Extremal black hole initial data deformations

Abstract

We study deformations of axially symmetric initial data for Einstein-Maxwell equations satisfying time-rotation (t-φ) symmetry and containing one asymptotically cylindrical end and one asymptotically flat end. We find that the t-φ symmetry implies the existence of a family of deformed data having the same horizon structure. This result allows us to measure how close the solutions are to the Lichnerowicz equation when arising from nearby free data.