 |
1 |
Alcubierre, M., Brandt, S., Brügmann, B., Gundlach, C., Massó, J., Seidel, E. and Walker,
P., “Test-beds and applications for apparent horizon finders in numerical relativity”, Class.
Quantum Grav., 17, 2159–2190, (2000). [ DOI], [ADS].
|
|
2 |
Alcubierre, M. et al., “Towards standard testbeds for numerical relativity”, Class. Quantum
Grav., 21, 589–613, (2004). [DOI], [ADS].
|
|
3 |
Amsterdamski, P., Bulik, T., Gondek-Rosińska, D. and Kluźniak, W., “Marginally stable
orbits around Maclaurin spheroids and low-mass quark stars”, Astron. Astrophys., 381,
L21–L24, (2002). [DOI], [ADS].
|
|
4 |
Anderson, M., Hirschmann, E.W., Lehner, L., Liebling, S.L., Motl, P.M., Neilsen, D.,
Palenzuela, C. and Tohline, J.E., “Simulating binary neutron stars: Dynamics and gravitational
waves”, Phys. Rev. D, 77, 024006, (2008). [DOI], [ADS].
|
|
5 |
Andersson, N. and Comer, G.L., “Relativistic Fluid Dynamics: Physics for Many Different
Scales”, Living Rev. Relativity, 10, lrr-2007-1, (2007). URL (accessed 20 February 2007):
http://www.livingreviews.org/lrr-2007-1.
|
|
6 |
Ansorg, M., “Double-domain spectral method for black hole excision data”, Phys. Rev. D, 72,
024018, 1–10, (2005). [DOI], [ADS].
|
|
7 |
Ansorg, M., “A multi-domain spectral method for initial data of arbitrary binaries in general
relativity”, Class. Quantum Grav., 24, S1–S14, (2007). [DOI], [ADS].
|
|
8 |
Ansorg, M., Brügmann, B. and Tichy, W., “Single-domain spectral method for black hole
puncture data”, Phys. Rev. D, 70, 064011, 1–13, (2004). [DOI], [ADS].
|
|
9 |
Ansorg, M., Kleinwächter, A. and Meinel, R., “Highly accurate calculation of rotating neutron
stars”, Astron. Astrophys., 381, L49–L52, (2002). [DOI], [ADS].
|
|
10 |
Ansorg, M., Kleinwächter, A. and Meinel, R., “Highly accurate calculation of rotating neutron
stars: Detailed description of the numerical methods”, Astron. Astrophys., 405, 711–721,
(2003). [DOI], [ADS].
|
|
11 |
Ansorg, M., Kleinwächter, A. and Meinel, R., “Relativistic Dyson Rings and Their Black Hole
Limit”, Astrophys. J. Lett., 582, L87–L90, (2003). [DOI], [ADS].
|
|
12 |
Ansorg, M., Kleinwächter, A. and Meinel, R., “Uniformly rotating axisymmetric fluid
configurations bifurcating from highly flattened Maclaurin spheroids”, Mon. Not. R. Astron.
Soc., 339, 515–523, (2003). [DOI], [ADS].
|
|
13 |
Ansorg, M. and Petroff, D., “Black holes surrounded by uniformly rotating rings”, Phys. Rev.
D, 72, 024019, 1–12, (2005). [DOI], [gr-qc/0505060v4].
|
|
14 |
Arnowitt, R., Deser, S. and Misner, C.W., “The dynamics of general relativity”, in Witten,
L., ed., Gravitation: An Introduction to Current Research, pp. 227–265, (Wiley, New York;
London, 1962). [DOI], [ADS], [gr-qc/0405109].
|
|
15 |
Babiuc, M.C., Szilágyi, B., Hawke, I. and Zlochower, Y., “Gravitational wave extraction based
on Cauchy-characteristic extraction and characteristic evolution”, Class. Quantum Grav., 22,
5089–5107, (2005). [DOI], [ADS].
|
|
16 |
Baiotti, L., Giacomazzo, B. and Rezzolla, L., “Accurate evolutions of inspiraling neutron-star
binaries: Prompt and delayed collapse to a black hole”, Phys. Rev. D, 78, 084033, (2008). [DOI],
[arXiv:0804.0594].
|
|
17 |
Baiotti, L., Hawke, I., Montero, P.J., Löffler, F., Rezzolla, L., Stergioulas, N., Font, J.A. and
Seidel, E., “Three-dimensional relativistic simulations of rotating neutron-star collapse to a
Kerr black hole”, Phys. Rev. D, 71, 024035, 1–30, (2005). [DOI], [ADS].
|
|
18 |
Baker, J.G., Centrella, J., Choi, D.-I., Koppitz, M. and van Meter, J., “Gravitational-Wave
Extraction from an Inspiraling Configuration of Merging Black Holes”, Phys. Rev. Lett., 96,
111102, (2006). [DOI].
|
|
19 |
Bardeen, J.M. and Piran, T., “General relativistic axisymmetric rotating systems: Coordinates
and equations”, Phys. Rep., 96, 205–250, (1983). [DOI], [ADS].
|
|
20 |
Bartnik, R., “Einstein equations in the null quasispherical gauge”, Class. Quantum Grav., 14,
2185–2194, (1997). [DOI], [ADS].
|
|
21 |
Bartnik, R. and Norton, A.H., “Numerical Methods for the Einstein Equations in Null
Quasi-Spherical Coordinates”, SIAM J. Sci. Comput., 22, 917–950, (2000). [DOI].
|
|
22 |
Baumgarte, T.W., “Innermost stable circular orbit of binary black holes”, Phys. Rev. D, 62,
024018, 1–8, (2000). [DOI], [ADS].
|
|
23 |
Baumgarte, T.W., Cook, G.B., Scheel, M.A., Shapiro, S.L. and Teukolsky, S.A., “Implementing
an apparent-horizon finder in three dimensions”, Phys. Rev. D, 54, 4849–4857, (1996). [DOI],
[ADS].
|
|
24 |
Baumgarte, T.W., Cook, G.B., Scheel, M.A., Shapiro, S.L. and Teukolsky, S.A., “General
relativistic models of binary neutron stars in quasiequilibrium”, Phys. Rev. D, 57, 7299–7311,
(1998). [DOI], [ADS].
|
|
25 |
Baumgarte, T.W. and Shapiro, S.L., “Numerical integration of Einstein’s field equation”, Phys.
