This content will become publicly available on January 1, 2023
 Publication Date:
 NSFPAR ID:
 10342480
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2022
 Issue:
 1
 ISSN:
 10298479
 Sponsoring Org:
 National Science Foundation
More Like this

A bstract In a companion paper [1] we showed that the symmetry group $$ \mathfrak{G} $$ G of nonexpanding horizons (NEHs) is a 1dimensional extension of the BondiMetznerSachs 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 ‘timetranslations’ are positive definite on perturbed NEHs. These results hold for zero as well as nonzero cosmological constant. In the asymptotically flat case, as noted in [1], $$ \mathcal{I} $$ I ± are NEHs in the conformally completed spacetimemore »

Abstract We use the formalism developed by Wald and Zoupas to derive explicit covariant expressions for the charges and fluxes associated with the Bondi–Metzner–Sachs symmetries at null infinity in asymptotically flat spacetimes in vacuum general relativity. Our expressions hold in nonstationary regions of null infinity, are local and covariant, conformallyinvariant, and are independent of the choice of foliation of null infinity and of the chosen extension of the symmetries away from null infinity. While similar expressions have appeared previously in the literature in Bondi–Sachs coordinates (to which we compare our own), such a choice of coordinates obscures these properties. Our covariant expressions can be used to obtain charge formulae in any choice of coordinates at null infinity. We also include detailed comparisons with other expressions for the charges and fluxes that have appeared in the literature: the Ashtekar–Streubel flux formula, the Komar formulae, and the linkage and twistor charge formulae. Such comparisons are easier to perform using our explicit expressions, instead of those which appear in the original work by Wald and Zoupas.

Abstract We study the mean curvature flow in 3dimensional null hypersurfaces. In a spacetime a hypersurface is called null, if its induced metric is degenerate. The speed of the mean curvature flow of spacelike surfaces in a null hypersurface is the projection of the codimensiontwo mean curvature vector onto the null hypersurface. We impose fairly mild conditions on the null hypersurface. Then for an outer untrapped initial surface, a condition which resembles the meanconvexity of a surface in Euclidean space, we prove that the mean curvature flow exists for all times and converges smoothly to a marginally outer trapped surface (MOTS). As an application we obtain the existence of a global foliation of the past of an outermost MOTS, provided the null hypersurface admits an untrapped foliation asymptotically.

A bstract As a black hole evaporates, each outgoing Hawking quantum carries away some of the black holes asymptotic charges associated with the extended BondiMetznerSachs group. These include the Poincaré charges of energy, linear momentum, intrinsic angular momentum, and orbital angular momentum or centerofmass charge, as well as extensions of these quantities associated with supertranslations and superLorentz transformations, namely supermomentum, superspin and super centerofmass charges (also known as soft hair). Since each emitted quantum has fluctuations that are of order unity, fluctuations in the black hole’s charges grow over the course of the evaporation. We estimate the scale of these fluctuations using a simple model. The results are, in Planck units: (i) The black hole position has a uncertainty of $$ \sim {M}_i^2 $$ ∼ M i 2 at late times, where M i is the initial mass (previously found by Page). (ii) The black hole mass M has an uncertainty of order the mass M itself at the epoch when M ∼ $$ {M}_i^{2/3} $$ M i 2 / 3 , well before the Planck scale is reached. Correspondingly, the time at which the evaporation ends has an uncertainty of order $$ \sim {M}_i^2 $$ ∼ M i 2more »

Generalizing from observed to new related environments (outofdistribution) is central to the reliability of classifiers. However, most classifiers fail to predict label from input when the change in environment is due a (stochastic) input transformation not observed in training, as in training we observe , where is a hidden variable. This work argues that when the transformations in train and test are (arbitrary) symmetry transformations induced by a collection of known equivalence relations, the task of finding a robust OOD classifier can be defined as finding the simplest causal model that defines a causal connection between the target labels and the symmetry transformations that are associated with label changes. We then propose a new learning paradigm, asymmetry learning, that identifies which symmetries the classifier must break in order to correctly predict in both train and test. Asymmetry learning performs a causal model search that, under certain identifiability conditions, finds classifiers that perform equally well indistribution and outofdistribution. Finally, we show how to learn counterfactuallyinvariant representations with asymmetry learning in two physics tasks.