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## Seminar on

**Mathematical General Relativity**

*Organizers:*

* *Philippe G. LeFloch *(Paris) *

*Ghani Zeghib (Lyon)*

**ANR Project**

#### “Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”

**Friday December 21, 2012**

### Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

**Lecture room ** 1525-3-21

**Lecture room**

**Speaker**

**11h15 – José A. Font (Valencia) Simulations of neutron star mergers and black hole-torus systems**

Abstract. Merging binary neutron stars are among the strongest sources of gravitational waves and have features compatible with the events producing short–hard gamma-ray bursts. Numerical relativity has reached a stage where a complete description of the inspiral, merger and post-merger phases of the late evolution of binary neutron star systems is possible. This talk presents an overview of numerical relativity simulations of binary neutron star mergers and the evolution of the resulting black hole–torus systems. Such numerical work is based upon a basic theoretical framework which comprises the Einstein’s equations for the gravitational field and the hydrodynamics equations for the evolution of the matter fields. The most well-established formulations for both systems of equations are briefly discussed, along with the numerical methods best suited for their numerical solution, specifically high-order finite-differencing for the case of the gravitational field equations and high-resolution shock-capturing schemes for the case of the relativistic Euler equations. A number of recent results are reviewed, namely the outcome of the merger depending on the initial total mass and equation of state of the binary, as well as the post-merger evolution phase once a black hole–torus system is produced. Such system has been shown to be subject to non-axisymmetric instabilities leading to the emission of large amplitude gravitational waves.

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