Rev. D, 59, 024007, (1998). [DOI], [ADS], [gr-qc/9810065].
|
|
26 |
Bejger, M., Gondek-Rosińska, D., Gourgoulhon, E., Haensel, P., Taniguchi, K. and Zdunik,
J.L., “Impact of the nuclear equation of state on the last orbits of binary neutron stars”, Astron.
Astrophys., 431, 297–306, (2005). [DOI], [ADS].
|
|
27 |
Bejger, M., Haensel, P. and Zdunik, J.L., “Rotation at 1122 Hz and the neutron star structure”,
Astron. Astrophys., 464, L49–L52, (2007). [DOI], [ADS].
|
|
28 |
Belczynski, K., Kalogera, V. and Bulik, T., “A Comprehensive Study of Binary Compact
Objects as Gravitational Wave Sources: Evolutionary Channels, Rates, and Physical
Properties”, Astrophys. J., 572, 407–431, (2002). [DOI], [ADS].
|
|
29 |
Ben Belgacem, F. and Bernardi, C., “Spectral Element Discretization of the Maxwell
Equations”, Math. Comput., 68, 1497–1520, (1999). [ADS].
|
|
30 |
Bičák, J., “Einstein equations: exact solutions”, in Françoise, J.-P., Naber, G.L. and Tsou,
S.T., eds., Encyclopedia of Mathematical Physics, 2, pp. 165–173, (Elsevier, Amsterdam, 2006).
[gr-qc/0604102].
|
|
31 |
Blanchet, L., “Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact
Binaries”, Living Rev. Relativity, 9, lrr-2006-4, (2006). URL (accessed 19 January 2007):
http://www.livingreviews.org/lrr-2006-4.
|
|
32 |
Bocquet, M., Bonazzola, S., Gourgoulhon, E. and Novak, J., “Rotating neutron star models
with a magnetic field”, Astron. Astrophys., 301, 757–775, (1995). [ADS].
|
|
33 |
Bonazzola, S., “Cyclotron lines in compact X-ray sources”, in Perola, G.C. and Salvati, M.,
eds., Non-thermal and very high temperature phenomena in X-ray astronomy, Proceedings of
an international workshop, held in Rome, Italy, December 19 – 20, 1983, pp. 55–75, (Università
‘La Sapienza’, Rome, 1985).
|
|
34 |
Bonazzola, S., Frieben, J. and Gourgoulhon, E., “Spontaneous Symmetry Breaking of Rapidly
Rotating Stars in General Relativity”, Astrophys. J., 460, 379–389, (1996). [DOI], [ADS].
|
|
35 |
Bonazzola, S., Frieben, J. and Gourgoulhon, E., “Spontaneous symmetry breaking of rapidly
rotating stars in general relativity: influence of the 3D-shift vector”, Astron. Astrophys., 331,
280–290, (1998). [ADS].
|
|
36 |
Bonazzola, S. and Gourgoulhon, E., “Gravitational waves from pulsars: emission by the
magnetic-field-induced distortion”, Astron. Astrophys., 312, 675–690, (1996). [ADS].
|
|
37 |
Bonazzola, S., Gourgoulhon, E., Grandclément, P. and Novak, J., “Constrained scheme for
the Einstein equations based on the Dirac gauge and spherical coordinates”, Phys. Rev. D, 70,
104007, 1–24, (2004). [DOI], [ADS].
|
|
38 |
Bonazzola, S., Gourgoulhon, E. and Marck, J.-A., “Numerical approach for high presicion 3D
relativistic star models”, Phys. Rev. D, 58, 104020, (1998). [DOI], [ADS].
|
|
39 |
Bonazzola, S., Gourgoulhon, E. and Marck, J.-A., “Numerical Models of Irrotational Binary
Neutron Stars in General Relativity”, Phys. Rev. Lett., 82, 892–895, (1999). [DOI], [ADS].
|
|
40 |
Bonazzola, S., Gourgoulhon, E. and Marck, J.-A., “Spectral methods in general astrophysics”,
J. Comput. Appl. Math., 109, 433–473, (1999). [DOI], [ADS].
|
|
41 |
Bonazzola, S., Gourgoulhon, E., Salgado, M. and Marck, J.-A., “Axisymmetric rotating
relativistic bodies: A new numerical approach for ‘exact’ solutions”, Astron. Astrophys., 278,
421–443, (1993). [ADS].
|
|
42 |
Bonazzola, S., Jaramillo, J.L. and Novak, J., “A fast stroboscopic spectral method for rotating
systems in numerical relativity”, Class. Quantum Grav., 24, 4037–4051, (2007). [DOI], [ADS].
|
|
43 |
Bonazzola, S. and Marck, J.-A., “Pseudo-spectral technique applied to numerical solutions for
stellar collapse”, Astron. Astrophys., 164, 300–309, (1986). [ADS].
|
|
44 |
Bonazzola, S. and Marck, J.-A., “Three-dimensional gas dynamics in a sphere”, J. Comput.
Phys., 87, 201–230, (1990). [DOI], [ADS].
|
|
45 |
Bonazzola, S. and Marck, J.-A., “A 1D exact treatment of shock waves within spectral methods
in plane geometry”, J. Comput. Phys., 97, 535–552, (1991). [DOI], [ADS].
|
|
46 |
Bonazzola, S. and Marck, J.-A., “Efficiency of gravitational radiation from axisymmetric and
3D stellar collapse. I. Polytropic case”, Astron. Astrophys., 267, 623–633, (1993). [ADS].
|
|
47 |
Boronski, P. and Tuckerman, L.S., “Poloidal toroidal decomposition in a finite cylinder.
