100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

Probing Space-Time Through Numerical Simulations 153spinning neutron stars, gamma ray bursts and stochastic backgrounds arejust a few examples of these sources. The detection of gravitational waves isa formidable undertaking, requiring innovative engineering, powerful dataanalysis tools and careful theoretical modelling. Among the sources of gravitationalradiation, binary systems consisting of black holes and/or neutronstars are expected to be dominant. The ultimate goal of source modellingis to develop generic numerical codes capable of modelling the inspiral,merger, and ringdown of a compact object binary. Over the last couple ofdecades, advances in numerical algorithms and computer hardware havebring us closer to this goal.General relativity and singularities come hand in hand. The mathematicalstudy of singularities has been mostly done analytically. An analytic approachhas obvious limitations; they are either restricted to over simplifiedsituations or are only able to produce broad general conclusions. Numericalsimulations are becoming an important tool in the exploration of theproperties of singularities. In particular, the numerical work by Berger andcollaborators 14 on investigations of naked singularities, chaos of the Mixmastersingularity and singularities in spatially inhomogeneous cosmologieshas already demonstrated the great potential that a numerical approach hasin producing detailed understanding of singularities in physically realisticsituations.The question of whether or not there is a minimum finite black hole massin the gravitational collapse of smooth, asymptotically flat initial data leadto what is perhaps currently the most exciting and elegant result in numericalrelativity. Choptuik used powerful adaptive mesh refinement methodsto prove that the mass is infinitesimal. 23 In addition, Choptuik’s work discoveredcompletely unexpected effects. One of them is the scaling relationM ≈ C |p − p ∗ | γ (1)with M the black hole mass and p a parameter characterizing the familyof initial data. Another unexpected effect found by Choptuik is that thesolution has a logarithmic scale-periodicity when p → p ∗ . Finally, Choptuikfound that the phenomena is universal, namely the “critical exponent”γ ≈ 0.37 and the “critical echoing period” ∆ ≈ 3.44 are the same for allone-parameter families of initial data. For a review of Choptuik’s criticalphenomena, its extensions and applications see Gundlach. 33Numerical relativity is now an area with many directions of research.The computational modelling of compact object binaries is, however, whatis attracting most of the attention. This article focuses on this effort. It