Aspects of Symmetry in Four Dimensions

Abstract

In this dissertation we analyze a variety of phenomena in four-dimensional asymptotically (locally) flat spacetimes, with symmetry always playing a prominent role. First we demonstrate that, surprisingly, the color memory effect can in principle be seen in experimental collider physics. Second, we use the hyperbolic foliation of Minkowski space to explore the relationship between the stress tensors in celestial conformal field theory and AdS$_3$/CFT$_2$, recasting previously established results into new coordinates along the way. Third, we consider scattering in $(2,2)$ split signature flat space and identify its conformal boundary as a Lorentzian celestial torus. We argue that its symmetries provide evidence for the primacy of half-integer weights in celestial conformal field theory. Fourth, we show that the recently discovered $w_{1+\infty}$ symmetry of tree-level, minimally coupled gravity amplitudes is perturbatively exact in quantum self-dual gravity. Fifth, we generalize the first law of black hole mechanics to an asymptotically locally flat accelerating black hole called the C-metric, whose conical singularity was previously thought to make it pathological. We also show that this first law passes some nontrivial checks on thermodynamic consistency. Finally, we further generalize the first law to two more classes of accelerating black holes.