Workshop »Advances in General Relativity« Mitschnitt einer Veranstaltung des Internationalen Erwin Schrödinger Instituts für Mathematik und Physik (ESI) am Donnerstag, dem 31. August 2017 im Boltzmann-Hörsaal des Internationalen Erwin Schrödinger Instituts für Mathematik und Physik (ESI) Teil 15: László Szabados: On gravity's role in the genesis of rest masses of classical fields Kamera: Johannes Sauer, Daniel Winkler Schnitt: Daniel Winkler Abstract: The classical Einstein-Standard Model system with conformally invariant coupling of the Higgs field to gravity is investigated. We show that the energy-momentum tensor may have two singularities: In cosmological spacetimes the usual Big Bang type singularity with diverging matter field variables, and a second, less violent one ('Small Bang'), in which it is only the geometry that is singular but the matter field variables remain finite. The latter provides a finite, universal upper bound for the pointwise norm of the Higgs field in terms of Newton's gravitational constant. As a consequence of this structure of the energy-momentum tensor, we also show that, in the presence of Friedman-Robertson-Walker or Kantowski-Sachs symmetries the energy density can have finite local minimum only if the transitivity hypersurfaces of the spacetime symmetries are locally hyperboloidal and their mean curvature is less than a finite critical value. In particular, in the very early era of an expanding universe or in a nearly spherically symmetric black hole near the central singularity, the Higgs sector does not have any instantaneous (symmetric or symmetry breaking) vacuum state, and hence the (zero or non-zero) rest mass of the matter fields is not defined. For smaller mean curvature instantaneous symmetry breaking vacuum states emerge, yielding non-zero rest mass and electric charge for some of the gauge and spinor fields via the Brout-Englert-Higgs mechanism. These rest masses are decreasing with decreasing mean curvature, but the charge remains constant. It is also shown that globally defined instantaneous symmetry breaking vacuum states do not exist at all in the k=1 cosmological model and inside spherically symmetric black holes. László Szabados ist Professor am Wigner Research Centre for Physics in Budapest. INHALT ====== Kapitel Titel Position --------------------------------------------------------------------- 1. Vorspann 00:00:00 2. Overview 00:00:10 3. The rest mass of classical fields 00:04:37 4. The Einstein-conformally coupled standard model 00:16:30 5. The instantaneous vacuum states 00:28:28 6. The genesis of the rest masses 00:35:01 7. Summary 00:48:20

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