  We consider a microscopic analogue of the BMS analysis of asymptotic
symmetries by analysing universal geometric structures on infinitesimal tangent
light cones. Thereby, two natural microscopic symmetry groups arise: A
non-trivially represented Lorentz group and a BMS-like group. The latter has a
rich mathematical structure, since it contains the former as a non-canonical
subgroup, next to infinitely many other Lorentz subgroups. None of those
Lorentz subgroups appears to be intrinsically preferred, and hence, the
microscopic BMS-like group constitutes a natural symmetry group for
infinitesimal tangent light cones. We compare our investigation with the
classical BMS analysis and show, that the microscopic BMS-like group is a gauge
group for the bundle of null vectors. Motivated by the various applications of
the original BMS group, our findings could have interesting implications: They
identify a geometric structure that could be suitable for a bulk analysis of
gravitational waves, they suggest a possible enlargement of the fundamental
gauge group of gravity and they motivate the possibility of an interrelation
between the UV structure of gauge theories, gravitational memory effects and
BMS-like symmetries. Also, our results imply, that BMS-like groups arise not
only as macroscopic, asymptotic symmetry groups in cosmology, but describe also
a fundamental and seemingly unknown microscopic symmetry of pseudo-Riemannian
geometry.
