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Computing spacetime curvature via differential algebraic equations. (English) Zbl 0861.65122
The paper deals with numerical solution of the Einstein field equations of general relativity. The method of lines and a differential-algebraic equations solver are used. The nonlinear partial differential equations are spatially discretized leading to a system of ordinary differential equations coupled with a system of algebraic equations. The method is applied to the spherically symmetric nonrotating black holes, the obtained numerical results are compared with analytically known solutions, and the accuracy is studied for different numbers of gridpoints at different time moments.
MSC:
65Z05 Applications to the sciences
35Q75 PDEs in connection with relativity and gravitational theory
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
83C57 Black holes
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
65L05 Numerical methods for initial value problems
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