I: Influence matrices for the magnetohydrodynamic equations”, J. Comput. Phys., 227,
1523–1543, (2007). [DOI], [ADS].
|
|
48 |
Boyd, J.B., Chebyshev and Fourier Spectral Methods, (Dover Publications, Mineola, N.Y.,
2001), 2nd edition. [Google Books].
|
|
49 |
Boyle, M., Lindblom, L., Pfeiffer, H., Scheel, M. and Kidder, L.E., “Testing the Accuracy and
Stability of Spectral Methods in Numerical Relativity”, Phys. Rev. D, 75, 024006, (2007).
[DOI], [gr-qc/0609047].
|
|
50 |
Brill, D.R. and Lindquist, R.W., “Interaction Energy in Geometrostatics”, Phys. Rev., 131,
471–476, (1963). [DOI], [ADS].
|
|
51 |
Brizuela, D., Martín-García, J.M. and Marugán, G.A.M., “Second- and higher-order
perturbations of a spherical spacetime”, Phys. Rev. D, 74, 044039, 1–17, (2006). [DOI], [ADS].
|
|
52 |
Brun, A.S., Miesch, M.S. and Toomre, J., “Global-scale turbulent convection and magnetic
dynamo action in the solar envelope”, Astrophys. J., 614, 1073–1098, (2004). [DOI], [ADS].
|
|
53 |
Buchman, L.T. and Sarbach, O., “Improved outer boundary conditions for Einstein’s field
equations”, Class. Quantum Grav., 24, S307–S326, (2007). [DOI], [ADS].
|
|
54 |
Calabrese, G., Pullin, J., Reula, O., Sarbach, O. and Tiglio, M., “Well Posed
Constraint-Preserving Boundary Conditions for the Linearized Einstein Equations”, Commun.
Math. Phys., 240, 377–395, (2003). [DOI], [ADS].
|
|
55 |
Campanelli, M., Lousto, C.O., Marronetti, P. and Zlochower, Y., “Accurate evolutions of
orbiting black-hole binaries without excision”, Phys. Rev. Lett., 96, 111101, (2006). [DOI],
[ADS].
|
|
56 |
Canuto, C., Hussaini, M.Y., Quarteroni, A. and Zang, T.A., Spectral Methods in Fluid
Dynamics, Springer Series in Computational Physics, (Springer, Berlin; New York, 1988).
|
|
57 |
Canuto, C., Hussaini, M.Y., Quarteroni, A. and Zang, T.A., Spectral Methods: Fundamentals
in Single Domains, Scientific Computation, (Springer, Berlin; New York, 2006). [Google Books].
|
|
58 |
Canuto, C., Hussaini, M.Y., Quarteroni, A. and Zang, T.A., Spectral Methods: Evolution to
Complex Geometries and Applications to Fluid Dynamics, Scientific Computation, (Springer,
Berlin; New York, 2007). [Google Books].
|
|
59 |
Caudill, M., Cook, G.B., Grigsby, J.D. and Pfeiffer, H.P., “Circular orbits and spin in black-hole
initial data”, Phys. Rev. D, 74, 064011, (2006). [DOI], [ADS].
|
|
60 |
Cook, G.B., “Three-dimensional initial data for the collision of two black holes. II. Quasicircular
orbits for equal-mass black holes”, Phys. Rev. D, 50, 5025–5032, (1994). [DOI], [ADS].
|
|
61 |
Cook, G.B., “Initial Data for Numerical Relativity”, Living Rev. Relativity, 3, lrr-2000-5,
(2000). URL (accessed 19 January 2007):
http://www.livingreviews.org/lrr-2000-5.
|
|
62 |
Cook, G.B., “Corotating and irrotational binary black holes in quasicircular orbits”, Phys. Rev.
D, 65, 084003, (2002). [DOI], [ADS].
|
|
63 |
Cook, G.B. and Pfeiffer, H.P., “Excision boundary conditions for black hole initial data”, Phys.
Rev. D, 70, 104016, (2004). [DOI], [ADS].
|
|
64 |
Cordero-Carrión, I., Ibáñez, J.M., Gourgoulhon, E., Jaramillo, J.L. and Novak, J.,
“Mathematical issues in a fully constrained formulation of Einstein equations”, Phys. Rev. D,
77, 084007, 1–13, (2008). [DOI], [ADS].
|
|
65 |
Courant, R. and Hilbert, D., Methods of Mathematical Physics, (Interscience Publishers, New
York, 1953).
|
|
66 |
Dahlquist, G.G., “A special stability problem for linear multistep methods”, BIT, 3(1), 27–43,
(1963). [DOI].
|
|
67 |
Damour, T., Gourgoulhon, E. and Grandclément, P., “Circular orbits of corotating binary
black holes: Comparison between analytical and numerical results”, Phys. Rev. D, 66, 024007,
1–15, (2002). [DOI], [ADS].
|
|
68 |
Dimmelmeier, H., Font, J.A. and Müller, E., “Relativistic simulations of rotational core
collapse I. Methods, initial models, and code tests”, Astron. Astrophys., 388, 917–935, (2002).
[DOI], [ADS], [arXiv:astro-ph/0204288].
|
|
69 |
Dimmelmeier, H., Novak, J., Font, J.A., Ibáñez, J.M. and Müller, E., “Combining spectral
and shock-capturing methods: A new numerical approach for 3D relativistic core collapse
simulations”, Phys. Rev. D, 71, 064023, (2005). [DOI], [ADS], [arXiv:astro-ph/0407174].
|
|
70 |
Dimmelmeier, H., Ott, C.D., Janka, H.-T., Marek, A. and Müller, E., “Generic
gravitational-wave signals from the collapse of rotating stellar cores”, Phys. Rev. Lett., 98,
251101, (2007). [DOI], [ADS], [arXiv:astro-ph/0702305].
|
|
71 |
Dimmelmeier, H., Stergioulas, N. and Font, J.A., “Non-linear axisymmetric pulsations of
rotating relativistic stars in the conformal flatness approximation”, Mon. Not. R. Astron. Soc.,
368, 1609–1630, (2006). [DOI], [ADS].
|
|
72 |
Erdös, P., “Problems and Results on the Theory of Interpolation. II”, Acta Math. Acad. Sci.
