Thin accretion disk and gravitational capture cross sections of a quantum Oppenheimer--Snyder black hole immersed in an external magnetic field

Abstract

We study a geometrically thin, optically thick Novikov--Thorne accretion disk and the gravitational capture cross sections of a quantum Oppenheimer--Snyder black hole immersed in an external, asymptotically uniform magnetic field. The exterior geometry carries a single quantum parameter, and we work over its entire admissible range, which contains a two-horizon black hole, an extremal configuration and a horizonless compact object, and which ends where the photon sphere disappears. Since the spacetime is static, the Wald potential is purely axial, so the field acts on the disk only through the Lorentz force on weakly charged accreting matter and all of its effects are controlled by a single magnetic coupling. We compute the charged circular orbits, the innermost stable circular orbit, the radiative flux, the effective temperature, the redshift factor, the differential and spectral luminosity and the radiative efficiency, together with the marginally bound orbit and the capture cross sections of massless, massive and charged particles. The construction is checked against the exact Schwarzschild limit and against the identity that relates the bolometric luminosity to the efficiency. The quantum parameter changes the disk observables only weakly, whereas the magnetic coupling raises the efficiency, the peak flux and the height of the spectral peak by large factors and shifts that peak to higher frequency. The two parameters act with opposite signs on absorption. The quantum parameter shrinks every capture cross section, while the magnetic coupling enlarges the one for massive particles and leaves the photon cross section unchanged, so that within this test-field model shadow observables respond to the quantum parameter alone. For charged particles the uniform field confines the motion, and no particle reaches the hole from beyond a magnetic shielding radius.