Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1997-01-31
Class.Quant.Grav. 14 (1997) 977-990
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
18 pages. To be published in Class. Quantum Grav
Scientific paper
10.1088/0264-9381/14/4/013
We present a finite difference version of the eth formalism, which allows use of tensor fields in spherical coordinates in a manner which avoids polar singularities. The method employs two overlapping stereographic coordinate patches, with interpolations between the patches in the regions of overlap. It provides a new and effective computational tool for dealing with a wide variety of systems in which spherical coordinates are natural, such as the generation of radiation from an isolated source. We test the formalism with the evolution of waves in three spatial dimensions and the calculation of the curvature scalar of arbitrarily curved geometries on topologically spherical manifolds. The formalism is applied to the solution of the Robinson-Trautman equation and reveals some new features of gravitational waveforms in the nonlinear regime.
Go'mez Roberto
Lehner Luis
Papadopoulos Philippos
Winicour Jeffrey
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