Hung., 12, 235–244, (1961). [DOI].
|
|
73 |
Faber, G., “Über die interpolarische Darstellung stetiger Funktionen”, Jahresber. Deutsch.
Math.-Verein., 23, 192–210, (1914). Online version (accessed 13 November 2008):
http://www.digizeitschriften.de/home/services/pdfterms/?ID=514871.
|
|
74 |
Faber, J.A., Baumgarte, T.W., Shapiro, S.L., Taniguchi, K. and Rasio, F., “Dynamical
evolution of black hole-neutron star binaries in general relativity: Simulations of tidal
disruption”, Phys. Rev. D, 73, 024012, (2006). [DOI], [ADS].
|
|
75 |
Faber, J.A., Grandclément, P. and Rasio, F.A., “Mergers of irrotational neutron star binaries
in conformally flat gravity”, Phys. Rev. D, 69, 124036, 1–26, (2004). [DOI], [ADS].
|
|
76 |
Faber, J.A., Grandclément, P., Rasio, F.A. and Taniguchi, K., “Measuring Neutron-Star Radii
with Gravitational-Wave Detectors”, Phys. Rev. Lett., 89, 231102, 1–4, (2002). [DOI], [ADS].
|
|
77 |
Font, J.A., “Numerical Hydrodynamics in General Relativity”, Living Rev. Relativity, 6,
lrr-2003-4, (2003). URL (accessed 19 January 2007):
http://www.livingreviews.org/lrr-2003-4.
|
|
78 |
Font, J.A. et al., “Three-dimensional numerical general relativistic hydrodynamics. II.
Long-term dynamics of single relativistic stars”, Phys. Rev. D, 65, 084024, 1–18, (2002). [DOI],
[ADS].
|
|
79 |
Fornberg, B., Practical Guide to Pseudospectral Methods, Cambridge Monographs on Applied
and Computational Mathematics, (Cambridge University Press, Cambridge; New York, 1995).
[Google Books].
|
|
80 |
Foucart, F., Kidder, L.E., Pfeiffer, H.P. and Teukolsky, S.A., “Initial value problem for black
hole-neutron star binaries: a flexible, high-accuracy spectral method”, Phys. Rev. D, 77, 124051,
1–20, (2008). [DOI], [ADS].
|
|
81 |
Frauendiener, J., “Calculating initial data for the conformal Einstein equations by
pseudo-spectral methods”, J. Comput. Appl. Math., 109, 475–491, (1999). [DOI], [ADS],
[gr-qc/9806103].
|
|
82 |
Friedrich, H., “On the hyperbolicity of Einstein’s and other gauge field equations”, Commun.
Math. Phys., 100, 525–543, (1985). [DOI].
|
|
83 |
Friedrich, H. and Nagy, G., “The Initial Boundary Value Problem for Einstein’s Vacuum Field
Equation”, Commun. Math. Phys., 201, 619–655, (1999). [DOI], [ADS].
|
|
84 |
Fryer, C.L. and New, K.C.B., “Gravitational Waves from Gravitational Collapse”, Living Rev.
Relativity, 6, lrr-2003-2, (2003). URL (accessed 19 January 2007):
http://www.livingreviews.org/lrr-2003-2.
|
|
85 |
Funaro, D. and Gottlieb, D., “A New Method of Imposing Boundary Conditions in
Pseudospectral Approximations of Hyperbolic Equations”, Math. Comput., 51, 599–613,
(1988). [DOI].
|
|
86 |
Garfinkle, D., “Harmonic coordinate method for simulating generic singularities”, Phys. Rev.
D, 65, 044029, (2002). [DOI], [ADS].
|
|
87 |
Gondek-Rosińska, D., Bejger, M., Bulik, T., Gourgoulhon, E., Haensel, P., Limousin, F.,
Taniguchi, K. and Zdunik, J.L., “The final phase of inspiral of neutron stars: Realistic equations
of state”, Adv. Space Res., 39, 271–274, (2007). [DOI], [ADS].
|
|
88 |
Gondek-Rosińska, D., Bulik, T., Zdunik, J.L., Gourgoulhon, E., Ray, S., Dey, J. and Dey, M.,
“Rapidly rotating compact strange stars”, Astron. Astrophys., 363, 1005–1012, (2000). [ADS].
|
|
89 |
Gondek-Rosińska, D. and Gourgoulhon, E., “Jacobi-like bar mode instability of relativistic
rotating bodies”, Phys. Rev. D, 66, 044021, 1–11, (2002). [DOI], [ADS].
|
|
90 |
Gondek-Rosińska, D., Gourgoulhon, E. and Haensel, P., “Are rotating strange quark stars
good sources of gravitational waves?”, Astron. Astrophys., 412, 777–790, (2003). [DOI], [ADS].
|
|
91 |
Gondek-Rosińska, D. and Limousin, F., “The final phase of inspiral of strange quark star
binaries”, arXiv, e-print, (2008). [arXiv:0801.4829].
|
|
92 |
Gondek-Rosińska, D., Stergioulas, N., Bulik, T., Kluźniak, W. and Gourgoulhon, E., “Lower
limits on the maximum orbital frequency around rotating strange stars”, Astron. Astrophys.,
380, 190–197, (2001). [DOI], [ADS].
|
|
93 |
González, J.A., Hannam, M., Sperhake, U., Brügmann, B. and Husa, S., “Supermassive
Recoil Velocities for Binary Black-Hole Mergers with Antialigned Spins”, Phys. Rev. Lett., 98,
231101, (2007). [DOI], [ADS].
|
|
94 |
Gottlieb, D. and Orszag, S.A., Numerical Analysis of Spectral Methods: Theory and
Applications, Regional Conference Series in Applied Mathematics, 26, (SIAM, Philadelphia,
1977). [Google Books].
|
|
95 |
Gourgoulhon, E., “Simple equations for general relativistic hydrodynamics in spherical
symmetry applied to neutron star collapse”, Astron. Astrophys., 252, 651–663, (1991). [ADS].
|
|
96 |
Gourgoulhon, E., “1D numerical relativity applied to neutron star collapse”, Class. Quantum
Grav., 9, S117–S125, (1992). [DOI], [ADS].
|
|
97 |
Gourgoulhon, E., “3+1 formalism and Bases of Numerical Relativity”, arXiv, e-print, (2007).
