Soldering freedom and Bondi-Metzner-Sachs-like transformations

Abstract

When two spacetimes are stitched across a null shell placed at the horizon of a black hole, Bondi-Metzner-Sachs (BMS) supertranslation-like soldering freedom arises if one demands the induced metric on the shell should remain invariant under the translations generated by the null generators of the shell. We revisit this phenomenon on the horizon of rotating shells and obtain BMS-like symmetries. We further show that superrotation-like soldering symmetries in the form of conformal isometries can emerge whenever the degenerate metric of any null hypersurface admits a dependency on a null (degenerate direction) coordinate. This kind of conformal isometry can also appear for a null surface situated very close to the horizon of black holes. We also study the intrinsic properties of different kinds of horizon shells considered in this article.

Memory effect and BMS-like symmetries for impulsive gravitational waves

“…and this is strikingly similar to supertranslation found at null infinity of asymptotically flat spacetimes [23]. This construction was then extended for the rotating blackhole spacetimes in [24].…”

“…null coordinates U or V ) then (2.17) offers a new kind of solution. This has been shown in [24]. This situation gives rise superrotations or conformal rescaling of the base space of null hypersurface.…”

“…Here we briefly review how BMS symmetries emerge while one tries to solder two spacetimes across a null hypersurface [23,24]. It is intriguing to find supertranslation and superrotation like symmetries as soldering freedom [23,24]. Throughout this note, we work in four dimensions.…”

“…Recently it has been shown that, the BMS symmetries can be recovered at any null hypersurface situated at some finite location of any spacetime [22]. In the context of soldering of two spacetimes across a null hypersurface (like black hole horizons), BMS-like symmetries have been recovered in [23,24]. Now a natural question arises: whether some kind of memory effect can be detected near the horizon of a black hole or at a null surface situated in some finite location in spacetime just like what has been found in far region?…”

“…In this note, we consider null hypersurfaces that represent the history of the IGW, produced by gluing two space-times across the null surface and study the effect of these burst of radiation on geodesics crossing it. As shown in [23] and [24], the gluing is not unique and one can construct infinitely many thin null-shells related to each other via BMS like transformations (on either side of the surface). Due to this, the geodesics crossing the IGW suffer BMS symmetry induced memory effect.…”