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Title: Charges and fluxes on (perturbed) non-expanding horizons
A bstract In a companion paper [1] we showed that the symmetry group $$ \mathfrak{G} $$ G of non-expanding horizons (NEHs) is a 1-dimensional extension of the Bondi-Metzner-Sachs group $$ \mathfrak{B} $$ B at $$ \mathcal{I} $$ I + . For each infinitesimal generator of $$ \mathfrak{G} $$ 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 $$ \mathcal{N} $$ N along the lines of [2–6]. However, $$ \mathcal{N} $$ N is required to be an NEH or a perturbed NEH. Consequently, charges and fluxes associated with generators of $$ \mathfrak{G} $$ G are free of physically unsatisfactory features that can arise if $$ \mathcal{N} $$ N is allowed to be a general null boundary. In particular, all fluxes vanish if $$ \mathcal{N} $$ 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], $$ \mathcal{I} $$ I ± are NEHs in the conformally completed space-time but with an extra structure that reduces $$ \mathfrak{G} $$ G to $$ \mathfrak{B} $$ B . The flux expressions at $$ \mathcal{N} $$ N reflect this synergy between NEHs and $$ \mathcal{I} $$ I + . In a forthcoming paper, this close relation between NEHs and $$ \mathcal{I} $$ I + will be used to develop gravitational wave tomography, enabling one to deduce horizon dynamics directly from the waveforms at $$ \mathcal{I} $$ I + .  more » « less
Award ID(s):
1806356
PAR ID:
10379264
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Journal of High Energy Physics
Volume:
2022
Issue:
2
ISSN:
1029-8479
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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