AT5 - Constructive gravity |
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Speaker |
Schuller, Frederic |
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| Talk Title |
Constructive Gravity -- Foundations and Applications |
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Abstract |
Constructive gravity allows to calculate the Lagrangian for gravity -- rather having to postulate it -- provided one previously prescribes the Lagrangian for all matter fields. Even if the matter field dynamics employ a more refined tensorial background geometry, it is precisely this geometry that is given dynamics. This result is built on key observations of the original geometrodynamics program and on significant new results, employing an intricate interplay of the modern theory of partial differential equations, convex analysis and algebraic geometry. The central physical mechanism exploited by the constructive gravity program is that the canonical evolutions of matter and geometry must proceed in lockstep, such as to evolve the respective canonical field data between sets of shared initial data hypersurfaces. This surprisingly turns out to be a condition so severe that the possible gravitational Lagrangians are ultimately forced to arise as the solutions of a particular immutable set of countably many linear homogeneous partial differential equations. The coefficient functions of the latter depend on -- and are easily calculated from -- the previously stipulated matter field equations. The thus formed so-called gravitational closure equations for the given matter field dynamics constitute the central theoretical result of the constructive gravity program. We explain the physical and mathematical foundation of the gravitational closure equations and show how one can now answer some questions about gravity that previously could not be addressed. |
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