Super-Geometrodynamics

Abstract

We present explicit solutions of the time-symmetric initial value constraints, expressed in terms of freely specfiable harmonic functions for examples of supergravity theories, which emerge as effective theories of compactified string theory. These results are a prequisite for the study of the time-evolution of topologically non-trivial initial data for supergravity theories, thus generalising the "Geometrodynamics" program of Einstein-Maxwell theory to that of supergravity theories. Specifically, we focus on examples of multiple electric Maxwell and scalar fields, and analyse the initial data problem for the general Einstein-Maxwell-Dilaton theory both with one and two Maxwell fields, and the STU model. The solutions are given in terms of up to eight arbitrary harmonic functions in the STU model. As a by-product, in order compare our results with known static solutions, the metric in isotropic coordinates and all the sources of the non-extremal black holes are expressed entirely in terms of harmonic functions. We also comment on generalizations to time-nonsymmetric initial data and their relation to cosmological solutions of gauged so-called fake supergravities with positive cosmological constant.

31 pages, typos corrected

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• The Einstein-Maxwell system in 3+1 form and initial data for multiple charged black holes
• Collisions of oppositely charged black holes
• Exact Evolution of Discrete Relativistic Cosmological Models
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Cited by in corpus (12)

• Photon Spheres and Sonic Horizons in Black Holes from Supergravity and Other Theories
• Weyl metrics and wormholes
• Ring wormholes via duality rotations
• Logarithmic correction to black hole entropy in universal low-energy string theory models
• Supergravity Black Holes, Love Numbers and Harmonic Coordinates
• Dyonic black holes at arbitrary locations
• STU Black Holes and SgrA*
• Thermodynamics of Asymptotically Conical Geometries
• Logarithmic correction to the entropy of a Kerr-Newman family of black holes in $U(1{)}^2$-charged STU supergravity models
• On the interactions and equilibrium between Einstein-Maxwell-Dilaton black holes
• Yang-Baxter structure of the extended space
• Super-Geometrodynamics in Higher Dimensions