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Construction of anti-de Sitter-like spacetimes using the metric conformal Einstein field equations: the vacuum case. (arXiv:1807.04212v1 [gr-qc])
来源于:arXiv
We make use of the metric version of the conformal Einstein field equations
to construct anti-de Sitter-like spacetimes by means of a suitably posed
initial-boundary value problem. The evolution system associated to this
initial-boundary value problem consists of a set of conformal wave equations
for a number of conformal fields and the conformal metric. This formulation
makes use of generalised wave coordinates and allows the free specification of
the Ricci scalar of the conformal metric via a conformal gauge source function.
We consider Dirichlet boundary conditions for the evolution equations at the
conformal boundary and show that these boundary conditions can, in turn, be
constructed from the 3-dimensional Lorentzian metric of the conformal boundary
and a linear combination of the incoming and outgoing radiation as measured by
certain components of the Weyl tensor. To show that a solution to the conformal
evolution equations implies a solution to the Einstein field equations we al 查看全文>>