The Newtonian limit of spacetimes for accelerated particles and black holes

TL;DR

This paper investigates the Newtonian limit of boost-rotation symmetric spacetimes, which describe uniformly accelerated particles and black holes, confirming their physical plausibility and connection to classical mechanics.

Contribution

It provides a detailed analysis of the Newtonian limit of these spacetimes using Ehlers frame theory, demonstrating their physical relevance and illustrating with specific examples.

Findings

Newtonian limit corresponds to classical point masses with uniform acceleration

Boost-rotation symmetric spacetimes are physically plausible models of accelerated objects

The analysis confirms the significance of these solutions in representing moving finite objects

Abstract

Solutions of vacuum Einstein's field equations describing uniformly accelerated particles or black holes belong to the class of boost-rotation symmetric spacetimes. They are the only explicit solutions known which represent moving finite objects. Their Newtonian limit is analyzed using the Ehlers frame theory. Generic spacetimes with axial and boost symmetries are first studied from the Newtonian perspective. The results are then illustrated by specific examples such as C-metric, Bonnor-Swaminarayan solutions, self-accelerating "dipole particles", and generalized boost-rotation symmetric solutions describing freely falling particles in an external field. In contrast to some previous discussions, our results are physically plausible in the sense that the Newtonian limit corresponds to the fields of classical point masses accelerated uniformly in classical mechanics. This corroborates the physical significance of the boost-rotation symmetric spacetimes.