메뉴 건너뛰기




Volumn 23, Issue 16, 2006, Pages

On the relation between mathematical and numerical relativity

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33746624356     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/23/16/S02     Document Type: Article
Times cited : (8)

References (69)
  • 2
    • 27144454897 scopus 로고    scopus 로고
    • Local existence of dynamical and trapping horizons
    • Andersson L, Mars M and Simon W 2005 Local existence of dynamical and trapping horizons Phys. Rev. Lett. 95 111102
    • (2005) Phys. Rev. Lett. , vol.95 , Issue.11 , pp. 111102
    • Andersson, L.1    Mars, M.2    Simon, W.3
  • 3
    • 0035531301 scopus 로고    scopus 로고
    • Quiescent cosmological singularities
    • Andersson L and Rendall A D 2001 Quiescent cosmological singularities Commun. Math. Phys. 218 479-511
    • (2001) Commun. Math. Phys. , vol.218 , Issue.3 , pp. 479-511
    • Andersson, L.1    Rendall, A.D.2
  • 4
    • 18144406505 scopus 로고    scopus 로고
    • Asymptotic silence of generic cosmological singularities
    • Andersson L, van Elst H, Lim W C and Uggla C 2005 Asymptotic silence of generic cosmological singularities Phys. Rev. Lett. 94 051101
    • (2005) Phys. Rev. Lett. , vol.94 , Issue.5 , pp. 051101
    • Andersson, L.1    Van Elst, H.2    Lim, W.C.3    Uggla, C.4
  • 6
    • 0037164977 scopus 로고    scopus 로고
    • Dynamical horizons: Energy, angular momentum, fluxes, and balance laws
    • Ashtekar A and Krishnan B 2002 Dynamical horizons: energy, angular momentum, fluxes, and balance laws Phys. Rev. Lett. 89 261101 4
    • (2002) Phys. Rev. Lett. , vol.89 , Issue.26 , pp. 261101
    • Ashtekar, A.1    Krishnan, B.2
  • 7
    • 0000716603 scopus 로고
    • A striking property of the gravitational Hamiltonian
    • Ashtekar A and Varadarajan M 1994 A striking property of the gravitational Hamiltonian Phys. Rev. D 50 4944
    • (1994) Phys. Rev. , vol.50 , Issue.8 , pp. 4944
    • Ashtekar, A.1    Varadarajan, M.2
  • 8
    • 0001848227 scopus 로고
    • Chaotic behaviour in general relativity
    • Barrow J D 1982 Chaotic behaviour in general relativity Phys. Rep. 85 1-49
    • (1982) Phys. Rep. , vol.85 , Issue.1 , pp. 1-49
    • Barrow, J.D.1
  • 9
    • 0014808945 scopus 로고
    • Oscillatory approach to a singular point in the relativistic cosmology
    • Belinsk V A, Khalatnikov I M and Lifshitz E M 1970 Oscillatory approach to a singular point in the relativistic cosmology Adv. Phys. 19 525-73
    • (1970) Adv. Phys. , vol.19 , Issue.80 , pp. 525-573
    • Belinsk, V.A.1    Khalatnikov, I.M.2    Lifshitz, E.M.3
  • 10
    • 84927770535 scopus 로고
    • A general solution of the Einstein equations with a time singularity
    • Belinsk V A, Khalatnikov I M and Lifshitz E M 1982 A general solution of the Einstein equations with a time singularity Adv. Phys. 31 639-67
    • (1982) Adv. Phys. , vol.31 , Issue.6 , pp. 639-667
    • Belinsk, V.A.1    Khalatnikov, I.M.2    Lifshitz, E.M.3
  • 11
    • 0001870459 scopus 로고
    • The dynamics of the Hénon map
    • Benedicks M and Carleson L 1991 The dynamics of the Hénon map Ann. Math. 133 73-169
    • (1991) Ann. Math. , vol.133 , Issue.1 , pp. 73-169
