Workshop »Advances in General Relativity« Mitschnitt einer Veranstaltung des Internationalen Erwin Schrödinger Instituts für Mathematik und Physik (ESI) am Dienstag, dem 29. August 2017 im Boltzmann-Hörsaal des Internationalen Erwin Schrödinger Instituts für Mathematik und Physik (ESI) Teil 8: Harvey Reall: On the local well-posedness of Lovelock and Horndeski theories Kamera: Johannes Sauer, Daniel Winkler Schnitt: Daniel Winkler Abstract: Lovelock theories of gravity are the most general diffeomorphism covariant theories of a metric tensor with second order equations of motion. Horndeski theories are the most general four-dimensional diffeomorphism covariant theories of a metric tensor and scalar field with second order equations of motion. I will discuss local well-posedness of the initial value problem for these theories. A necessary condition for local well-posedness is strong hyperbolicity of the equations of motion. Even weak hyperbolicity can fail for strong fields so we restrict to weak fields. We study Lovelock theories in harmonic gauge. We show that the equation of motion is always weakly hyperbolic for weak fields but, in a generic weak-field background, it is not strongly hyperbolic. For Horndeski theories, we prove that, for weak fields, the equation of motion is always weakly hyperbolic in any generalized harmonic gauge. For some Horndeski theories there exists a generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a weak-field background. This includes "k-essence" like theories. However, for more general Horndeski theories, there is no generalized harmonic gauge for which the equation of motion is strongly hyperbolic in a generic weak-field background. Our results show that the standard method used to establish local well-posedness of the Einstein equation does not extend to Lovelock or general Horndeski theories. This raises the possibility that these theories may not admit a well-posed initial value problem even for weak fields. Harvey Reall ist Professor für Theoretische Physik an der Universität Cambridge (Großbritannien). INHALT ====== Kapitel Titel Position --------------------------------------------------------------------- 1. Vorspann 00:00:00 2. Lovelock's theorem. Horndeski theories 00:00:10 3. Causality. Well-posedness of initial value problem 00:10:09 4. Hyperbolicity 00:12:58 5. Results: weak hyperbolicity 00:34:52 6. Horndeski theories 00:47:34 7. Summary 00:52:44

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