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Burnett's conjecture in generalized wave coordinates (2403.03470v1)
Published 6 Mar 2024 in gr-qc and math.AP
Abstract: We prove Burnett's conjecture in general relativity when the metrics satisfy a generalized wave coordinate condition, i.e., suppose ${g_n}_{n=1}\infty$ is a sequence of Lorentzian metrics (in arbitrary dimensions $d \geq 3$) satisfying a generalized wave coordinate condition and such that $g_n\to g$ in a suitably weak and "high-frequency" manner, then the limit metric $g$ satisfies the Einstein--massless Vlasov system. Moreover, we show that the Vlasov field for the limiting metric can be taken to be a suitable microlocal defect measure corresponding to the convergence. The proof uses a compensation phenomenon based on the linear and nonlinear structure of the Einstein equations.
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