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 Binary Neutron Star Evolution | Motivations
Gravitational wave astronomy and high-energy astrophysics are two emerging areas of modern astronomy. Despite the fact that the scientists in these two fields observe our universe with fundamentally different radiations: one gravitational and the other electromagnitic, they all apply the theory of GR, originated by Albert Einstein. Furthermore, high-energy radiations (X-ray, gamma-ray) are often emitted in regions of strong gravitational fields near compact objects, such as NSs and blackholes (BHs), which are usually sources of gravitational radiations. Although the primary goal of this work is to study the gravitational waves emitted from coalescing binary NSs, some results from our work might shed light on modeling GRBs as well. | | 3+1 Decomposition
We use BSSN (Shibata & Nakamura 1995; Baumgarte & Shapiro 1999) formulism, which is based on 3+1 ADM (Arnowitt, Deser, Misner) formulism to solve the full EEs. 4-D Spacetime is decomposed into layers of 3-D space-like hypersurfaces sitting along 1-D time-like streamline (with a time-like tagent vector at every point on it). Each hypersurface is labeled by a number which is regarded as the coordinate time and 3 other numbers are used as spatial coordinates on each hypersurface. How the 4-D spacetime is sliced and how all these numbers are assigned have nothing to do with the physics involved. These are gauge conditions which can help to change the outfit of your physical eqations and the way to solve those equations mathematically but nothing fundamental changed underneath. The freedom to choose arbitrary gauge conditions is authorized by the equivalence principle, which is the foundation of Einstein's theory of general relativity. | | General Relativistic Hydrodynamics
Perfect fluid (fluid without shear stresses, viscosity and heat conduction) is widely used to model neutron stars. | | Multiple Length Scale Initial Value Problem
The coalescence of two NSs involves multiple length scales:
A short length scale of the star radius: requires high enough resolution in each star is necessary to resolve hydrodynamical variables to maintain a stable configuration in the Einstein theory.
A long length scale of the orbital radius: requires enough resolution to resolve the interactions between two stars.
A longer length scale of the gravitational wave length due to the orbital motion: requires big enough computational domain to cover those GWs due to the orbital motion.
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