Abstract
In a companion paper [1] we showed that the symmetry group \( \mathfrak{G} \) of non-expanding horizons (NEHs) is a 1-dimensional extension of the Bondi-Metzner-Sachs group \( \mathfrak{B} \) at \( \mathcal{I} \)+. For each infinitesimal generator of \( \mathfrak{G} \), we now define a charge and a flux on NEHs as well as perturbed NEHs. The procedure uses the covariant phase space framework in presence of internal null boundaries \( \mathcal{N} \) along the lines of [2,3,4,5,6]. However, \( \mathcal{N} \) is required to be an NEH or a perturbed NEH. Consequently, charges and fluxes associated with generators of \( \mathfrak{G} \) are free of physically unsatisfactory features that can arise if \( \mathcal{N} \) is allowed to be a general null boundary. In particular, all fluxes vanish if \( \mathcal{N} \) is an NEH, just as one would hope; and fluxes associated with symmetries representing ‘time-translations’ are positive definite on perturbed NEHs. These results hold for zero as well as non-zero cosmological constant. In the asymptotically flat case, as noted in [1], \( \mathcal{I} \)± are NEHs in the conformally completed space-time but with an extra structure that reduces \( \mathfrak{G} \) to \( \mathfrak{B} \). The flux expressions at \( \mathcal{N} \) reflect this synergy between NEHs and \( \mathcal{I} \)+. In a forthcoming paper, this close relation between NEHs and \( \mathcal{I} \)+ will be used to develop gravitational wave tomography, enabling one to deduce horizon dynamics directly from the waveforms at \( \mathcal{I} \)+.
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Ashtekar, A., Khera, N., Kolanowski, M. et al. Charges and fluxes on (perturbed) non-expanding horizons. J. High Energ. Phys. 2022, 66 (2022). https://doi.org/10.1007/JHEP02(2022)066
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DOI: https://doi.org/10.1007/JHEP02(2022)066