메뉴 건너뛰기




Volumn 249, Issue 3, 2004, Pages 529-548

A definition of total energy-momenta and the positive mass theorem on asymptotically hyperbolic 3-manifolds. I

Author keywords

[No Author keywords available]

Indexed keywords


EID: 4544257930     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-004-1056-0     Document Type: Article
Times cited : (56)

References (55)
  • 1
    • 0002925943 scopus 로고    scopus 로고
    • Scalar curvature rigidity for asymptotically locally hyperbolic manifolds
    • [AnD] Andersson, L., Dahl, M.: Scalar curvature rigidity for asymptotically locally hyperbolic manifolds. Ann. Glob. Anal. Geom. 16, 1-27 (1998)
    • (1998) Ann. Glob. Anal. Geom. , vol.16 , pp. 1-27
    • Andersson, L.1    Dahl, M.2
  • 2
    • 0000177308 scopus 로고
    • Coordinate invariance and energy expressions in general relativity
    • [ADM] Arnowitt, S., Deser, S., Misner, C.: Coordinate invariance and energy expressions in general relativity. Phys. Rev. 122, 997-1006 (1961)
    • (1961) Phys. Rev. , vol.122 , pp. 997-1006
    • Arnowitt, S.1    Deser, S.2    Misner, C.3
  • 3
    • 0034695292 scopus 로고    scopus 로고
    • Asymptotically anti-de Sitter spacetimes: Conserved quantities
    • [AsD] Ashtekar, A., Das, S.: Asymptotically anti-de Sitter spacetimes: conserved quantities. Class Quantum Grav. 17, L17-L30 (2000)
    • (2000) Class Quantum Grav. , vol.17
    • Ashtekar, A.1    Das, S.2
  • 4
    • 36749105734 scopus 로고
    • A unified treatment of null and spatial infinity in general relativity. I. Universal structure, asymptotic symmetries, and conserved quantities at spatial infinity
    • [AsHa] Ashtekar, A., Hansen, R.: A unified treatment of null and spatial infinity in general relativity. I. Universal structure, asymptotic symmetries, and conserved quantities at spatial infinity. J. Math. Phys. 19, 1542-1566 (1978)
    • (1978) J. Math. Phys. , vol.19 , pp. 1542-1566
    • Ashtekar, A.1    Hansen, R.2
  • 5
    • 0001918310 scopus 로고
    • Energy-momentum of isolated systems cannot be null
    • [AsHo] Ashtekar, A., Horowitz, G.: Energy-momentum of isolated systems cannot be null. Phys. Lett. 89A, 181-184 (1982)
    • (1982) Phys. Lett. , vol.89 A , pp. 181-184
    • Ashtekar, A.1    Horowitz, G.2
  • 6
    • 0000297685 scopus 로고
    • From i° to the 3 + 1 description of spatial infinity
    • [AM] Ashtekar, A., Magnon, A.: From i° to the 3 + 1 description of spatial infinity. J. Math. Phys. 25, 2682-2690 (1984)
    • (1984) J. Math. Phys. , vol.25 , pp. 2682-2690
    • Ashtekar, A.1    Magnon, A.2
  • 7
    • 84990556234 scopus 로고
    • The mass of an asymptotically flat manifold
    • [Ba1] Bartnik, R.: The mass of an asymptotically flat manifold. Comm. Pure Appl. Math. 36, 661-693 (1986)
    • (1986) Comm. Pure Appl. Math. , vol.36 , pp. 661-693
    • Bartnik, R.1
  • 8
    • 84972545815 scopus 로고
    • Quasi-spherical metrics and prescribed scalar curvature
    • [Ba2] Bartnik, R.: Quasi-spherical metrics and prescribed scalar curvature. J. Diff. Geom. 37, 31-71 (1993)
    • (1993) J. Diff. Geom. , vol.37 , pp. 31-71
    • Bartnik, R.1
  • 9
    • 0002250731 scopus 로고
    • Gravitational waves in general relativity VII. Waves from isolated axi-symmetric systems
