2025/03/31 by Gurriaran, Sebastian · 1 citation
#35Q75 #58J37 #58J45 #58K55 #83C57 #83C75 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)
paper · doi:10.48550/arxiv.2503.24114
We prove the precise asymptotics of the spin -2 Teukolsky field in the interior and along the Cauchy horizon of a subextremal Kerr black hole. Together with the oscillatory blow-up asymptotics of the spin +2 Teukolsky field proven in our previous work arXiv:2409.02670, our result suggests that generic perturbations of a Kerr black hole build up to form a coordinate-independent curvature singularity at the Cauchy horizon. This supports the Strong Cosmic Censorship conjecture in Kerr spacetimes. Unlike in the spin +2 case, the spin -2 Teukolsky field is regular on the Cauchy horizon and the first term in its asymptotic development vanishes. As a result, the derivation of a precise lower bound for the spin -2 field is more delicate than in the spin +2 case, and relies on a novel ODE method based on a decomposition of the Teukolsky operator between radial and time derivatives.