Abstract:
We study the dynamics of a self-interacting spherically symmetric scalar field propagating on the Schwarzschild-anti-de Sitter background.
We consider two parameters in the model: the size of the black hole and the Robin boundary parameter. In addition, we study both the focusing and defocusing nonlinearities.
We find a pitchfork bifurcation in the defocusing case and for the focusing nonlinearity, a region of the phase space where all solutions blow up in finite time.
An extensive study of static solutions and their linear stability allows us to provide a precise asymptotic description of global-in-time solutions and solutions near the threshold of finite-time blowup.
This work is a first step in extending arxiv.org/abs/2001.03980 to asymptotically anti-de Sitter black hole spacetimes. Based on arxiv.org/abs/2312.02760.
Zoom-Link:
https://univienna.zoom.us/j/6540036841?pwd=SytyVkZJZzNyRG9lMm13ejlHeHRRUT09