    • [BBM] Bondi, H., van der Burg, H., Metzner, A.: Gravitational waves in general relativity VII. Waves from isolated axi-symmetric systems. Proc. Roy. Soc. Lond. A 269, 21-52 (1962)
    • (1962) Proc. Roy. Soc. Lond. A , vol.269 , pp. 21-52
    • Bondi, H.1    Van Der Burg, H.2    Metzner, A.3
  • 10
    • 0035497450 scopus 로고    scopus 로고
    • Proof of the Riemannian Penrose conjecture using the positive mass theorem
    • [Bra] Bray, H.: Proof of the Riemannian Penrose conjecture using the positive mass theorem. J. Diff. Geom. 59, 177-267 (2001)
    • (2001) J. Diff. Geom. , vol.59 , pp. 177-267
    • Bray, H.1
  • 11
    • 0001271263 scopus 로고
    • Surfaces of mean curvature one in hyperbolic space
    • [Bry] Bryant, R.: Surfaces of mean curvature one in hyperbolic space. Astérisque 154-155, 321-347 (1987)
    • (1987) Astérisque , pp. 154-155
    • Bryant, R.1
  • 12
    • 0002057789 scopus 로고
    • Boundary conditions at spatial infinity from a Hamiltonian point of view
    • NATO, Adv. Sci. Inst. Ser. B: Phys., New York: Plenum
    • [Ch1] Chruściel, P.: Boundary conditions at spatial infinity from a Hamiltonian point of view. In: Topological Properties and Global Structure of Space-Time (Erice, 1985), NATO, Adv. Sci. Inst. Ser. B: Phys. 138, New York: Plenum 1986, pp. 49-59
    • (1986) Topological Properties and Global Structure of Space-Time (Erice, 1985) , vol.138 , pp. 49-59
    • Chruściel, P.1
  • 13
    • 0038918866 scopus 로고
    • On angular momentum at spatial infinity
    • [Ch2] Chruściel, P.: On angular momentum at spatial infinity. Class. Quantum Grav. 4, L205-210 (1987)
    • (1987) Class. Quantum Grav. , vol.4
    • Chruściel, P.1
  • 16
    • 79551487240 scopus 로고    scopus 로고
    • The mass of spacelike hypersurfaces in asymptotically anti-de Sitter space-times
    • [CN] Chruściel, P., Nagy, G.: The mass of spacelike hypersurfaces in asymptotically anti-de Sitter space-times. Adv. Theor. Math. Phys. 5, 697-754 (2001)
    • (2001) Adv. Theor. Math. Phys. , vol.5 , pp. 697-754
    • Chruściel, P.1    Nagy, G.2
  • 17
    • 0009324211 scopus 로고    scopus 로고
    • Analyse précisée d'équations semi-linéaires elliptiques sur l'espace hyperbolique et application à la courbure scalaire conforme
    • [D] Delay, E.: Analyse précisée d'équations semi-linéaires elliptiques sur l'espace hyperbolique et application à la courbure scalaire conforme. Bull. Soc. Math. France 125, 345-381 (1997)
    • (1997) Bull. Soc. Math. France , vol.125 , pp. 345-381
    • Delay, E.1
  • 20
    • 33646050447 scopus 로고
    • Einstein metrics with prescribed conformal infinity on the ball
    • [GL] Graham, C., Lee, J.: Einstein metrics with prescribed conformal infinity on the ball. Adv. Math. 87, 186-225 (1991)
    • (1991) Adv. Math. , vol.87 , pp. 186-225
    • Graham, C.1    Lee, J.2
  • 21
    • 0031536628 scopus 로고    scopus 로고
    • A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds
    • [He1] Herzlich, M.: A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds. Commun. Math. Phys. 188, 121-133 (1997)
    • (1997) Commun. Math. Phys. , vol.188 , pp. 121-133
    • Herzlich, M.1
  • 22
    • 0032093450 scopus 로고    scopus 로고
    • The positive mass theorem for black holes revisited
