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Using a metric conformal formulation of the Einstein equations, we develop aconstruction of 4-dimensional anti-de Sitter-like spacetimes coupled totracefree matter models. Our strategy relies on the formulation of aninitial-boundary problem for a system of quasilinear wave equations for variousconformal fields by exploiting the conformal and coordinate gauges. Byanalysing the conformal constraints we show a systematic procedure to prescribeinitial and boundary data. This analysis is complemented by the propagation ofthe constraints, showing that a solution to the wave equations implies asolution to the Einstein field equations. In addition, we study three explicittracefree matter models: the conformally invariant scalar field, the Maxwellfield and the Yang-Mills field. For each one of these we identify the basicdata required to couple them to the system of wave equations. As our mainresult, we establish the local existence and uniqueness of solutions for theevolution system in a neighbourhood around the corner, provided compatibilityconditions for the initial and boundary data are imposed up to a certain order.

Construction of anti-de Sitter-like spacetimes using the metric conformal Einstein field equations: the tracefree matter case