Einstein constraints on a characteristic cone
Yvonne Choquet-Bruhat, Piotr T. Chru\'sciel, Jos\'e M., Mart\'in-Garc\'ia
TL;DR
This paper investigates the Einstein equations on a characteristic cone, including the vertex, in arbitrary dimensions, solving the constraints using a wave map gauge and demonstrating gauge conservation.
Contribution
It provides a detailed analysis of the Cauchy problem on a characteristic cone for Einstein equations in arbitrary dimensions, including constraint solutions and gauge conservation.
Findings
Constraints are solved explicitly on the cone.
Gauge conservation is demonstrated.
Analysis applies to arbitrary dimensions.
Abstract
We analyse the Cauchy problem on a characteristic cone, including its vertex, for the Einstein equations in arbitrary dimensions. We use a wave map gauge, solve the obtained constraints and show gauge conservation.
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Taxonomy
TopicsCosmology and Gravitation Theories · Advanced Differential Geometry Research · Black Holes and Theoretical Physics