# Geodesics in supersymmetric microstate geometries

## TL;DR

This paper investigates the classical instability of supersymmetric microstate geometries by analyzing geodesic behavior, trapping phenomena, and energy extraction processes, revealing key differences from black hole geometries.

## Contribution

It provides a detailed study of null geodesic trapping and instability mechanisms in microstate geometries, highlighting differences from black hole spacetimes.

## Key findings

- Existence of multiple types of trapped null geodesics
- Instability triggered by particles far from the ergosurface
- Differences in geodesic behavior compared to black holes

## Abstract

It has been argued that supersymmetric microstate geometries are classically unstable. One argument for instability involves considering the motion of a massive particle near the ergosurface of such a spacetime. It is shown that the instability can be triggered by a particle that starts arbitrarily far from the ergosurface. Another argument for instability is related to the phenomenon of stable trapping of null geodesics in these geometries. Such trapping is studied in detail for the most symmetrical microstate geometries. It is found that there are several distinct types of trapped null geodesic, both prograde and retrograde. Several important differences between geodesics in microstate geometries and black hole geometries are noted. The Penrose process for energy extraction in these geometries is discussed.