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arXiv · 2608.25566

Two-branch detector response for Dirac infall into a Schwarzschild--MOG black hole

Nikko John Leo S. Lobos·Emmanuel T. Rodulfo
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Abstract

We study a localized spin-$1/2$ detector falling into a Schwarzschild--MOG black hole. The detector interacts with a neutral massless scalar field through a charge-preserving two-level transition, while its translational wave packet obeys the MOG-charged Dirac equation. Near the outer horizon, the separated radial system reduces to an inverse-square equation with index $\Theta_{\rm D}=E_{\rm H}/(2\hbar\kappa_\alpha)$. The gauge-invariant horizon energy satisfies $E_{\rm H}=m_\psi U_{\rm H}>0$ for every future-directed crossing trajectory. We quantize the scalar field in a globally normalized Boulware scattering basis and retain both radial-flux branches of a mode that is outgoing at infinity. This treatment does not identify a local outgoing ansatz with a complete mode. A finite radial gate $\chi_p(x)=(x/L_\chi)^p e^{-x/L_\chi}$ gives closed-form excitation and absorption probability densities that include the ingoing contribution and scattering-phase interference. Within the controlled near-horizon approximation, the full detailed-balance ratio factorizes into a branch-resolved outgoing ratio and a two-branch factor. Only the outgoing ratio approaches $\exp(-2\pi\nu/\kappa_\alpha)$ when the near-horizon, adiabatic, high-gap, and branch-isolation conditions all hold. The leading switching correction is controlled by $(\nu/\kappa_\alpha)/(S_\pm L_\chi)$, not by $(S_\pm L_\chi)^{-1}$ alone. In a weak-MOG expansion, the local correction separates into surface-gravity, trajectory-prefactor, and finite-gate terms. The full response also contains a contribution from global scattering. This separation shows which terms follow from the local horizon geometry and which depend on the detector protocol and scalar propagation outside the horizon region.

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Nikko John Leo S. Lobos, Emmanuel T. Rodulfo. 2026-08-26. Two-branch detector response for Dirac infall into a Schwarzschild--MOG black hole. https://arxiv.org/abs/2608.25566

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