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@article{Abrahams92b,
author = {Abrahams, A. M. and Evans, C. R.},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Axisymmetric black holes, Black holes, Gravitational collapse, Maximal slicing, Numerical relativity},
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journal = {Phys. Rev. D},
keywords = {Apparent horizons, Axisymmetric black holes, Black holes, Brill waves, Cosmic censorship, Curvature, Hoop conjecture, Multi black hole spacetimes, Numerical relativity, Prolate collapse},
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title = {Vacuum initial data, singularities, and cosmic censorship},
volume = {46},
year = {1992}
}
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author = {Abrahams, A. M. and Cook, G. B. and Shapiro, S. L. and Teukolsky, S. A.},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Angular momentum, Axial symmetry, Axisymmetric black holes, Black hole formation, Black holes, Collisionless matter, Distorted black holes, Event horizons, Finite difference methods, Gravitational collapse, Kerr black holes, Numerical relativity, Partial differential equations, Prolate collapse, Rotating black holes},
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cited = {9 January 2006},
doi = {10.1088/0264-9381/17/11/301},
journal = {Class. Quantum Grav.},
keywords = {Apparent horizons, Axial symmetry, Axisymmetric black holes, Black holes, Distorted black holes, Finite difference methods, Minimization, Kerr black holes, Multi black hole solutions, Numerical methods, Numerical relativity, Ordinary differential equations, Spectral methods},
onlineversion = {http://arXiv.org/abs/gr-qc/9809004},
pages = {2159--2190},
title = {Test-beds and applications for apparent horizon finders in numerical relativity},
volume = {17},
year = {2000}
}
@article{Alcubierre2003:pre-ISCO-coalescence-times,
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cited = {9 January 2006},
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journal = {Phys. Rev. D},
keywords = {Apparent horizons, Black hole angular momentum, Black hole collisions, Black hole formation, Black holes, Distorted black holes, Event horizons, Excision, Finite difference methods, Multi black hole spacetimes, Numerical methods, Numerical relativity, Partial differential equations, Rotating black holes, Smarr formula, Vacuum Einstein equations, Innermost stable circular orbits (ISCO)},
onlineversion = {http://arXiv.org/abs/gr-qc/0411149},
title = {Dynamical evolution of quasi-circular binary black hole data},
volume = {72},
year = {2005}
}
@misc{Andersson-Metzger-2007:conditions-for-MOTS-to-intersect,
author = {Andersson, L. and Metzger, J.},
format = {personal communication},
keywords = {Apparent horizons, Trapped surfaces},
note = {Personal communication from Lars Andersson to Bela Szil\'{a}gyi},
year = {2007}
}
@article{Anninos94e,
adsurl = {http://adsabs.harvard.edu/abs/1995PhRvD..51.5562A},
archiveprefix = {arXiv},
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doi = {10.1103/PhysRevD.51.5562},
eprint = {gr-qc/9412069},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Black holes, Boundary conditions, Excision, Numerical relativity},
pages = {5562--5578},
title = {Horizon boundary conditions for black hole spacetimes},
volume = {51},
year = {1995}
}
@article{Anninos94f,
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cited = {9 January 2006},
doi = {10.1103/PhysRevLett.74.630},
journal = {Phys. Rev. Lett.},
keywords = {Apparent horizons, Black holes, Distorted black holes, Event horizons, Multi black hole spacetimes, Null surfaces},
onlineversion = {http://arXiv.org/abs/gr-qc/9403011},
pages = {630--633},
title = {Dynamics of Apparent and Event Horizons},
volume = {74},
year = {1995}
}
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journal = {Phys. Rev. D},
keywords = {Apparent horizons, Axisymmetric black holes, Black holes, Distorted black holes, Kerr black holes, Minimization, Multi black hole spacetimes, Numerical methods, Numerical relativity, Schwarzschild solution, Spectral methods},
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adsurl = {http://adsabs.harvard.edu/abs/2003A&A...405..711A},
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cited = {9 January 2006},
doi = {10.1051/0004-6361:20030618},
journal = {Astron. Astrophys.},
keywords = {Axial symmetry, Boundary value problems, Nonlinear algebraic equations, Numerical methods, Numerical relativity, Relativistic fluids, Rotating stars, Spectral methods, Stationary solutions},
onlineversion = {http://arXiv.org/abs/astro-ph/0301173},
pages = {711--721},
title = {Highly accurate calculation of rotating neutron stars: Detailed description of the numerical methods},
volume = {405},
year = {2003}
}
@article{Ansorg:2004ds,
adsurl = {http://adsabs.harvard.edu/abs/2004PhRvD..70f4011A},
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cited = {9 January 2006},
doi = {10.1103/PhysRevD.70.064011},
eid = {064011},
journal = {Phys. Rev. D},
keywords = {Boundary conditions, Boundary value problems, Elliptic equations, Linear equations, Nonlinear algebraic equations, Multi black hole solutions, Nonlinear equations, Numerical methods, Numerical relativity, Spectral methods},
