Fate of initially bound timelike geodesics in spherical boson stars

TL;DR

This paper investigates the evolution of bound timelike geodesics in spherical boson stars, revealing how their fate depends on stability, collapse, or migration, and identifying critical radii influencing whether orbits plunge into black holes or remain bound.

Contribution

It provides the first detailed analysis of the behavior of initially bound geodesics in different boson star scenarios, including collapse and migration, highlighting critical radii and orbit stability.

Findings

Bound orbits in stable boson stars remain stable.

In collapsing boson stars, orbits either become unbound or plunge into black holes.

In migrating boson stars, orbits can remain bound or become unbound depending on initial radius.

Abstract

Boson stars are horizonless compact objects and they could possess novel geodesic orbits under the equilibrium assumption, which differ from those in black hole backgrounds. However, unstable boson stars may collapse into black holes or migrate to stable states, resulting in an inability to maintain the initially bound geodesic orbits within the backgrounds of unstable boson stars. To elucidate the fate of initially bound geodesic orbits in boson stars, we present a study of geodesics within the spherical space-times of stable, collapsing, and migrating boson stars. We focus on timelike geodesics that are initially circular or reciprocating. We verify that orbits initially bound within a stable boson star persist in their bound states. For a collapsing boson star, we show that orbits initially bound and reciprocating finally either become unbound or plunge into the newly formed black hole, depending on their initial maximal radii. {For initially circular geodesics, we have discovered the existence of a critical radius. Orbits with radii below this critical value are found to plunge into the newly formed black hole, whereas those with radii larger than the critical radius continue to orbit around the vicinity of the newly formed black hole, exhibiting nonzero eccentricities}. For the migrating case, a black hole does not form. In this case, the reciprocating orbits span a wider radial range. For initially circular geodesics, orbits with small radii become unbound, and orbits with large radii remain bound with nonvanishing eccentricities. This geodesic study provides a novel approach to investigating the gravitational collapse and migration of boson stars.