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arXiv:2405.06035gr-qc

Solving the Einstein Equations Numerically

David Hilditch

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Abstract

There are many complementary approaches to the construction of solutions to the field equations of general relativity. Among these, numerical approximation offers the only possibility to compute a variety of dynamical spacetimes, and so has come to play an important role for theory and experiment alike. Presently we give a brief introduction to this, the science of numerical relativity. We discuss the freedom in formulating general relativity as an initial (boundary) value problem. We touch on the fundamental concepts of well-posedness and gauge freedom and review the standard computational methods employed in the field. We discuss the physical interpretation of numerical spacetime data and end with an overview of a number of 3d codes that are either in use or under active development.

arXiv comments
36 pages, 2 figures. Invited chapter for the edited book "New Frontiers in GRMHD Simulations" (Eds. C. Bambi, Y. Mizuno, S. Shashank and F. Yuan, Springer Singapore, expected in 2024)
Journal reference
DOI
Subjects
gr-qcGeneral Relativity and Quantum Cosmology

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Discussed in comments1 thread

    • As with all such articles, there is no real help with getting through the hurdle. Very surface-level, sounding like AI summary at times. Also, AFAICT, nobody has yet actually worked out spacetime with masses properly, right? Where masses influence and are influenced by space…

      hosejaView on HNParent context

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