Semilinear wave equations on the Witten bubble spacetime
Abstract
We initiate the study of nonlinear wave equations on the Witten bubble spacetime (also known as the "bubble of nothing"), which is an SO(3,1)× 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 R3+1× S1 (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 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).
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BibTeX
@misc{gautam2026semilinear,
title = {{Semilinear wave equations on the Witten bubble spacetime}},
author = {Onyx Gautam},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06609},
eprint = {2609.06609},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06609},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Semilinear wave equations on the Witten bubble spacetime
AU - Onyx Gautam
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06609
UR - https://arxiv.org/abs/2609.06609
AB - We initiate the study of nonlinear wave equations on the Witten bubble spacetime (also known as the "bubble of nothing"), which is an SO(3,1)× 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 R^3+1× 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 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).
ER -