Bounds on the Bondi energy by a flux of curvature
| Autor: | Spyros Alexakis, Arick Shao |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
General Mathematics
media_common.quotation_subject FOS: Physical sciences General Relativity and Quantum Cosmology (gr-qc) Curvature 01 natural sciences General Relativity and Quantum Cosmology Momentum Mathematics - Analysis of PDEs 0103 physical sciences FOS: Mathematics 010306 general physics Mathematical Physics Mathematics Mathematical physics media_common Spacetime 010308 nuclear & particles physics Applied Mathematics Null (mathematics) Mathematical Physics (math-ph) Infinity 83C30 (Primary) 35Q75 83C05 53C12 53C21 (Secondary) Cone (topology) Uniformization (set theory) Schwarzschild radius Analysis of PDEs (math.AP) |
| Zdroj: | Journal of the European Mathematical Society. 18:2045-2106 |
| ISSN: | 1435-9855 |
| DOI: | 10.4171/jems/638 |
| Popis: | We consider smooth null cones in a vacuum spacetime that extend to future null infinity. For such cones that are perturbations of shear-free outgoing null cones in Schwarzschild spacetimes, we prove bounds for the Bondi energy, momentum, and rate of energy loss. The bounds depend on the closeness between the given cone and a corresponding cone in a Schwarzschild spacetime, measured purely in terms of the differences between certain weighted $L^2$-norms of the space-time curvature on the cones, and of the geometries of the spheres from which they emanate. A key step in this paper is the construction of a family of asymptotically round cuts of our cone, relative to which the Bondi energy is measured. 53 pages; slightly altered some discussions near main theorem |
| Databáze: | OpenAIRE |
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