Uniqueness of Smooth Stationary Black Holes in Vacuum: Small Perturbations of the Kerr Spaces |
| |
Authors: | S Alexakis A D Ionescu S Klainerman |
| |
Institution: | 1. Massachusetts Institute of Technology, Cambridge, MA, 02139, USA 2. University of Wisconsin – Madison, Madison, WI, 53706, USA 3. Princeton University, Princeton, NJ, 08544, USA
|
| |
Abstract: | The goal of the paper is to prove a perturbative result, concerning the uniqueness of Kerr solutions, a result which we believe
will be useful in the proof of their nonlinear stability. Following the program started in Ionescu and Klainerman (Invent.
Math. 175:35–102, 2009), we attempt to remove the analyticity assumption in the the well known Hawking-Carter-Robinson uniqueness
result for regular stationary vacuum black holes. Unlike (Ionescu and Klainerman in Invent. Math. 175:35–102, 2009), which
was based on a tensorial characterization of the Kerr solutions, due to Mars (Class. Quant. Grav. 16:2507–2523, 1999), we
rely here on Hawking’s original strategy, which is to reduce the case of general stationary space-times to that of stationary
and axi-symmetric spacetimes for which the Carter-Robinson uniqueness result holds. In this reduction Hawking had to appeal
to analyticity. Using a variant of the geometric Carleman estimates developed in Ionescu and Klainerman (Invent. Math. 175:35–102,
2009), in this paper we show how to bypass analyticity in the case when the stationary vacuum space-time is a small perturbation
of a given Kerr solution. Our perturbation assumption is expressed as a uniform smallness condition on the Mars-Simon tensor.
The starting point of our proof is the new local rigidity theorem established in Alexakis et al. (Hawking’s local rigidity
theorem without analyticity. , 2009). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|