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Algorithms for the explicit computation of Penrose diagrams

Research paper by J C Schindler, A Aguirre

Indexed on: 06 Feb '18Published on: 06 Feb '18Published in: arXiv - General Relativity and Quantum Cosmology



Abstract

An algorithm is given for explicitly computing Penrose diagrams for spacetimes of the form $ds^2 = -f(r)\, dt^2 + f(r)^{-1} \, dr^2 + r^2 \, d\Omega^2$. The resulting diagram coordinates are shown to extend the metric continuously and nondegenerately across an arbitrary number of horizons. The method is extended to include piecewise approximations to dynamically evolving spacetimes using a standard hypersurface junction procedure. Examples generated by an implementation of the algorithm are shown for standard and new cases. In the appendix, this algorithm is compared to existing methods.