onlineversion = {http://arXiv.org/abs/gr-qc/0404056},
pages = {1--13},
title = {Single-domain spectral method for black hole puncture data},
volume = {70},
year = {2004}
}
@article{Ansorg:2005bp,
adsurl = {http://adsabs.harvard.edu/abs/2005PhRvD..72b4018A},
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cited = {30 January 2007},
doi = {10.1103/PhysRevD.72.024018},
eid = {024018},
journal = {Phys. Rev. D},
keywords = {Boundary conditions, Boundary value problems, Elliptic equations, Linear equations, Nonlinear algebraic equations, Multi black hole solutions, Numerical methods, Numerical relativity, Spectral methods},
onlineversion = {http://arxiv.org/abs/gr-qc/0505059},
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title = {Double-domain spectral method for black hole excision data},
volume = {72},
year = {2005}
}
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cited = {9 January 2006},
doi = {10.1103/PhysRevD.72.024019},
eid = {024019},
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journal = {Phys. Rev. D},
keywords = {Axial symmetry, Black holes, Boundary value problems, Event horizons, Linear equations, Nonlinear algebraic equations, Numerical methods, Numerical relativity, Relativistic fluids, Rotating black holes, Spectral methods, Stationary solutions},
numpages = {12},
onlineversion = {http://arXiv.org/abs/gr-qc/0505060},
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year = {2005}
}
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onlineversion = {http://arXiv.org/abs/gr-qc/0405109},
pages = {227--265},
primaryclass = {gr-qc},
publisher = {Wiley},
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@book{Ascher-Mattheij-Russel-1988,
address = {Englewood Cliffs, U.S.A.},
author = {Ascher, U. M. and Mattheij, R. M. M. and Russell, R. D.},
keywords = {Boundary value problems, Finite difference methods, Nonlinear algebraic equations, Ordinary differential equations},
publisher = {Prentice-Hall},
title = {Numerical Solution of Boundary Value Problems for Ordinary Differential Equations},
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@article{Ashtekar98a,
archiveprefix = {arXiv},
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cited = {9 January 2006},
doi = {10.1088/0264-9381/16/2/027},
eprint = {gr-qc/9812065},
journal = {Class. Quantum Grav.},
keywords = {Boundary conditions, Dynamical horizons, Event horizons, Horizons, Null surfaces, Quasi-local black holes, Three-manifolds, Trapping horizons},
onlineversion = {http://arXiv.org/abs/gr-qc/9812065},
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eid = {261101},
eprint = {gr-qc/0207080},
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keywords = {Black holes, Constraint equations, Dynamical horizons, Event horizons, Hamiltonian constraint, Horizons, Killing field, Killing horizons, Null surfaces, Quasi-local black holes, Three-manifolds, Trapped surfaces, Trapping horizons},
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@article{Ashtekar03a,
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journal = {Phys. Rev. D},
keywords = {Black holes, Constraint equations, Dynamical horizons, Event horizons, Hamiltonian constraint, Horizons, Killing field, Killing horizons, Null surfaces, Quasi-local black holes, Three-manifolds, Trapped surfaces, Trapping horizons},
numpages = {25},
onlineversion = {http://arXiv.org/abs/gr-qc/0308033},
title = {Dynamical horizons and their properties},
volume = {68},
year = {2003}
}
@article{Ashtekar05,
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cited = {9 January 2006},
eprint = {gr-qc/0503109},
journal = {Adv. Theor. Math. Phys.},
keywords = {Apparent horizons, Area increase law, Black holes, Dynamical horizons, Event horizons, Horizons, Isolated horizons, Killing field, Null surfaces, Three-manifolds, Trapped surfaces, Trapping horizons},
onlineversion = {http://arXiv.org/abs/gr-qc/0503109},
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title = {Some uniqueness results for dynamical horizons},
volume = {95},
year = {2005}
}
@article{Ashtekar:2004cn,
archiveprefix = {arXiv},
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cited = {9 January 2006},
eid = {lrr-2004-10},
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journal = {Living Rev. Relativity},
keywords = {Black holes, Constraint equations, Dynamical horizons, Event horizons, Hamiltonian constraint, Horizons, Killing field, Killing horizons, Null surfaces, Quasi-local black holes, Three-manifolds, Trapped surfaces, Trapping horizons},
title = {Isolated and Dynamical Horizons and Their Applications},
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year = {2004}
}
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doi = {10.1103/PhysRevD.71.024035},
eid = {024035},
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journal = {Phys. Rev. D},
keywords = {Angular momentum, Apparent horizons, Black hole formation, Black holes, Computational fluid dynamics, Constraints, Distorted black holes, Event horizons, Excision, Finite difference methods, Finite volume methods, Gravitational collapse, Hamiltonian constraint, Horizons, Instability, Mass formula, Numerical methods, Numerical relativity, Relativistic fluid dynamics, Relativistic hydrodynamics, Rotating black holes, Rotating stars, Smarr formula, Trapped surfaces},
