Hawking radiation with dispersion: reconciling the Bogoliubov and tunneling approaches

TL;DR

This paper analytically connects Bogoliubov and tunneling approaches to Hawking radiation in dispersive analogue gravity systems, showing the robustness of thermal emission under ultraviolet modifications.

Contribution

It extends the near-horizon S-matrix method to dispersive systems and demonstrates the agreement between Bogoliubov and tunneling descriptions in this context.

Findings

Outgoing modes are governed by an effective horizon induced by dispersion.

Bogoliubov coefficients agree with tunneling results in low-energy limits.

Emission spectrum deviations from thermality are controlled by an effective surface gravity.

Abstract

We investigate Hawking-like particle production in analogue gravity systems with superluminal modified dispersion relations. For a broad class of even, convex, and polynomially bounded dispersion relations, we show that the relevant outgoing modes are governed by an effective horizon induced by dispersive propagation. Extending the near-horizon S-matrix method beyond the purely sonic regime, we compute the Bogoliubov coefficients and demonstrate that, in the low-energy and adiabatic limits, they agree with the tunneling result obtained from the approximant ray. In both cases, the emission spectrum is controlled by an effective surface gravity associated to the effective horizon, leading to controlled deviations from exact thermality. Our results establish an analytical connection between the Bogoliubov and tunneling descriptions in dispersive settings and clarify the conditions under which Hawking radiation remains robust against ultraviolet modifications, with implications extending beyond analogue gravity.