    • Benedicks, M.1    Carleson, L.2
  • 12
    • 0242373118 scopus 로고    scopus 로고
    • Numerical approaches to spacetime singularities
    • Berger B K 2002 Numerical approaches to spacetime singularities Living Rev. Rel. 5 (2002-1) 58 (electronic)
    • (2002) Living Rev. Rel. , vol.5 , Issue.1-2002 , pp. 58
    • Berger, B.K.1
  • 16
    • 0001505323 scopus 로고
    • Numerical investigation of cosmological singularities
    • Berger B K and Moncrief V 1993 Numerical investigation of cosmological singularities Phys. Rev. D 48 4676-87
    • (1993) Phys. Rev. , vol.48 , Issue.10 , pp. 4676-4687
    • Berger, B.K.1    Moncrief, V.2
  • 17
    • 0012465738 scopus 로고    scopus 로고
    • Exact U(1) symmetric cosmologies with local Mixmaster dynamics
    • Berger B K and Moncrief V 2000 Exact U(1) symmetric cosmologies with local Mixmaster dynamics Phys. Rev. D 62 023509
    • (2000) Phys. Rev. , vol.62 , Issue.2 , pp. 023509
    • Berger, B.K.1    Moncrief, V.2
  • 18
    • 18144378428 scopus 로고    scopus 로고
    • Signature for local Mixmaster dynamics in U(1) symmetric cosmologies
    • Berger B K and Moncrief V 2000 Signature for local Mixmaster dynamics in U(1) symmetric cosmologies Phys. Rev. D 62 123501
    • (2000) Phys. Rev. , vol.62 , Issue.12 , pp. 123501
    • Berger, B.K.1    Moncrief, V.2
  • 19
    • 0034215570 scopus 로고    scopus 로고
    • Dispersion and collapse of wave maps
    • Bizoń P, Chmaj T and Zbisław T 2000 Dispersion and collapse of wave maps Nonlinearity 13 1411-23
    • (2000) Nonlinearity , vol.13 , Issue.4 , pp. 1411-1423
    • Bizoń, P.1    Chmaj, T.2    Zbisław, T.3
  • 20
    • 0007502239 scopus 로고    scopus 로고
    • Formation of singularities for equivariant (2 + 1)-dimensional wave maps into the 2-sphere
    • Bizoń P, Chmaj T and Zbisław T 2001 Formation of singularities for equivariant (2 + 1)-dimensional wave maps into the 2-sphere Nonlinearity 14 1041-53
    • (2001) Nonlinearity , vol.14 , Issue.5 , pp. 1041-1053
    • Bizoń, P.1    Chmaj, T.2    Zbisław, T.3
  • 21
    • 0242373125 scopus 로고
    • Chitre D M 1972 Investigations of vanishing of a horizon for Bianchy type X (the Mixmaster) Universe PhD Thesis
    • (1972) PhD Thesis
    • Chitre, D.M.1
  • 22
    • 0002984217 scopus 로고
    • 'Critical' behaviour in massless scalar field collapse
    • Choptuik M W 1992 'Critical' behaviour in massless scalar field collapse Approaches to Numerical Relativity (Southampton, 1991) (Cambridge: Cambridge University Press) pp 202-22
    • (1992) Approaches to Numerical Relativity , pp. 202-222
    • Choptuik, M.W.1
  • 23
    • 17744371460 scopus 로고    scopus 로고
    • Topologically general u(1) symmetric vacuum space-times with AVTD behaviour
    • Choquet-Bruhat Y, Isenberg J and Moncrief V 2004 Topologically general u(1) symmetric vacuum space-times with AVTD behaviour Nuovo Cimento Soc. Ital. Fis. B 119 625-38
    • (2004) Nuovo Cimento Soc. Ital. Fis. , vol.119 , pp. 625-638
    • Choquet-Bruhat, Y.1    Isenberg, J.2    Moncrief, V.3
  • 27
    • 84990602498 scopus 로고
    • Global solutions of nonlinear hyperbolic equations for small initial data