onlineversion = {http://arXiv.org/abs/gr-qc/0403029},
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volume = {71},
year = {2005}
}
@misc{Bartnik-proof:mean-curvature-flow-cant-move-through-AH,
author = {Bartnik, R.},
format = {personal communication},
keywords = {Apparent horizons, Inverse mean curvature flow, Ricci flow},
note = {Personal communication from Robert Bartnik to Carsten Gundlach}
}
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keywords = {Apparent horizons, Black holes, Minimization, Numerical methods, Numerical relativity, Spectral methods},
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keywords = {Apparent horizons, Black holes, Event horizons, Finite difference methods, Numerical methods, Numerical relativity, Spectral methods},
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year = {2003}
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address = {Urbana-Champaign, U.S.A.},
author = {Bernstein, D.},
keywords = {Apparent horizons, Finite difference methods, Inverse mean curvature flow, Numerical methods, Numerical relativity, Ricci flow},
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format = {project homepage},
keywords = {Numerical methods, Partial differential equations},
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@phdthesis{Caveny-2002,
address = {Austin, U.S.A.},
author = {Caveny, S. A.},
format = {phd},
keywords = {Apparent horizons, Black hole collisions, Black holes, Distorted black holes, Event horizons, Finite difference methods, Multi black hole spacetimes, Numerical methods, Numerical relativity, Topology change},
school = {University of Texas at Austin},
title = {Tracking Black Holes in Numerical Relativity: Foundations and Applications},
year = {2002}
}
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@phdthesis{Choptuik86,
address = {Vancouver, Canada},
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format = {phd},
keywords = {Apparent horizons, Boundary conditions, Finite difference methods, Initial boundary value problem, Mass functions, Numerical methods, Numerical relativity, Partial differential equations, Scalar fields, Spherical symmetry},
school = {University of British Columbia},
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address = {Cambridge, U.K.; New York, U.S.A.},
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editor = {Evans, C. R. and Finn, L. S. and Hobill, D. W.},
keywords = {Apparent horizons, Boundary conditions, Finite difference methods, Initial boundary value problem, Mass functions, Numerical methods, Numerical relativity, Partial differential equations, Scalar fields, Spherical symmetry},
pages = {206--221},
publisher = {Cambridge University Press},
title = {Experiences with an Adaptive Mesh Refinement Algorithm in Numerical Relativity},
year = {1989}
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cited = {9 January 2006},
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volume = {193},
year = {1998}
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@phdthesis{Cook90,
address = {Chapel Hill, U.S.A.},
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format = {phd},
keywords = {Apparent horizons, Axial symmetry, Axisymmetric black holes, Black holes, Boundary value problems, Constraint equations, Distorted black holes, Elliptic equations, Finite difference methods, Multi black hole solutions, Numerical methods, Numerical relativity, Rotating black holes},
school = {University of North Carolina at Chapel Hill},
title = {Initial Data for the Two-Body Problem of General Relativity},
year = {1990}
}
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author = {Cook, G. B. and York Jr, J. W.},
journal = {Phys. Rev. D},
keywords = {Angular momentum, Axisymmetric black holes, Black holes, Boundary value problems, Constraint equations, Distorted black holes, Elliptic equations, Finite difference methods, Maximal hypersurfaces, Numerical methods, Numerical relativity},
pages = {1077--1085},
title = {Apparent Horizons for Boosted or Spinning Black Holes},
volume = {41},
year = {1990}
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author = {Cook, G. B. and Abrahams, A. M.},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Axisymmetric black holes, Black holes, Boundary value problems, Causal structure, Elliptic equations, Event horizons, Finite difference methods, Horizon geometry, Maximal hypersurfaces, Numerical methods, Numerical relativity, Trapped surfaces},
pages = {702--713},
title = {Horizon Structure of Initial-Data Sets for Axisymmetric Two-Black-Hole Collisions},
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keywords = {Numerical methods},
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cited = {9 January 2006},
doi = {10.1145/992200.992205},
journal = {ACM Trans. Math. Software},
keywords = {Linear equations, Numerical methods},
note = {TR-02-001},
onlineversion = {http://www.cise.ufl.edu/~davis/},
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volume = {30},
year = {2004}
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cited = {9 January 2006},