    • [He2] Herzlich, M.: The positive mass theorem for black holes revisited. J. Geom. Phys. 26, 97-111 (1998)
    • (1998) J. Geom. Phys. , vol.26 , pp. 97-111
    • Herzlich, M.1
  • 23
    • 0032273339 scopus 로고    scopus 로고
    • Scalar curvature and rigidity of odd-dimensional complex hyperbolic spaces
    • [He3] Herzlich, M.: Scalar curvature and rigidity of odd-dimensional complex hyperbolic spaces. Math. Ann. 312, 641-657 (1998)
    • (1998) Math. Ann. , vol.312 , pp. 641-657
    • Herzlich, M.1
  • 24
    • 0035526412 scopus 로고    scopus 로고
    • The inverse mean curvature flow and the Riemannian Penrose inequality
    • [HI] Huisken, G., Ilmanen, T.: The inverse mean curvature flow and the Riemannian Penrose inequality. J. Diff. Geom. 59, 353-437 (2001)
    • (2001) J. Diff. Geom. , vol.59 , pp. 353-437
    • Huisken, G.1    Ilmanen, T.2
  • 25
    • 16444380512 scopus 로고    scopus 로고
    • The AdS/CFT correspondence and a new positive energy conjecture for general relativity
    • [HM] Horowitz, G., Myers, R.: The AdS/CFT correspondence and a new positive energy conjecture for general relativity. Phys. Rev. D59, 026005 (1999)
    • (1999) Phys. Rev. D , vol.59 , pp. 026005
    • Horowitz, G.1    Myers, R.2
  • 26
    • 4243685945 scopus 로고
    • Gravitational energy cannot become negative
    • [HP] Horowitz, G., Perry, M.: Gravitational energy cannot become negative. Phys. Rev. Lett. 48, 371-374 (1982)
    • (1982) Phys. Rev. Lett. , vol.48 , pp. 371-374
    • Horowitz, G.1    Perry, M.2
  • 27
    • 0001443659 scopus 로고
    • A relation between local and total energy in general relativity
    • [HT] Horowitz, G., Tod, P.: A relation between local and total energy in general relativity. Commun. Math. Phys. 85, 429-447 (1982)
    • (1982) Commun. Math. Phys. , vol.85 , pp. 429-447
    • Horowitz, G.1    Tod, P.2
  • 28
    • 0000173536 scopus 로고
    • Positivity of the Bondi gravitational mass
    • [IN] Israel, W., Nester, J.: Positivity of the Bondi gravitational mass. Phys. Lett. 85A, 259-260 (1981)
    • (1981) Phys. Lett. , vol.85 A , pp. 259-260
    • Israel, W.1    Nester, J.2
  • 29
    • 0003933802 scopus 로고
    • Princeton Math. Series, Princeton, NJ: Princeton University Press
    • [LM] Lawson, H., Michelsohn, M.: Spin Geometry. Princeton Math. Series, Vol. 38, Princeton, NJ: Princeton University Press, 1989
    • (1989) Spin Geometry , vol.38
    • Lawson, H.1    Michelsohn, M.2
  • 30
    • 0000850417 scopus 로고
    • The specturm of an asymptotically hyperbolic Einstein manifold
    • [Le] Lee, J.: The specturm of an asymptotically hyperbolic Einstein manifold. Comm. Anal. Geom. 3, 253-271 (1995)
    • (1995) Comm. Anal. Geom. , vol.3 , pp. 253-271
    • Lee, J.1
  • 32
    • 0002705315 scopus 로고
    • A simple proof of the positivity of the Bondi mass
    • [LV] Ludvigsen, M., Vickers, J.: A simple proof of the positivity of the Bondi mass. J. Phys. A: Math. Gen. 15, L67-L70 (1982)
    • (1982) J. Phys. A: Math. Gen. , vol.15
    • Ludvigsen, M.1    Vickers, J.2
  • 33
    • 0002258037 scopus 로고
    • Scalar curvature rigidity of asymptotically hyperbolic spin manifolds
    • [M] Min-Oo, M.: Scalar curvature rigidity of asymptotically hyperbolic spin manifolds. Math. Ann. 285, 527-539 (1989)
    • (1989) Math. Ann. , vol.285 , pp. 527-539