    • Christodoulou D 1986 Global solutions of nonlinear hyperbolic equations for small initial data Commun. Pure Appl. Math. 39 267-82
    • (1986) Commun. Pure Appl. Math. , vol.39 , pp. 267-282
    • Christodoulou, D.1
  • 31
    • 11744382930 scopus 로고
    • Velocity-dominated singularities in irrotational dust cosmologies
    • Eardley D, Liang E and Sachs R K 1972 Velocity-dominated singularities in irrotational dust cosmologies J. Math. Phys. 13 99-107
    • (1972) J. Math. Phys. , vol.13 , Issue.1 , pp. 99-107
    • Eardley, D.1    Liang, E.2    Sachs, R.K.3
  • 32
    • 12044254590 scopus 로고
    • Critical phenomena and self-similarity in the gravitational collapes of radiation fluid
    • Evans C R and Coleman J S 1994 Critical phenomena and self-similarity in the gravitational collapes of radiation fluid Phys. Rev. Lett. 72 1782-5
    • (1994) Phys. Rev. Lett. , vol.72 , Issue.12 , pp. 1782-1785
    • Evans, C.R.1    Coleman, J.S.2
  • 33
    • 0001816458 scopus 로고
    • Quantitative universality for a class of nonlinear transformations
    • Feigenbaum M J 1978 Quantitative universality for a class of nonlinear transformations J. Stat. Phys. 19 25-52
    • (1978) J. Stat. Phys. , vol.19 , Issue.1 , pp. 25-52
    • Feigenbaum, M.J.1
  • 34
    • 33646002667 scopus 로고    scopus 로고
    • Decay of solutions of the wave equation in the Kerr geometry
    • Finster F, Kamran N, Smoller J and Yau S-T 2006 Decay of solutions of the wave equation in the Kerr geometry Commun. Math. Phys. 264 465-503
    • (2006) Commun. Math. Phys. , vol.264 , Issue.2 , pp. 465-503
    • Finster, F.1    Kamran, N.2    Smoller, J.3    Yau, S.-T.4
  • 35
    • 0000168417 scopus 로고
    • On the existence of n-geodesically complete or future complete solutions of Einstein's field equations with smooth asymptotic structure
    • Friedrich H 1986 On the existence of n-geodesically complete or future complete solutions of Einstein's field equations with smooth asymptotic structure Commun. Math. Phys. 107 587-609
    • (1986) Commun. Math. Phys. , vol.107 , Issue.4 , pp. 587-609
    • Friedrich, H.1
  • 36
    • 85038288691 scopus 로고    scopus 로고
    • Harmonic coordinate method for simulating generic singularities
    • Garfinkle D 2002 Harmonic coordinate method for simulating generic singularities Phys. Rev. D 65 044029 6
    • (2002) Phys. Rev. , vol.65 , Issue.4 , pp. 044029
    • Garfinkle, D.1
  • 37
    • 14644443796 scopus 로고    scopus 로고
    • Numerical simulations of generic singuarities
    • Garfinkle D 2004 Numerical simulations of generic singuarities Phys. Rev. Lett. 93 161101
    • (2004) Phys. Rev. Lett. , vol.93 , Issue.16 , pp. 161101
    • Garfinkle, D.1
  • 39
    • 84943153812 scopus 로고    scopus 로고
    • Critical phenomena in gravitational collapse
    • Gundlach C 1999 Critical phenomena in gravitational collapse Living Rev. Rel. 2 (1999-4) 58 (electronic)
    • (1999) Living Rev. Rel. , vol.2 , Issue.4-1999 , pp. 58
    • Gundlach, C.1
  • 40
    • 0002591468 scopus 로고
    • A two-dimensional mapping with a strange attractor
    • Hénon M 1976 A two-dimensional mapping with a strange attractor Commun. Math. Phys. 50 69-77
    • (1976) Commun. Math. Phys. , vol.50 , Issue.1 , pp. 69-77
