The conformal flow of metrics and the general Penrose inequality. (English) Zbl 1440.83003
Summary: The conformal flow of metrics has been used to successfully establish a special case of the Penrose inequality, which yields a lower bound for the total mass of a spacetime in terms of horizon area. Here we show how to adapt the conformal flow of metrics, so that it may be applied to the Penrose inequality for general initial data sets of the Einstein equations. The Penrose conjecture without the assumption of time symmetry is then reduced to solving a system of PDE with desirable properties.
MSC:
| 83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
| 53E30 | Flows related to complex manifolds (e.g., Kähler-Ricci flows, Chern-Ricci flows) |
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