Abstract
I review the development of numerical evolution codes for general relativity based upon the characteristic initial-value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D-axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black-hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black-hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.
Highlights
I review the development of numerical evolution codes for general relativity based upon the characteristic initial-value problem
We trace the development of characteristic algorithms from model 1D problems to a 2D axisymmetric code, which computes the gravitational radiation from the oscillation and gravitational collapse of a relativistic star, to a 3D code designed to calculate the waveform emitted in the merger to ringdown phase of a binary black hole
Using a combination of numerical and analytic techniques based upon null coordinates, Hod and Piran have made an extensive series of investigations of the spherically-symmetric charged Einstein– Klein–Gordon system dealing with the effect of charge on critical gravitational collapse [165] and the late time tail decay of a charged scalar field on a Reissner–Nordstrom black hole [166, 169, 167, 168]
Summary
We are in an era in which Einstein’s equations can effectively be considered solved at the local level. We trace the development of characteristic algorithms from model 1D problems to a 2D axisymmetric code, which computes the gravitational radiation from the oscillation and gravitational collapse of a relativistic star, to a 3D code designed to calculate the waveform emitted in the merger to ringdown phase of a binary black hole. Several numerical relativity codes for treating the problem of a neutron star near a black hole have been developed, as described in the Living Review on “Numerical Hydrodynamics in General Relativity” by Font [109]. Most of these efforts concentrate on Cauchy evolution, the characteristic approach has shown remarkable robustness in dealing with a single black hole or relativistic star. Axisymmetric studies of the oscillation and gravitational collapse of relativistic stars have been achieved (see Section 7.2) and progress has been made in the 3D simulation of a body in close orbit about a Schwarzschild black hole (see Sections 4.6 and 7.3)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
