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### Condensed Matter Seminars

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Numerical relativity simulations have made dramatic advances in recent years. Most of these simulations adopt Cartesian coordinates, which have some very useful properties for many types of applications. Spherical polar coordinates, on the other hand, have significant advantages for others. Until recently, the new coordinate singularities in spherical polar coordinates have hampered the development of numerical relativity codes adopting such coordinates, at least in the absence of symmetry assumptions. With a combination of different techniques – a reference-metric formulation of the relevant equations, a proper rescaling of all tensorial quantities, and a partially-implicit Runge-Kutta method – we have been able to solve these problems. In this talk I will start with a brief review of numerical relativity, including the 3+1 decomposition of Einstein’s equations, I will then explain the above techniques for applications in spherical polar coordinates, and will finally show some tests – both for vacuum black hole spacetimes, and including relativistic hydrodynamics.