Related Experiment Video
Updated: Aug 4, 2026

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
Published on: January 3, 2016
Nonlinear perturbations of the Kaluza-Klein monopole
Piotr Bizoń1, Tadeusz Chmaj, Gary Gibbons
1M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland.
Abstract:
We consider the nonlinear stability of the Kaluza-Klein monopole viewed as the static solution of the five-dimensional vacuum Einstein equations. Using both numerical and analytical methods, we give evidence that the Kaluza-Klein monopole is asymptotically stable within the cohomogeneity-two biaxial Bianchi type-IX ansatz recently introduced by Bizoń, Chmaj, and Schmidt. We also show that for sufficiently large perturbations the Kaluza-Klein monopole loses stability and collapses to a Kaluza-Klein black hole. The relevance of our results for the stability of Bogomol'nyi-Prasad-Sommerfield states in M or string theory is briefly discussed.
Related Concept Videos
Atomic Nuclei: Nuclear Relaxation Processes
Symmetry in Maxwell's Equations
Potential Due to a Polarized Object
Differential Form of Maxwell's Equations
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...

