Spectroscopy of Einstein–Skyrme gravitational atom: exact solution, black hole bomb, and Hawking radiation

Abstract

We examine the behavior of relativistic scalar fields around an extremely rare exact, static, spherically symmetric Einstein–Skyrme black hole in 3+1 dimensions that exhibits nonlinear matter interactions. Starting from the covariant Klein–Gordon equation, the angular and radial dynamics are exactly separable: the angular sector is described by spherical harmonics, while the radial equation admits closed-form solutions in terms of confluent Heun functions. Enforcing regularity through the polynomial condition leads to a discrete spectrum of scalar quasibound states with complex energies, where the real part encodes the relativistic binding structure and the imaginary part controls the lifetime of the atom-like configuration. We find that the dominant imaginary contribution is always negative for light scalar fields, implying that the Einstein–Skyrme gravitational atom is intrinsically dissipative and cannot support superradiant amplification or black hole bomb instabilities. Using the same exact wave functions, we analyze Hawking radiation from the outer horizon via the Damour–Ruffini method and extract the associated Hawking temperature. The presence of the Skyrme coupling modifies the horizon geometry, leading to an enhanced decay of quasibound states and a systematic reduction of the Hawking temperature relative to the Schwarzschild case. Our results highlight how nonlinear Skyrme interactions simultaneously stabilize gravitational atoms and reshape black hole thermodynamics.