Gravitational Atoms from Topological Stars

TL;DR

This paper investigates the bound states of a massive scalar field around topological stars, revealing a gravitational atom with unique spectral properties that distinguish these objects from black holes.

Contribution

It introduces the concept of a gravitational atom formed by scalar fields around topological stars and analyzes the spectral regimes based on field wavelength and star size.

Findings

Bound states are strictly normal modes, forming a genuine gravitational atom.

The spectrum varies from hydrogen-like to localized modes depending on the Compton wavelength.

The spectrum becomes richer when the field's wavelength is comparable to the star's size, including charge and Kaluza--Klein modes.

Abstract

We study the bound states of a massive scalar field around a topological star, and show that these are strictly normal modes. This yields a genuine gravitational atom, sharply distinguishing horizonless objects from black holes. We show that the modes are controlled by the field's Compton wavelength compared to the size of the star. When the Compton wavelength is large, the field forms a cloud with a hydrogen-like spectrum, while in the opposite regime it is localized along timelike trajectories. When the two scales are comparable the spectrum becomes richer, and we characterize it in detail allowing the field to carry electric charge and Kaluza--Klein momentum.