Ponente
Descripción
We characterise the geometrical nature of smooth supertranslations
defined on a generic non-expanding horizon (NEH) embedded in vacuum. To this
end we consider the constraints imposed by the vacuum Einstein’s equations on the
NEH structure, and discuss the transformation properties of their solutions under
supertranslations. We present a freely specifiable data set which is both necessary
and sufficient to reconstruct the full horizon geometry, and is composed of objects
which are invariant under supertranslations. We conclude that smooth supertranslations
do not transform the geometry of the NEH, and that they should be regarded
as pure gauge. Our results apply both to stationary, and non-stationary states of a
NEH, the later ones being able to describe radiative processes taking place on the
horizon. As a consistency check we repeat the analysis for BMS supertranslations
defined on null infinity, I. Using the same framework as for the NEH we recover the
well known result that BMS supertranslations act non-trivially on the free data on
I. The full analysis is done in exact, non-linear, general relativity.
