchronous frame and the direct analogue of the Lemaitre metric, the singularities of which are exhausted by the physical Kerr singularity (the singularity ring).