On smoothness-asymmetric null infinities
arXiv:gr-qc/0605056 · doi:10.1088/0264-9381/23/10/022
Abstract
We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past and a future null infinity of different smoothness. For simplicity, the analysis is restricted to the class of conformally flat, axially symmetric initial data sets. It is shown how the free parameters in the second fundamental form of the data can be used to satisfy certain obstructions to the smoothness of null infinity. The resulting initial data sets could be interpreted as those of some sort of (non-linearly) distorted Schwarzschild black hole. Its developments would be so that they admit a peeling future null infinity, but at the same time have a polyhomogeneous (non-peeling) past null infinity.
arXiv comment13 pages, 1 figure
References in corpus (9)
- Existence of non-trivial, vacuum, asymptotically simple space-times
- Spin-2 fields on Minkowski space near space-like and null infinity
- Asymptotically Flat Initial Data with Prescribed Regularity at Infinity
- Late time behaviour of the maximal slicing of the Schwarzschild black hole
- A new class of obstructions to the smoothness of null infinity
- The Momentum Constraints of General Relativity and Spatial Conformal Isometries
- Does asymptotic simplicity allow for radiation near spatial infinity?
- Time asymmetric spacetimes near null and spatial infinity. I. Expansions of developments of conformally flat data
- Time asymmetric spacetimes near null and spatial infinity. II. Expansions of developments of initial data sets with non-smooth conformal metrics