Abstract
We discuss modifications to the Hawking spectrum that arise when the asymptotic states are supertranslated or superrotated. For supertranslations we find nontrivial off-diagonal phases in the two-point correlator although the emission spectrum is eventually left unchanged, as previously pointed out in the literature. In contrast, superrotations give rise to modifications which manifest themselves in the emission spectrum and depend nontrivially on the associated conformal factor at future null infinity. We study Lorentz boosts and a class of superrotations whose conformal factors do not depend on the azimuthal angle on the celestial sphere and whose singularities at the north and south poles have been associated to the presence of a cosmic string. In spite of such singularities, superrotations still lead to finite spectral emission rates of particles and energy which display a distinctive power-law behavior at high frequencies for each angular momentum state. The integrated particle emission rate and emitted power, on the contrary, while finite for boosts, do exhibit ultraviolet divergences for superrotations, between logarithmic and quadratic. Such divergences can be ascribed to modes with support along the cosmic string. In the logarithimic case, corresponding to a superrotation which covers the sphere twice, the total power emitted still presents the Stefan-Boltzmann form but with an effective area which diverges logarithmically in the ultraviolet.
Highlights
The asymptotic symmetry group of asymptotically flat spacetimes, the BMS group, made its first appearance long ago and was named after its authors Bondi, Metzner, van der Burg and Sachs [1,2,3]
Point singularities due to superrotations have been related to the appearance of cosmic strings [70] or to an effective deformation of the celestial sphere to an elongated object, a “cosmic football” [71]. Keeping in mind these possible shortcomings associated to superrotations, in this work we investigate whether the Hawking spectrum is corrected if one allows the asymptotic states at past (I −) and future (I +) null infinity to be supertranslated or superrotated
In the pure-absorption approximation, we find that the expansion of the particle emission spectrum dNlm(ω) for large frequencies, 2πω/κ 1, c with κ the black hole surface gravity, still exhibits the familiar exponential decay in ω
Summary
The asymptotic symmetry group of asymptotically flat spacetimes, the BMS group, made its first appearance long ago and was named after its authors Bondi, Metzner, van der Burg and Sachs [1,2,3] (see e.g. [4,5,6] for introductory presentations). In the case of superrotations, we show that the Bogolyubov coefficients, the two-point function and the emission spectra all depend nontrivially on the associated conformal transformations and conformal factors at I + This aligns with the expectation that, while ordinary rotations clearly cannot alter Hawking radiation for a spherically symmetric setup, already Lorentz boosts ought to affect the spectrum via Doppler effect. Both for supertranslations and for superrotations, the twopoint function is only sensitive to the asymptotic symmetry at future null infinity, while the dependence on the corresponding transformation at past null infinity drops out. Appendix F discusses the frequency behavior of the transmission coefficients, and their associated density of states, for massless minimally coupled scalar fields
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