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

160 P. Lagunaimportance of the explicit knowledge of the field characteristics. Black holeexcision has been performed with BSSN codes without explicit reference tothe characteristic fields.The essential point in black hole excision is to locate the event horizon.This task requires, however, the complete future development of the spacetime.To circumvent this obvious difficulty, an apparent horizon (outer mosttrapped surface) is used instead. If an apparent horizon is found, an eventhorizon exists and surrounds the former. 67 For excision to work, one onlyneeds to know that the removed region is entirely contained within the horizon,thus the precise location of the event horizon is not required, findingapparent horizons suffices. Historically, because excision requires trackingthe apparent horizon, the approach was incorrectly called Apparent HorizonBoundary Condition. 52 The name is incorrect in the sense that blackhole excision does not require a boundary condition. The same equationsthat are applied in the interior of the domain are used at the boundary.4. Initial Data: The Astrophysical ConnectionWe are still at the stage in which the primary focus of simulations of neutronstars and/or black hole binaries is to achieve evolutions timescales for whichmore refined calculations would be able to deliver astrophysically interestingresults. This is a natural situation, not exclusive to numerical relativity.Progress is made in incremental steps. At the early stages, simplificationsare needed at the expense of sacrificing the accuracy of the models.Even if codes are able to handle long enough evolutions, the astrophysicalcontent of a numerical simulation is completely determined by boundaryconditions and initial data. In general relativity, constructing initial data isa non-trivial exercise. Data must satisfy the Hamiltonian and momentumconstraints:R + K 2 − K ij K ij = 0 (9)∇ j (K ij − h ij K) = 0 . (10)The challenge in constructing initial data is separating the four componentsin (h ij , K ij ) that are fixed by (9) and (10) from those that are freely specifiable.The pioneer work to develop such framework is due to Lichnerowicz,York and collaborators. 40,70 York in particular was fundamental in formulatingthe Initial Data Problem with a structure amenable to numericalrelativity (see Appendix B for details).Early work on multiple black hole initial data was mostly concernedwith finding any solution, without paying close attention to whether these