    • Hénon, M.1
  • 42
    • 0036425026 scopus 로고    scopus 로고
    • Asymptotic behaviour in polarized and half-polarized U(1) symmetric vacuum spacetimes
    • Isenberg J and Moncrief V 2002 Asymptotic behaviour in polarized and half-polarized U(1) symmetric vacuum spacetimes Class. Quantum Grav. 19 5361-86
    • (2002) Class. Quantum Grav. , vol.19 , Issue.21 , pp. 5361-5386
    • Isenberg, J.1    Moncrief, V.2
  • 43
    • 0032378032 scopus 로고    scopus 로고
    • Analytic description of singularities in Gowdy spacetimes
    • Kichenassamy S and Rendall A D 1998 Analytic description of singularities in Gowdy spacetimes Class. Quantum Grav. 15 1339-55
    • (1998) Class. Quantum Grav. , vol.15 , Issue.5 , pp. 1339-1355
    • Kichenassamy, S.1    Rendall, A.D.2
  • 44
    • 84990556241 scopus 로고
    • 1 estimates for solutions to the classical wave equation in three space dimensions
    • 1 estimates for solutions to the classical wave equation in three space dimensions Commun. Pure Appl. Math. 37 269-88
    • (1984) Commun. Pure Appl. Math. , vol.37 , pp. 269-288
    • Klainerman, S.1
  • 46
    • 0038372932 scopus 로고    scopus 로고
    • Peeling properties of asymptotically flat solutions to the Einstein vacuum equations
    • Klainerman S and Nicolò F 2003 Peeling properties of asymptotically flat solutions to the Einstein vacuum equations Class. Quantum Grav. 20 3215-57
    • (2003) Class. Quantum Grav. , vol.20 , Issue.14 , pp. 3215-3257
    • Klainerman, S.1    Nicolò, F.2
  • 47
    • 0000360396 scopus 로고
    • Critical behavior in gravitational collapse of radiation fluid: A renormalization group (linear perturbation) analysis
    • Koike T, Hara T and Adachi S 1995 Critical behavior in gravitational collapse of radiation fluid: a renormalization group (linear perturbation) analysis Phys. Rev. Lett. 74 5170-3
    • (1995) Phys. Rev. Lett. , vol.74 , Issue.26 , pp. 5170-5173
    • Koike, T.1    Hara, T.2    Adachi, S.3
  • 48
    • 0004229474 scopus 로고
    • Lakatos I 1976 Proofs and Refutations (The Logic of Mathematical Discovery) ed J Worrall and E Zahar (Cambridge: Cambridge University Press)
    • (1976) Proofs and Refutations
    • Lakatos, I.1
  • 49
    • 84966250718 scopus 로고
    • A computer-assisted proof of the Feigenbaum conjectures
    • Lanford O E III 1982 A computer-assisted proof of the Feigenbaum conjectures Bull. Am. Math. Soc. (NS) 6 427-34
    • (1982) Bull. Am. Math. Soc. (NS) , vol.6 , pp. 427-434
    • Lanford, O.E.1
  • 50
    • 17444370107 scopus 로고    scopus 로고
    • Global existence for the Einstein vacuum equations in wave coordinates
    • Lindblad H and Rodnianski I 2005 Global existence for the Einstein vacuum equations in wave coordinates Commun. Math. Phys. 256 43-110
    • (2005) Commun. Math. Phys. , vol.256 , Issue.1 , pp. 43-110
    • Lindblad, H.1    Rodnianski, I.2
  • 51
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flow
    • Lorentz E N 1963 Deterministic nonperiodic flow J. Atmos. Sci. 20 130-41
    • (1963) J. Atmos. Sci. , vol.20 , Issue.2 , pp. 130-141
    • Lorentz, E.N.1
  • 53
    • 0002406273 scopus 로고
    • The Mixmaster cosmological metrics
