Year: 2026
Type: preprint
Abstract: We initiate the study of nonlinear wave equations on the Witten bubble spacetime (also known as the "bubble of nothing"), which is an $\mathrm{SO}(3,1)\times \mathrm{U}(1)$-symmetric solution to the Einstein vacuum equations in $(4 + 1)$ dimensions. This spacetime was introduced by Witten to model the semiclassical instability of the Kaluza--Klein spacetime $\mathbf{R}^{3+1}\times S^1$ (which is classically stable by work of Huneau--Stingo--Wyatt (arXiv:2307.15267)). We prove a small-data global existence result without symmetry assumptions and an improved decay result for $\mathrm{U}(1)$-symmetric solutions to a class of semilinear equations satisfying a version of the null condition. Key to the proof are novel estimates for the linear wave equation, which has been studied in the physics literature by Bhawal and Viveshwara and in the mathematics literature by Bachelot (arXiv:1601.03682).
Source: arXiv (Cornell University)
Author: Gautam, Onyx
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212067769