doi = {10.1145/992200.992206},
journal = {ACM Trans. Math. Software},
keywords = {Linear equations, Numerical methods},
note = {TR-02-002},
onlineversion = {http://www.cise.ufl.edu/~davis/},
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title = {Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method},
volume = {30},
year = {2004}
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keywords = {Linear equations, Numerical methods},
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volume = {18},
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journal = {ACM Trans. Math. Software},
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keywords = {Apparent horizons, Black hole collisions, Multi black hole spacetimes, Numerical relativity},
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year = {2006}
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author = {Diener, P.},
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cited = {9 January 2006},
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numpages = {14},
onlineversion = {http://arXiv.org/abs/gr-qc/0206008},
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address = {Oxford, U.K.; New York, U.S.A.},
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keywords = {Linear equations, Numerical methods},
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address = {Austin, U.S.A.},
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format = {phd},
keywords = {Apparent horizons, Axial symmetry, Axisymmetric black holes, Black hole formation, Black holes, Brill waves, Computational fluid dynamics, Distorted black holes, Finite difference methods, Gravitational collapse, Maximal slicing, Numerical methods, Numerical relativity, Ordinary differential equations, Partial differential equations, Relativistic fluid dynamics},
school = {University of Texas at Austin},
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@article{Eardley75,
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journal = {Phys. Rev. D},
keywords = {Apparent horizons, Black hole formation, Black holes, Collisionless matter, Dust, Elliptic equations, Finite difference methods, Gravitational collapse, Prolate collapse},
pages = {3072--3076},
title = {Gravitational Collapse of Marginally Bound Spheroids: Initial Conditions},
volume = {12},
year = {1975}
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@phdthesis{Eppley75,
address = {Princeton, U.S.A.},
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format = {phd},
keywords = {ADM formalism, Apparent horizons, Asymptotically flat data, Axisymmetric black holes, Black hole collisions, Black holes, Boundary value problems, Elliptic equations, Finite difference methods, Foliations, Instability, Maximal hypersurfaces, Maximal slicing, Multi black hole spacetimes, Numerical methods, Numerical relativity, Ordinary differential equations, Partial differential equations},
school = {Princeton University},
title = {The numerical evolution of the collision of two black holes},
year = {1975}
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journal = {Phys. Rev. D},
keywords = {Apparent horizons, Axisymmetric black holes, Black holes, Brill waves, Finite difference methods, Mass formula, Maximal slicing, Numerical methods, Numerical relativity, Partial differential equations, Quasi-local mass, Scalar curvature},
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year = {1977}
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address = {Cambridge; New York},
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onlineversion = {http://www.netlib.org/odepack/index.html},
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publisher = {North-Holland},
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address = {Austin, U.S.A.},
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year = {1996}
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onlineversion = {http://arXiv.org/abs/gr-qc/0503113},
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address = {Englewood Cliffs, U.S.A.},
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journal = {Class. Quantum Grav.},
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cited = {9 January 2006},
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eid = {084026},
journal = {Phys. Rev. D},
keywords = {Axial symmetry, Boundary value problems, Brill waves, Constraint equations, Numerical methods, Numerical relativity, Rotating black holes, Spectral methods},
onlineversion = {http://arXiv.org/abs/gr-qc/9911014},
pages = {1--13},
title = {Spectral methods for numerical relativity: The initial data problem},
volume = {62},
year = {2000}
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adsurl = {http://adsabs.harvard.edu/abs/2000PhRvD..62h4032K},
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cited = {9 January 2006},
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eid = {084032},
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journal = {Phys. Rev. D},
keywords = {Black holes, Boundary conditions, Hyperbolic partial differential equations, Initial boundary value problem, Numerical methods, Numerical relativity, Spectral methods, Spherical symmetry},