[arXiv:gr-qc/0703035].
|
|
98 |
Gourgoulhon, E., Grandclément, P. and Bonazzola, S., “Binary black holes in circular orbits.
I. A global spacetime approach”, Phys. Rev. D, 65, 044020, (2002). [DOI], [ADS].
|
|
99 |
Gourgoulhon, E., Grandclément, P., Marck, J.-A. and Novak, J., “LORENE: Langage Objet
pour la RElativité NumériquE”, project homepage, L’Observatoire de Paris. URL (accessed
9 March 2007):
http://www.lorene.obspm.fr.
|
|
100 |
Gourgoulhon, E., Grandclément, P., Taniguchi, K., Marck, J.-A. and Bonazzola, S.,
“Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general
relativity. Methods and tests”, Phys. Rev. D, 63, 064029, (2001). [DOI], [ADS].
|
|
101 |
Gourgoulhon, E. and Haensel, P., “Upper bounds on the neutrino burst from collapse of a
neutron star into a black hole”, Astron. Astrophys., 271, 187–208, (1993). [ADS].
|
|
102 |
Gourgoulhon, E., Haensel, P. and Gondek, D., “Maximum mass instability of neutron stars
and weak interaction processes in dense matter”, Astron. Astrophys., 294, 747–756, (1995).
[ADS].
|
|
103 |
Gourgoulhon, E., Haensel, P., Livine, R., Paluch, E., Bonazzola, S. and Marck, J.-A., “Fast
rotation of strange stars”, Astron. Astrophys., 349, 851–862, (1999). [ADS].
|
|
104 |
Gourgoulhon, E. and Jaramillo, J.L., “A 3+1 perspective on null hypersurfaces and isolated
horizons”, Phys. Rep., 423, 159–294, (2006). [DOI], [ADS].
|
|
105 |
Gourgoulhon, E. and Jaramillo, J.L., “Area evolution, bulk viscosity, and entropy principles for
dynamical horizons”, Phys. Rev. D, 74, 087502, 1–4, (2006). [DOI], [ADS], [gr-qc/0607050v2].
|
|
106 |
Goussard, J.O., Haensel, P. and Zdunik, J.L., “Rapid uniform rotation of protoneutron stars”,
Astron. Astrophys., 321, 822–834, (1997). [ADS].
|
|
107 |
Goussard, J.O., Haensel, P. and Zdunik, J.L., “Rapid differential rotation of protoneutron stars
and constraints on radio pulsars periods”, Astron. Astrophys., 330, 1005–1016, (1998). [ADS].
|
|
108 |
Grandclément, P., “Accurate and realistic initial data for black hole-neutron star binaries”,
Phys. Rev. D, 74, 124002, (2006). [DOI], [ADS].
|
|
109 |
Grandclément, P., Bonazzola, S., Gourgoulhon, E. and Marck, J.-A., “A multidomain spectral
method for scalar and vectorial poisson equations with noncompact sources”, J. Comput. Phys.,
170, 231–260, (2001). [DOI], [ADS].
|
|
110 |
Grandclément, P., Gourgoulhon, E. and Bonazzola, S., “Binary black holes in circular orbits.
II. Numerical methods and first results”, Phys. Rev. D, 65, 044021, 1–18, (2002). [DOI], [ADS].
|
|
111 |
Gundlach, C., Calabrese, G., Hinder, I. and Martín-García, J.M., “Constraint damping in
the Z4 formulation and harmonic gauge”, Class. Quantum Grav., 22, 3767–3773, (2005). [DOI],
[ADS].
|
|
112 |
Guo, B.-Y., Ma, H.-P. and Tadmor, E., “Spectral Vanishing Viscosity Method For Nonlinear
Conservation Laws”, SIAM J. Numer. Anal., 39, 1254–1268, (2001). [DOI].
|
|
113 |
Hennig, J. and Ansorg, M., “A Fully Pseudospectral Scheme for Solving Singular Hyperbolic
Equations on Conformally Compactified Space-Times”, arXiv, e-print, (2008). [arXiv:0801.1455].
|
|
114 |
Herrmann, F., Hinder, I., Shoemaker, D.M., Laguna, P. and Matzner, R.A., “Binary black
holes: Spin dynamics and gravitational recoil”, Phys. Rev. D, 76, 084032, 1–11, (2007). [DOI],
[ADS].
|
|
115 |
Hesthaven, J.S., “Spectral penalty methods”, Appl. Numer. Math., 33, 23–41, (2000). [DOI].
|
|
116 |
Hesthaven, J.S. and Gottlieb, D., “A Stable Penalty Method for the Compressible Navier-Stokes
Equations: I. Open Boundary Conditions”, SIAM J. Sci. Comput., 17, 579–612, (1996). [DOI].
|
|
117 |
Hesthaven, J.S., Gottlieb, S. and Gottlieb, D., Spectral Methods for Time-Dependent Problems,
Cambridge Monographs on Applied and Computational Mathematics, 21, (Cambridge
University Press, Cambridge; New York, 2007). [Google Books].
|
|
118 |
Hockney, R.W. and Eastwood, J.W., Computer Simulation Using Particles, (McGraw-Hill, New
York, 1981). [Google Books].
|
|
119 |
Hollerbach, R., “A spectral solution of the magneto-convection equations in spherical
geometry”, Int. J. Numer. Meth. Fluids, 32, 773–797, (2000). [DOI], [ADS].
|
|
120 |
Holst, M., Lindblom, L., Owen, R., Pfeiffer, H.P., Scheel, M.A. and Kidder, L.E., “Optimal
constraint projection for hyperbolic evolution systems”, Phys. Rev. D, 70, 084017, 1–17, (2004).
