Asymptotic Spinspacetime

TL;DR

This paper introduces the concept of spinspacetime, a complexified Minkowski space unifying spacetime and spin, derived from Poincaré invariance, and explains its relation to black hole physics via twistorial methods.

Contribution

It proposes the novel idea of spinspacetime, a complexified Minkowski space that unifies spacetime and spin, and connects it to the Newman-Janis shift in black hole solutions.

Findings

Spinspacetime unifies spacetime and spin in a complexified framework.

Holomorphic coordinates in spinspacetime commute despite noncommutative spin.

The twistorial construction reproduces the Newman-Janis shift for spinning black holes.

Abstract

We show that Poincar\'e invariance directly implies the existence of a complexified Minkowski space whose real and imaginary directions unify spacetime and spin, which we dub spinspacetime. Despite the intrinsic noncommutativity of spin, spinspacetime exhibits mutually commuting holomorphic coordinates. Its twistorial construction derives the Newman-Janis shift property of spinning black holes by massive half-Fourier transforming complexified on-shell kinematics, which encode a spinning analog of equivalence principle.