Abstract
We construct numerically time-symmetric initial data that are Schwarzschildean at spatial infinity and Brill-Lindquist in the interior. The transition between these two data sets takes place along a finite gluing region equipped with an axisymmetric Brill wave metric. The construction is based on an application of Corvino's gluing method using Brill waves due to Giulini and Holzegel. Here, we use a gluing function that includes a simple angular dependence. We also investigate the dependence of the ADM mass of our construction on the details of the gluing procedure.
Highlights
The long lasting question of whether it is possible to construct solutions to the vacuum constraint equations that are static in a neighbourhood of space-like infinity and non-static in the interior was answered to the affirmative by Corvino [1]
We investigate the dependence of the ADM mass of our construction on the details of the gluing procedure
In the present short contribution, we focus on a setting where the gluing function acquires a simple angular dependence
Summary
The long lasting question of whether it is possible to construct solutions to the vacuum constraint equations that are static in a neighbourhood of space-like infinity and non-static in the interior was answered to the affirmative by Corvino [1]. The initial data could be evolved using a Cauchy evolution in the framework of the conformal representation of Einstein’s equations [10], where space-like infinity i0 has been blown up to a cylinder I = [−1, 1] × S2 of finite length along the time direction. This approach has been already proven to be successfully numerically implementable, e.g. This approach has been already proven to be successfully numerically implementable, e.g. [11, 12]
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