Deformations of the Kerr-(A)dS near horizon geometry

We investigate deformations of the Kerr-(A)dS near horizon geometry and derive partial infinitesimal rigidity results for it. The proof comprises two parts. First, we follow the analysis of Jezierski and Kamiński (2013 Gen. Rel. Grav. 45 987–1004) to eliminate all but a finite number of Fourier modes of linear perturbations. In the second part, we give an argument using analyticity to prove that there are no odd Fourier modes.