    • Misner C W 1994 The Mixmaster cosmological metrics Deterministic Chaos in General Relativity (Kananaskis, AB, 1993) (NATO Advanced Science Institutes Series B: Physics vol 332) (New York: Plenum) pp 317-28
    • (1994) Deterministic Chaos in General Relativity , pp. 317-328
    • Misner, C.W.1
  • 54
    • 0031530993 scopus 로고    scopus 로고
    • Global dynamics of the Mixmaster model
    • Rendall A D 1997 Global dynamics of the Mixmaster model Class. Quantum Grav. 14 2341-56
    • (1997) Class. Quantum Grav. , vol.14 , Issue.8 , pp. 2341-2356
    • Rendall, A.D.1
  • 55
    • 1942495033 scopus 로고    scopus 로고
    • Theorems on existence and global dynamics for the e instein equations
    • Rendall A D 2002 Theorems on existence and global dynamics for the E instein equations Living Rev. Rel. 5 (2002-6) 62 (electronic MR MR1932418 (2003h:83016))
    • (2002) Living Rev. Rel. , vol.5 , Issue.6-2002 , pp. 62
    • Rendall, A.D.1
  • 56
    • 0035536851 scopus 로고    scopus 로고
    • Manufacture of Gowdy spacetimes with spikes
    • Rendall A D and Weaver M 2001 Manufacture of Gowdy spacetimes with spikes Class. Quantum Grav. 18 2959-75
    • (2001) Class. Quantum Grav. , vol.18 , Issue.15 , pp. 2959-2975
    • Rendall, A.D.1    Weaver, M.2
  • 57
    • 0034338081 scopus 로고    scopus 로고
    • Curvature blow up in Bianchi VIII and IX vacuum spacetimes
    • Ringström H 2000 Curvature blow up in Bianchi VIII and IX vacuum spacetimes Class. Quantum Grav. 17 713-31
    • (2000) Class. Quantum Grav. , vol.17 , Issue.4 , pp. 713-731
    • Ringström, H.1
  • 59
    • 0035535043 scopus 로고    scopus 로고
    • The Bianchi IX attractor
    • Ringström H 2001 The Bianchi IX attractor Ann. Henri Poincaré 2 405-500
    • (2001) Ann. Henri Poincaré , vol.2 , Issue.3 , pp. 405-500
    • Ringström, H.1
  • 60
    • 1142290685 scopus 로고    scopus 로고
    • Asymptotic expansions close to the singularity in Gowdy spacetimes
    • Ringström H 2004 Asymptotic expansions close to the singularity in Gowdy spacetimes Class. Quantum Grav. 21 S305-S322 (A spacetime safari: essays in honour of Vincent Moncrief)
    • (2004) Class. Quantum Grav. , vol.21 , Issue.3
    • Ringström, H.1
  • 61
    • 2442450500 scopus 로고    scopus 로고
    • On a wave map equation arising in general relativity
    • Ringström H 2004 On a wave map equation arising in general relativity Commun. Pure Appl. Math. 57 657-703
    • (2004) Commun. Pure Appl. Math. , vol.57 , Issue.5 , pp. 657-703
    • Ringström, H.1
  • 65
    • 2442506870 scopus 로고    scopus 로고
    • Equivariant wave maps in two space dimensions
    • Struwe M 2003 Equivariant wave maps in two space dimensions Commun. Pure Appl. Math. 56 815-23 (dedicated to the memory of Jürgen K Moser)
    • (2003) Commun. Pure Appl. Math. , vol.56 , Issue.7 , pp. 815-823
    • Struwe, M.1
  • 67
    • 0002061016 scopus 로고    scopus 로고
    • A rigorous ODE solver and Smale's 14th problem
    • Tucker W 2002 A rigorous ODE solver and Smale's 14th problem Found. Comput. Math. 2 53-117
    • (2002) Found. Comput. Math. , vol.2 , Issue.1 , pp. 53-117
    • Tucker, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.