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| Name | Hybrid Math Physics Seminar 5: Siddiqur Rahman Milon |
| Video Uploader | Video From Tensor |
| Upload Date | This Video Uploaded At 08-12-2022 13:03:20 |
| Video Discription | Title: The linearization Stability of Bach Equations Speaker: Siddiqui Rahman Milon (Oklahoma State University, USA) Date: 30 November 2022 Abstract: In dimension 4, the Bach tensor is a symmetric, trace-free, divergence-free, and conformally invariant weight -2 two-tensor. The Einstein tensor satisfies these properties, except for the trace-freeness and conformal invariance. The vanishing of the Einstein tensor implies the vanishing of the Bach tensor, so we could think the Bach tensor is the "conformal analog" of the Einstein tensor. Therefore, we expect that the solutions to Einstein's equations and the Bach equations have ``similar behaviors.'' In a series of papers, Fisher, Marsden, and Moncrief proved the characterization of the linearization stability of a given solution to Einstein's equations. They showed the linearization stability of Einstein's equation at a given metric g is equivalent to the non-existence of Killing vector fields of g. Later they also showed the necessary and sufficient conditions for a given linearized solution to integrate to a nonlinear solution of Einstein equations in the presence of Killing fields. We hope to prove similar results for the Bach equations in dimension 4. |
| Category | Science & Technology |
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