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theoreticalbrackground_gw [2022/07/18 10:54]
theoastro [Gravitational-Wave Emission] 		theoreticalbrackground_gw [2022/07/18 11:05] (current)
theoastro [Gravitational-Wave Modelling]
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 At the lowest order, gravitational-wave radiation can be approximated through the quadrupole formula  At the lowest order, gravitational-wave radiation can be approximated through the quadrupole formula 
 {{quadrupole_formula_small.png}} {{quadrupole_formula_small.png}}
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 in which the left-hand side (the spatial part of the trace reversed perturbation of the metric) depends on the distance to the source D, as well as the second time derivative of the quadrupole moment of the source Q. Due to the prefactor G/c^4 it becomes evident that only objects with an extremely large second time derivative of the quadrupole tensor could create detectable gravitational waves. Because of this reason, it is understandable that all previously detected gravitational-wave signals originated from compact binaries (binary black holes, binary neutron stars, black hole - neutron stars) in which the compact objects orbit around each other with velocities that can reach a few tenths of the speed of light.  in which the left-hand side (the spatial part of the trace reversed perturbation of the metric) depends on the distance to the source D, as well as the second time derivative of the quadrupole moment of the source Q. Due to the prefactor G/c^4 it becomes evident that only objects with an extremely large second time derivative of the quadrupole tensor could create detectable gravitational waves. Because of this reason, it is understandable that all previously detected gravitational-wave signals originated from compact binaries (binary black holes, binary neutron stars, black hole - neutron stars) in which the compact objects orbit around each other with velocities that can reach a few tenths of the speed of light. 
  
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 ==== Gravitational-Wave Modelling ==== ==== Gravitational-Wave Modelling ====
  
 +Due to the complexity of Einstein's field theory, there is to date no closed form solution to the two-body problem and one requires models to describe model the compact binary coalescence and the emitted gravitational-wave signals. Among the most important approaches are: numerical-relativity simulations, Post-Newtonian predictions, the effective-one-body approach, or black hole perturbation theory (see image below  A. Buonanno, B.S. Sathyaprakash in: General Relativity and Gravitation: A Centennial Perspective; Cambridge, University Press (2015) ) 
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 +{{GWmodels.png}}
  
 +Considering binary neutron star and black hole - neutron star systems, one also has to incorporate finite-size effects and the internal structure of neutron stars, i.e., the tidal deformability --describing the deformability of the neutron star -- enter gravitational-wave model descriptions. Over the last years, there has been significant progress in modeling binary neutron star systems capturing the strong-gravity and tidally dominated regime of the late-inspiral, but current models will not be sufficient to provide unbiased source predictions of future gravitational-wave detections. 
Last modified: le 2022/07/18 10:54

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