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Gravitational atom spectroscopy

Matteo Della Rocca1,2,*, Thomas F. M. Spieksma3,4, Francisco Duque5, Leonardo Gualtieri1,2, and Vitor Cardoso3,6

  • *Contact author: matteo.dellarocca@phd.unipi.it
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Phys. Rev. D 113, 044043 – Published 17 February, 2026

DOI: https://doi.org/10.1103/c7gl-zzhh

Abstract

Black holes in our Universe are rarely truly isolated, being instead embedded in astrophysical environments such as plasma or dark matter. A particularly intriguing possibility is that light scalar fields form bound states around black holes, producing extended “clouds” known as gravitational atoms. When these clouds become sufficiently compact, the spacetime can no longer be described by a vacuum solution of general relativity. In this regime, one can construct quasistationary, spherically symmetric, self-gravitating scalar gravitational atom configurations. Here, we explore an observationally relevant aspect of these systems by computing their fundamental quasinormal mode. We present a fully relativistic calculation of the axial modes in both the time and frequency domains, finding frequency shifts relative to the vacuum case that depend mostly on the compactness of the gravitational atom. For sufficiently compact configurations, these shifts may be detectable by current or future gravitational wave detectors.

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Phys. Rev. D 113, 044043– Published 17 February, 2026
  • Received 24 November 2025
  • Accepted 28 January 2026
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