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Seminari by Shalabh Gautam from ICTS, Bengaluru, India

  • June 19th, 2023
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Title:Compactified Hyperboloidal Evolution in Numerical Relativity

Place: DAA Seminar. Jeroni Muñoz Research Building, fourth floor, in Campus de Burjassot.

Day: Wednesday, June 21 , 2023. Time: 12:00.

Abstract:
One symmetric hyperbolic formulation of the Einstein Field Equations (EFEs) is in generalized harmonic gauge. The choice of gauge is generally related to the coordinates used to cast the EFEs within a spacetime foliation. A naive choice of gauge adapted to hyperboloidal coordinates may not be the most optimal way to solve the EFEs on these slices. In this talk, we shall discuss a choice of compactified hyperboloidal coordinates that not only are physically motivated but also facilitate mapping future-null infinity onto a finite computational grid. We decouple our choice of gauge from this choice of coordinates to maintain the hyperbolicity of the EFEs via the dual-foliation formalism. We introduce a numerical scheme that assures stability for a class of linear hyperbolic systems on these slices. Finally, we discuss the possibility of extending this numerical scheme for studying initial value problems for the EFEs on these slices.