Kinematics of discretely self-similar spherically symmetric spacetimes

TL;DR

This paper explores the global structure of spherically symmetric spacetimes with discrete self-similarity, introducing fundamental building blocks called 'fan' and 'splash' that contain invariant null geodesics.

Contribution

It provides a framework for constructing such spacetimes from basic components, enhancing understanding of their geometric and causal properties.

Findings

All such spacetimes can be built from 'fan' and 'splash' blocks.

Each block contains a self-similarity horizon with an invariant null geodesic.

The structure elucidates the global causal and geometric features of discretely self-similar spacetimes.

Abstract

We summarize the consequences of the twin assumptions of (discrete) self-similarity and spherical symmetry for the global structure of a spacetime. All such spacetimes can be constructed from two building blocks, the "fan" and "splash". Each building block contains one radial null geodesic that is invariant under the self-similarity (self-similarity horizon).