Importance of being nonminimally coupled: Scalar Hawking radiation from regular black holes

In curved space-time, a scalar field phi is generically expected to couple to curvature, via a coupling of the form xiphi2R. Yet in the study of Hawking emission from regular black holes (RBHs), where scalar fields are often introduced as test field probes of the geometry, and the Ricci scalar is generically non-zero, this non-minimal coupling is almost always ignored. We revisit this assumption by studying scalar Hawking emission from four representative RBHs (the Bardeen, Hayward, Simpson-Visser, and D’Ambrosio-Rovelli space-times), within two benchmark cases: the conformal case xi=1/6, and a large negative value xi=-10e4 motivated by Higgs inflation. We compute the graybody factors and emission spectra, showing that the latter can be either enhanced or suppressed, even by several orders of magnitude. A crucial role is played by the sign of the term xifR, with f(r)=-gtt in Schwarzschild-like coordinates, as it determines whether the nonminimal coupling suppresses or enhances the geometric potential barrier. For the D’Ambrosio-Rovelli case with large negative xi, the low-energy emission spectrum is enhanced by up to five orders of magnitude, since xifR<0 throughout the space-time, leading to a deep potential well which broadens the transmissive window. The deviations we find can be particularly relevant in the case where primordial RBHs are dark matter candidates, given the impact of the nonminimal coupling on their evaporation history.