Speaker
Description
This work investigates, as a first step, the four branches of BMS
transformations, motivated by the classification into elliptic, parabolic,
hyperbolic and loxodromic proposed a few years ago in the literature. We
first prove that to each normal elliptic transformation of the complex
variable z used in the metric for cuts of null infinity, there is a
corresponding BMS supertranslation. We then study the conformal factor in
the BMS transformation of the u variable as a function of the squared
modulus of z. In the loxodromic and hyperbolic cases, this conformal
factor is either monotonically increasing or monotonically decreasing as a
function of the real variable given by the modulus of z. The Killing
vector field of the Bondi metric is also studied in correspondence with
the four admissible families of BMS transformations. Eventually, all BMS
transformations are re-expressed in the homogeneous coordinates suggested
by projective geometry. It is then found that BMS transformations are the
restriction to a pair of unit circles of a more general set of
transformations. Within this broader
framework, the geometry of such transformations is studied by means of its
Segre manifold.