[DOI], [ADS].
|
|
121 |
Ierley, G., Spencer, B. and Worthing, R., “Spectral Methods in Time for a Class of Parabolic
Partial Differential Equations”, J. Comput. Phys., 102, 88–97, (1992). [DOI], [ADS].
|
|
122 |
Isaacson, E. and Keller, H.B., Analysis of Numerical Methods, (John Wiley and Sons, New
York, 1966). [Google Books].
|
|
123 |
Jaramillo, J.L., Ansorg, M. and Limousin, F., “Numerical implementation of isolated horizon
boundary conditions”, Phys. Rev. D, 75, 024019, 1–11, (2007). [DOI], [ADS].
|
|
124 |
Kassam, A.-K. and Trefethen, L.N., “Fourth-Order Time-Stepping for Stiff PDEs”, SIAM J.
Sci. Comput., 26, 1214–1233, (2005). [DOI].
|
|
125 |
Kidder, L.E. and Finn, L.S., “Spectral methods for numerical relativity: The initial data
problem”, Phys. Rev. D, 62, 084026, 1–13, (2000). [DOI], [ADS].
|
|
126 |
Kidder, L.E., Lindblom, L., Scheel, M.A., Buchman, L.T. and Pfeiffer, H.P., “Boundary
conditions for the Einstein evolution system”, Phys. Rev. D, 71, 064020, 1–22, (2005). [DOI],
[ADS].
|
|
127 |
Kidder, L.E., Scheel, M.A. and Teukolsky, S.A., “Extending the lifetime of 3D black hole
computations with a new hyperbolic system of evolution equations”, Phys. Rev. D, 64, 064017,
1–13, (2001). [DOI], [ADS].
|
|
128 |
Kidder, L.E., Scheel, M.A., Teukolsky, S.A., Carlson, E.D. and Cook, G.B., “Black hole
evolution by spectral methods”, Phys. Rev. D, 62, 084032, 1–20, (2000). [DOI], [ADS].
|
|
129 |
Klein, C., “Fourth-Order Time-Stepping for Low Dispersion Korteweg-de Vries and Nonlinear
Schrödinger Equation”, Electron. Trans. Numer. Anal., 29, 116–135, (2008). URL (accessed
10 June 2008):
http://etna.mcs.kent.edu/vol.29.2007-2008/pp116-135.dir/pp116-135.html.
|
|
130 |
Kokkotas, K.D. and Schmidt, B.G., “Quasi-Normal Modes of Stars and Black Holes”, Living
Rev. Relativity, 2, lrr-1999-2, (1999). URL (accessed 19 January 2007):
http://www.livingreviews.org/lrr-1999-2.
|
|
131 |
Korn, G.A. and Korn, T.M., in Mathematical Handbook for Scientists and Engineers:
Definitions, Theorems, and Formulas for Reference and Review, 6, pp. 179–186, (McGraw-Hill,
New York, 1961). [Google Books].
|
|
132 |
Kudoh, H. and Wiseman, T., “Connecting Black Holes and Black Strings”, Phys. Rev. Lett.,
94, 161102, (2005). [DOI], [ADS].
|
|
133 |
Limousin, F., Gondek-Rosińska, D. and Gourgoulhon, E., “Last orbits of binary strange quark
stars”, Phys. Rev. D, 71, 064012, 1–11, (2005). [DOI], [ADS].
|
|
134 |
Lin, L.-M. and Novak, J., “Rotating star initial data for a constrained scheme in numerical
relativity”, Class. Quantum Grav., 23, 4545–4561, (2006). [DOI], [ADS].
|
|
135 |
Lin, L.-M. and Novak, J., “A new spectral apparent horizon finder for 3D numerical relativity”,
Class. Quantum Grav., 24, 2665–2676, (2007). [DOI], [ADS].
|
|
136 |
Lindblom, L., Matthews, K.D., Rinne, O. and Scheel, M.A., “Gauge Drivers for the Generalized
Harmonic Einstein Equations”, Phys. Rev. D, 77, 084001, 1–17, (2008). [DOI], [ADS].
|
|
137 |
Lindblom, L., Scheel, M.A., Kidder, L.E., Owen, R. and Rinne, O., “A new generalized
harmonic evolution system”, Class. Quantum Grav., 23, S447–S462, (2006). [DOI], [ADS].
|
|
138 |
Lindblom, L., Scheel, M.A., Kidder, L.E., Pfeiffer, H.P., Shoemaker, D. and Teukolsky, S.A.,
“Controlling the growth of constraints in hyperbolic evolution systems”, Phys. Rev. D, 69,
124025, 1–14, (2004). [DOI], [ADS].
|
|
139 |
Lindblom, L., Tohline, J.E. and Vallisneri, M., “Numerical evolutions of nonlinear r-modes in
neutron stars”, Phys. Rev. D, 65, 084039, 1–15, (2002). [DOI], [ADS], [arXiv:astro-ph/0109352].
|
|
140 |
Lindquist, R.W., “Initial-Value Problem on Einstein-Rosen Manifolds”, J. Math. Phys., 4,
938–950, (1963). [DOI], [ADS].
|
|
141 |
Liu, Y.T., Shapiro, S.L., Etienne, Z.B. and Taniguchi, K., “General relativistic simulations of
magnetized binary neutron star mergers”, Phys. Rev. D, 78, 024012, 1–20, (2008). [DOI], [ADS].
|
|
142 |
Lockitch, K.H., Friedman, J.L. and Andersson, N., “Rotational modes of relativistic stars:
Numerical results”, Phys. Rev. D, 68, 124010, 1–23, (2003). [DOI], [ADS].
|
|
143 |
Lovelace, G., Owen, R., Pfeiffer, H.P. and Chu, T., “Binary-black-hole initial data with nearly
extremal spins”, Phys. Rev. D, 78, 084017, (2008). [DOI], [ADS], [arXiv:0805.4192].
|
|
144 |
Løvgren, A.E., Maday, Y. and Rønquist, E.M., “The Reduced Basis Element Method for Fluid
Flows”, in Calgaro, C., Coulombel, J.-F. and Goudon, T., eds., Analysis and Simulation of
Fluid Dynamics, Advances in Mathematical Fluid Mechanics, pp. 129–154, (Birkhäuser, Basel;
Boston, 2007).
|
|
145 |
Martí, J.M. and Müller, E., “Numerical Hydrodynamics in Special Relativity”, Living Rev.