onlineversion = {http://arXiv.org/abs/gr-qc/0005056},
primaryclass = {gr-qc},
title = {Black hole evolution by spectral methods},
volume = {62},
year = {2000}
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@unpublished{Kidder00b,
author = {Kidder, L. E. and Scheel, M. A. and Teukolsky, S. A. and Cook, G. B.},
conference = {Miniprogram on Colliding Black Holes: Mathematical Issues in Numerical Relativity, held at the Institute for Theoretical Physics, UC at Santa Barbara, 10\,--\,28 January 2000},
format = {conference paper},
keywords = {Black holes, Boundary conditions, Hyperbolic partial differential equations, Initial boundary value problem, Numerical methods, Numerical relativity, Spectral methods},
title = {Spectral Evolution of Einstein's Equations},
year = {2000}
}
@article{Kriele97,
author = {Kriele, M. and Hayward, S. A.},
doi = {10.1063/1.532010},
journal = {J. Math. Phys.},
keywords = {Apparent horizons, Black holes, Trapped surfaces},
pages = {1593--1604},
title = {Outer trapped surfaces and their apparent horizon},
volume = {38},
year = {1997}
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@article{Lehner-etal-1999:BH-coalescence-geometry,
adsurl = {http://adsabs.harvard.edu/abs/1999PhRvD..60d4005L},
archiveprefix = {arXiv},
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eid = {044005},
eprint = {gr-qc/9809034},
journal = {Phys. Rev. D},
keywords = {Black hole collisions, Event horizons, Multi black hole spacetimes, Numerical relativity, Topology change},
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volume = {60},
year = {1999}
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cited = {9 January 2006},
format = {institutional homepage},
keywords = {Black hole collisions, Event horizons, Multi black hole spacetimes, Numerical relativity, Topology change},
publisher = {Pittsburgh Supercomputing Center},
title = {Bagels Form When Black Holes Collide},
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conference = {Proceedings of the meeting held at Stanford University, July 24\,--\,30, 1994},
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keywords = {Apparent horizons, Numerical methods, Numerical relativity, Spectral methods},
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publisher = {World Scientific},
title = {A 3D Apparent Horizon Finder},
year = {1996}
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author = {Lin, L.-M. and Novak, J.},
format = {personal communication},
keywords = {Apparent horizons, Kerr black holes, Numerical methods, Numerical relativity, Spectral methods},
note = {Personal communication from Lap-Ming Lin to Jonathan Thornburg},
title = {Three-dimensional apparent horizon finder in LORENE},
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keywords = {Numerical methods},
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year = {1987}
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@misc{Madderom-1984:ILUCG,
author = {Madderom, P.},
format = {unknown},
keywords = {Linear equations, Numerical methods},
note = {Fortran 66 subroutine},
title = {Incomplete LU-Decomposition -- Conjugate Gradient},
year = {1984}
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doi = {10.1016/S0010-4655(99)00501-9},
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journal = {Science},
keywords = {Axial symmetry, Axisymmetric black holes, Black hole collisions, Black holes, Causal structure, Collisionless matter, Dust, Event horizons, Finite difference methods, Geodesics, Gravitational collapse, Multi black hole spacetimes, Numerical relativity, Partial differential equations},
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editor = {Sato, H. and Nakamura, T.},
keywords = {Apparent horizons, Black hole collisions, Multi black hole solutions, Numerical methods, Spectral methods},
pages = {313--319},
publisher = {World Scientific},
title = {Apparent Horizon of Initial Data for Black Hole-Collisions},
year = {1986}
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keywords = {Inverse mean curvature flow, Numerical methods, Parabolic equations, Ricci flow},
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publisher = {University of T{\"{u}}bingen},
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url = {http://www.uni-tuebingen.de/uni/opx/reports.html},
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keywords = {Apparent horizons, Black hole formation, Collisionless matter, Dust, Gravitational collapse, Maximal slicing, Numerical relativity, Spherical symmetry},
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year = {1985}
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cited = {20 August 2003},
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number = {ANL-95/11 -- Revision 2.1.5},
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publisher = {Birkh\"auser},
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cited = {9 January 2006},
format = {arxiv},
keywords = {Apparent horizons, Elliptic equations, Linear equations, Nonlinear algebraic equations, Numerical methods, Numerical relativity},
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keywords = {Apparent horizons, Elliptic equations, Linear equations, Nonlinear algebraic equations, Numerical methods, Numerical relativity},
