Abstract
In this paper we establish a relation between the non-linearly conserved New-man-Penrose charges and certain subleading terms in a large-r expansion of the BMS charges in an asymptotically-flat spacetime. We define the subleading BMS charges by considering a 1/r-expansion of the Barnich-Brandt prescription for defining asymptotic charges in an asymptotically-flat spacetime. At the leading order, i.e. 1/r0, one obtains the standard BMS charges, which would be integrable and conserved in the absence of a flux term at null infinity, corresponding to gravitational radiation, or Bondi news. At subleading orders, analogous terms in general provide obstructions to the integrability of the corresponding charges. Since the subleading terms are defined close to null infinity, but vanish actually at infinity, the analogous obstructions are not associated with genuine Bondi news. One may instead describe them as corresponding to “fake news”. At order r−3, we find that a set of integrable charges can be defined and that these are related to the ten non-linearly conserved Newman-Penrose charges.
Highlights
At first glance there is no obvious relation between these two sets of charges, but, given that they are both defined in the asymptotic region of asymptotically-flat spacetimes, it would seem natural that there should exist some connection between them
The asymptotic BMS symmetry is determined by imposing that the variation of the metric under the generators of the asymptotic symmetry group respects the form of the metric and the gauge choices
Comparing with equation (4.13) we find that the charge above is the real part of the BMS charge as defined by Newman-Penrose (see equation (4.15) of ref. [16])
Summary
We introduce Bondi coordinates (u, r, xI = {θ, φ}), such that the metric takes the form ds2 = −F e2βdu2 − 2e2βdudr + r2hIJ (dxI − CI du)(dxJ − CJ du). Where ωIJ is the standard metric on the round 2-sphere with coordinates xI = {θ, φ} and C2 ≡ CIJ CIJ. A parameterisation of hIJ , which makes this gauge choice obvious is one for which [9]. Note that there are no terms above for f and g at order r−2 because of regularity conditions on the metric [9]. Since we are using the gauge (2.3) in which the determinant of hIJ is equal to the determinant of the round metric on the 2-sphere, this implies that CIJ and DIJ are both trace-free, while tr E.
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