Relativity, 6, lrr-2003-7, (2003). URL (accessed 20 February 2007):
http://www.livingreviews.org/lrr-2003-7.
|
|
146 |
Mathews, J., “Gravitational multipole radiation”, J. Soc. Ind. Appl. Math., 10, 768–780,
(1962). [DOI].
|
|
147 |
Matzner, R.A., Huq, M.F. and Shoemaker, D.M., “Initial value problem and coordinates for
multiple black hole systems.”, Phys. Rev. D, 59, 024015, 1–6, (1998). [DOI], [ADS].
|
|
148 |
May, M.M. and White, R.H., “Hydrodynamic Calculations of General-Relativistic Collapse”,
Phys. Rev., 141, 1232–1241, (1966). [DOI], [ADS].
|
|
149 |
Meinardus, G., Approximation of Functions: Theory and Numerical Methods, Springer Tracts
in Natural Philosophy, 13, (Springer, Berlin; New York, 1967).
|
|
150 |
Misner, C.W., “The Method of Images in Geometrostatics”, Ann. Phys. (N.Y.), 24, 102–117,
(1963). [DOI], [ADS].
|
|
151 |
Moore, S., Healy, D., Rockmore, D. and Kostelec, P., “Fast Spherical Harmonic Transforms:
SpharmonicKit”, project homepage, Dartmouth College. URL (accessed 19 January 2007):
http://www.cs.dartmouth.edu/~geelong/sphere/.
|
|
152 |
Nakamura, T., Kojima, Y. and Oohara, K., “A method of determining apparent horizons in
three-dimensional numerical relativity”, Phys. Lett. A, 106, 235–238, (1984). [DOI], [ADS].
|
|
153 |
Nakamura, T. and Sato, H., “General Relativistic Collapse of Rotating Supermassive Stars”,
Prog. Theor. Phys., 66, 2038–2051, (1981). [DOI], [ADS].
|
|
154 |
Nakamura, T. and Sato, H., “General Relativistic Collapse of Non-Rotating, Axisymmetric
Stars”, Prog. Theor. Phys., 67, 1396–1405, (1982). [DOI], [ADS].
|
|
155 |
Novak, J., “Neutron star transition to a strong-scalar-field state in tensor-scalar gravity”, Phys.
Rev. D, 58, 064019, (1998). [DOI], [ADS].
|
|
156 |
Novak, J., “Spherical neutron star collapse toward a black hole in a tensor-scalar theory of
gravity”, Phys. Rev. D, 57, 4789–4801, (1998). [DOI], [ADS].
|
|
157 |
Novak, J. and Bonazzola, S., “Absorbing boundary conditions for simulation of gravitational
waves with spectral methods in spherical coordinates”, J. Comput. Phys., 197, 186–196, (2004).
[DOI], [ADS].
|
|
158 |
Novak, J. and Ibáñez, J.M., “Gravitational Waves from the Collapse and Bounce of a Stellar
Core in Tensor-Scalar Gravity”, Astrophys. J., 533, 392–405, (2000). [DOI], [ADS].
|
|
159 |
Novak, J. and Marcq, E., “The gyromagnetic ratio of rapidly rotating compact stars in general
relativity”, Class. Quantum Grav., 20, 3051–3060, (2003). [DOI], [ADS].
|
|
160 |
Nozawa, T., Stergioulas, N., Gourgoulhon, E. and Eriguchi, Y., “Construction of highly
accurate models of rotating neutron stars - comparison of three different numerical schemes”,
Astron. Astrophys. Suppl., 132, 431–454, (1998). [DOI], [ADS].
|
|
161 |
Oechslin, R. and Janka, H.-T., “Gravitational Waves from Relativistic Neutron-Star Mergers
with Microphysical Equations of State”, Phys. Rev. Lett., 99, 121102, (2007). [DOI], [ADS].
|
|
162 |
Oppenheimer, J.R. and Snyder, H., “On Continued Gravitational Contraction”, Phys. Rev.,
56, 455–459, (1939). [DOI], [ADS].
|
|
163 |
Ott, C.D., Dimmelmeier, H., Marek, A., Janka, H.-T., Hawke, I., Zink, B. and Schnetter, E.,
“3D Collapse of Rotating Stellar Iron Cores in General Relativity Including Deleptonization
and a Nuclear Equation of State”, Phys. Rev. Lett., 98, 261101, (2007). [DOI], [ADS].
|
|
164 |
Ott, C.D., Dimmelmeier, H., Marek, A., Janka, H.-T., Zink, B., Hawke, I. and Schnetter,
E., “Rotating collapse of stellar iron cores in general relativity”, Class. Quantum Grav., 24,
S139–S154, (2007). [DOI], [ADS].
|
|
165 |
Pan, Y. et al., “A data-analysis driven comparison of analytic and numerical coalescing binary
waveforms: Nonspinning case”, Phys. Rev. D, 77, 024014, (2008). [DOI], [arXiv:0704.1964].
|
|
166 |
Patera, A.T., “A spectral element method for fluid dynamics: Laminar flow in a channel
expansion”, J. Comput. Phys., 54, 468–488, (1984). [DOI], [ADS].
|
|
167 |
Pfeiffer, H.P., Initial value problem for black hole evolution, Ph.D. Thesis, (Cornell University,
Ithaca, N.Y., 2003). [gr-qc/0510016].