onlineversion = {http://arXiv.org/abs/gr-qc/0306006},
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keywords = {Apparent horizons, Black hole formation, Black holes, Event horizons, Geodesics, Gravitational collapse, Maximal slicing, Numerical methods, Numerical relativity, Relativistic fluid dynamics, Spherical symmetry},
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volume = {235},
year = {1980}
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keywords = {Apparent horizons, Black hole formation, Black holes, Collisionless matter, Dust, Event horizons, Geodesics, Gravitational collapse, Maximal slicing, Numerical methods, Numerical relativity, Spherical symmetry},
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keywords = {Apparent horizons, Axial symmetry, Axisymmetric black holes, Black hole collisions, Black hole formation, Collisionless matter, Dust, Gravitational collapse, Maximal slicing, Numerical methods, Numerical relativity, Ordinary differential equations},
pages = {2739--2750},
title = {Collision of relativistic clusters and the formation of black holes},
volume = {45},
year = {1992}
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@article{Shibata97a,
author = {Shibata, M.},
journal = {Phys. Rev. D},
keywords = {Apparent horizons, Axisymmetric black holes, Elliptic equations, Nonlinear algebraic equations, Linear equations, Numerical methods, Numerical relativity},
pages = {2002--2013},
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volume = {55},
year = {1997}
}
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journal = {Phys. Rev. D},
keywords = {Apparent horizons, Elliptic equations, Nonlinear algebraic equations, Linear equations, Numerical methods, Numerical relativity},
title = {Apparent Horizon Finder for General Three-Dimensional Spaces},
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year = {2000}
}
@phdthesis{Shoemaker99,
address = {Austin, U.S.A.},
author = {Shoemaker, D. M.},
format = {phd},
keywords = {Apparent horizons, Inverse mean curvature flow, Multi black hole spacetimes, Numerical methods, Numerical relativity, Ricci flow, Topology change},
school = {The University of Texas at Austin},
title = {Apparent Horizons in Binary Black Hole Spacetimes},
year = {1999}
}
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keywords = {Apparent horizons, Inverse mean curvature flow, Multi black hole spacetimes, Numerical methods, Numerical relativity, Ricci flow, Topology change},
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year = {2000}
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adsurl = {http://adsabs.harvard.edu/abs/2007CQGra..24S.275S},
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title = {Finding apparent horizons in numerical relativity},
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volume = {59},
year = {1999}
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cited = {9 January 2006},
format = {arxiv},
keywords = {Apparent horizons, Black holes, Initial boundary value problem, Numerical methods, Numerical relativity, Scalar fields, Spherical symmetry},
title = {A 3+1 Computational Scheme for Dynamic Spherically Symmetric Black Hole Spacetimes -- II: Time Evolution},
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year = {1999}
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doi = {10.1088/0264-9381/21/2/026},
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journal = {Class. Quantum Grav.},
keywords = {Apparent horizons, Elliptic equations, Linear equations, Nonlinear algebraic equations, Numerical methods, Numerical relativity},
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pages = {743--766},
title = {A fast apparent horizon finder for three-dimensional Cartesian grids in numerical relativity},
volume = {21},
year = {2004}
}
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journal = {Class. Quantum Grav.},
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year = {1991}
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@phdthesis{Walker98a,
address = {Urbana, U.S.A.},
author = {Walker, P.},
format = {phd},
keywords = {Apparent horizons, Axial symmetry, Axisymmetric black holes, Distorted black holes, Event horizons, Excision, Finite difference methods, Hyperbolic partial differential equations, Multi black hole spacetimes, Null surfaces, Numerical methods, Numerical relativity, Rotating black holes, Spherical symmetry},
school = {University of Illinois at Urbana-Champaign},
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year = {1998}
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editor = {Smarr, L. L.},
gbs_id = {rJBOAAAAIAAJ{\&}pg=PA83},
keywords = {ADM formalism, Cauchy problem, Constraint equations},
pages = {83--126},
publisher = {Cambridge University Press},
title = {Kinematics and Dynamics of General Relativity},
year = {1979}
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keywords = {ADM formalism, Apparent horizons, Cauchy problem, Constraint equations},
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publisher = {Cambridge University Press},
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