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Numerical Relativity: Solving Einstein's Equations on the Computer
Numerical relativity is one of the major fields of contemporary general relativity and is developing continually. Yet three years ago, no textbook was available on this subject. The first textbook…
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3+1 Formalism and Bases of Numerical Relativity
These lecture notes provide some introduction to the 3+1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-contained, with detailed…
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3+1 Formalism in General Relativity: Bases of Numerical Relativity
Basic Differential Geometry.- Geometry of Hypersurfaces.- Geometry of Foliations.- 3+1 decomposition of Einstein Equation.- 3+1 Equations for Matter and Electromagnetic Field.- Conformal…
3 + 1 formalism in general relativity
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A 3+1 perspective on null hypersurfaces and isolated horizons
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Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity: 1. Method and tests
We present a numerical method to compute quasiequilibrium configurations of close binary neutron stars in the precoalescing stage. A hydrodynamical treatment is performed under the assumption that…
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Numerical approach for high precision 3D relativistic star models
A multidomain spectral method for computing very high precision three-dimensional stellar models is presented. The boundary of each domain is chosen in order to coincide with a physical discontinuity…
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Axisymmetric rotating relativistic bodies: a new numerical approach for exact' solutions
A new set of equations and a new numerical method for computing stationary axisymmetric rapidly rotating star models within general relativity is presented. The source term of the gravitational field…
Prospects for fundamental physics with LISA
In this paper, which is of programmatic rather than quantitative nature, we aim to further delineate and sharpen the future potential of the LISA mission in the area of fundamental physics. Given the…
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GYOTO: a new general relativistic ray-tracing code
GYOTO, a general relativistic ray-tracing code, is presented. It aims at computing images of astronomical bodies in the vicinity of compact objects, as well as trajectories of massive bodies in…
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