|
|
168 |
Pfeiffer, H.P., Brown, D.A., Kidder, L.E., Lindblom, L., Lovelace, G. and Scheel, M.A.,
“Reducing orbital eccentricity in binary black hole simulations”, Class. Quantum Grav., 24,
S59–S81, (2007). [DOI], [ADS].
|
|
169 |
Pfeiffer, H.P., Cook, G.B. and Teukolsky, S.A., “Comparing initial-data sets for binary black
holes”, Phys. Rev. D, 66, 024047, 1–17, (2002). [DOI], [ADS].
|
|
170 |
Pfeiffer, H.P., Kidder, L.E., Scheel, M.A. and Shoemaker, D.M., “Initial value problem for
Einstein’s equations with superposed gravitational waves”, Phys. Rev. D, 71, 024020, 1–9,
(2005). [DOI], [ADS].
|
|
171 |
Pfeiffer, H.P., Kidder, L.E., Scheel, M.A. and Teukolsky, S.A., “A multidomain spectral method
for solving elliptic equations”, Comput. Phys. Commun., 152, 253–273, (2003). [DOI], [ADS].
|
|
172 |
Pfeiffer, H.P., Teukolsky, S.A. and Cook, G.B., “Quasicircular orbits for spinning binary black
holes”, Phys. Rev. D, 62, 104018, (2000). [DOI], [ADS], [gr-qc/0006084].
|
|
173 |
Pollney, D. et al., “Recoil velocities from equal-mass binary black-hole mergers: a systematic
investigation of spin-orbit aligned configurations”, Phys. Rev. D, 76, 124002, (2007). [DOI],
[arXiv:0707.2559].
|
|
174 |
Postnov, K.A. and Yungelson, L.R., “The Evolution of Compact Binary Star Systems”, Living
Rev. Relativity, 9, lrr-2006-6, (2006). URL (accessed 19 January 2007):
http://www.livingreviews.org/lrr-2006-6.
|
|
175 |
Pretorius, F., “Evolution of Binary Black-Hole Spacetimes”, Phys. Rev. Lett., 95, 121101,
(2005). [DOI], [ADS].
|
|
176 |
Pretorius, F., “Numerical relativity using a generalized harmonic decomposition”, Class.
Quantum Grav., 22, 425–451, (2005). [DOI], [ADS].
|
|
177 |
Prix, R., Novak, J. and Comer, G.L., “Relativistic numerical models for stationary superfluid
neutron stars”, Phys. Rev. D, 71, 043005, 1–18, (2005). [DOI], [ADS].
|
|
178 |
Quarteroni, A., Sacco, R. and Saleri, F., Méthodes Numériques: Algorithmes, analyse et
applications, (Springer Italia, Milano, 2007).
|
|
179 |
Rinne, O., “Stable radiation-controlling boundary conditions for the generalized harmonic
Einstein equations”, Class. Quantum Grav., 23, 6275–6300, (2006). [DOI], [ADS].
|
|
180 |
Rinne, O., Lindblom, L. and Scheel, M.A., “Testing outer boundary treatments for the Einstein
equations”, Class. Quantum Grav., 24, 4053–4078, (2007). [DOI], [ADS].
|
|
181 |
Ruiz, M., Rinne, O. and Sarbach, O., “Outer boundary conditions for Einstein’s field equations
in harmonic coordinates”, Class. Quantum Grav., 24, 6349–6377, (2007). [DOI], [ADS].
|
|
182 |
Saijo, M. and Gourgoulhon, E., “Viscosity driven instability in rotating relativistic stars”, Phys.
Rev. D, 74, 084006, 1–13, (2006). [DOI], [ADS].
|
|
183 |
Salgado, M., Bonazzola, S., Gourgoulhon, E. and Haensel, P., “High precision rotating neutron
star models I. Analysis of neutron star properties”, Astron. Astrophys., 291, 155–170, (1994).
[ADS].
|
|
184 |
Salgado, M., Bonazzola, S., Gourgoulhon, E. and Haensel, P., “High precision rotating neutron
star models. II. Large sample of neutron star properties”, Astron. Astrophys. Suppl., 108,
455–459, (1994). [ADS].
|
|
185 |
Scheel, M.A., Boyle, M., Chu, T., Kidder, L.E., Matthews, K.D. and Pfeiffer, H.P.,
“High-accuracy waveforms for binary black hole inspiral, merger, and ringdown”, Phys. Rev.
D, 79, 024003, (2009). [DOI], [arXiv:0810.1767].
|
|
186 |
Scheel, M.A., Erickcek, A.L., Burko, L.M., Kidder, L.E., Pfeiffer, H.P. and Teukolsky, S.A.,
“3D simulations of linearized scalar fields in Kerr spacetime”, Phys. Rev. D, 69, 104006, 1–11,
(2004). [DOI], [ADS].
|
|
187 |
Scheel, M.A., Kidder, L.E., Lindblom, L., Pfeiffer, H.P. and Teukolsky, S.A., “Toward stable 3D
numerical evolutions of black-hole spacetimes”, Phys. Rev. D, 66, 124005, 1–4, (2002). [DOI],
[ADS].
|
|
188 |
Scheel, M.A., Pfeiffer, H.P., Lindblom, L., Kidder, L.E., Rinne, O. and Teukolsky, S.A., “Solving
Einstein’s equations with dual coordinate frames”, Phys. Rev. D, 74, 104006, 1–13, (2006).
[DOI], [ADS].
|
|
189 |
Shen, J., Tachim Medjo, T. and Wang, S., “On a Wind-Driven, Double-Gyre,
Quasi-Geostrophic Ocean Model: Numerical Simulations and Structural Analysis”, J. Comput.
Phys., 155, 387–409, (1999). [DOI], [ADS].
|
|
190 |
Shibata, M., “Axisymmetric Simulations of Rotating Stellar Collapse in Full General Relativity
– Criteria for Prompt Collapse to Black Holes –”, Prog. Theor. Phys., 104, 325–358, (2000).
[DOI], [ADS].
|