    • Min-Oo, M.1
  • 34
    • 0000480951 scopus 로고
    • A new gravitational energy expression with a simple positivity proof
    • [N] Nester, J.: A new gravitational energy expression with a simple positivity proof. Phys. Lett. 83A, 241-242 (1981)
    • (1981) Phys. Lett. , vol.83 A , pp. 241-242
    • Nester, J.1
  • 35
    • 0001180073 scopus 로고
    • On Witten's proof of the positive energy theorem
    • [PT] Parker, T., Taubes, C.: On Witten's proof of the positive energy theorem. Commun. Math. Phys. 84, 223-238 (1982)
    • (1982) Commun. Math. Phys. , vol.84 , pp. 223-238
    • Parker, T.1    Taubes, C.2
  • 36
    • 0000965397 scopus 로고
    • Some unsolved problems in classical general relativity
    • ed. S.-T. Yau, Annals of Math. Stud. 102, Princeton, NJ: Princeton Univ. Press
    • [Pe] Penrose, R.: Some unsolved problems in classical general relativity. In: Seminar on Differential Geometry, ed. S.-T. Yau, Annals of Math. Stud. 102, Princeton, NJ: Princeton Univ. Press, 1982, pp. 631-668
    • (1982) Seminar on Differential Geometry , pp. 631-668
    • Penrose, R.1
  • 37
    • 0000973997 scopus 로고
    • Role of surface integrals in the Hamiltonian formulation of general relativity
    • [RegT] Regge, T., Teitelboim, C.: Role of surface integrals in the Hamiltonian formulation of general relativity. Ann. Phys. 88, 286-318 (1974)
    • (1974) Ann. Phys. , vol.88 , pp. 286-318
    • Regge, T.1    Teitelboim, C.2
  • 38
    • 0000930119 scopus 로고
    • Positivity of the Bondi energy
    • [ReuT] Reula, O., Tod, K.: Positivity of the Bondi energy. J. Math. Phys. 25, 1004-1008 (1984)
    • (1984) J. Math. Phys. , vol.25 , pp. 1004-1008
    • Reula, O.1    Tod, K.2
  • 41
    • 0000204773 scopus 로고
    • Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time
    • [Sa] Sachs, R.: Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time. Proc. Roy. Soc. Lond, A 270, 103-126 (1962)
    • (1962) Proc. Roy. Soc. Lond, A , vol.270 , pp. 103-126
    • Sachs, R.1
  • 42
    • 34250263023 scopus 로고
    • On the proof of the positive mass conjecture in general relativity
    • [SY1] Schoen, R., Yau, S.-T.: On the proof of the positive mass conjecture in general relativity. Commun. Math. Phys. 65, 45-76 (1979)
    • (1979) Commun. Math. Phys. , vol.65 , pp. 45-76
    • Schoen, R.1    Yau, S.-T.2
  • 43
    • 0002081241 scopus 로고
    • The energy and the linear momentum of spacetimes in general relativity
    • [SY2] Schoen, R., Yau, S.-T.: The energy and the linear momentum of spacetimes in general relativity. Commun. Math. Phys. 79, 47-51 (1981)
    • (1981) Commun. Math. Phys. , vol.79 , pp. 47-51
    • Schoen, R.1    Yau, S.-T.2
  • 44
    • 29244463784 scopus 로고
    • Proof of the positive mass theorem. II
    • [SY3] Schoen, R., Yau, S.-T.: Proof of the positive mass theorem. II. Commun. Math. Phys. 79, 231-260 (1981)
    • (1981) Commun. Math. Phys. , vol.79 , pp. 231-260
    • Schoen, R.1    Yau, S.-T.2
  • 45
    • 25344449221 scopus 로고
    • Proof that the Bondi mass is positive
    • [SY4] Schoen, R., Yau, S.-T.: Proof that the Bondi mass is positive. Phys. Rev. Lett. 48, 369-371 (1982)
    • (1982) Phys. Rev. Lett. , vol.48 , pp. 369-371
    • Schoen, R.1    Yau, S.-T.2
  • 46
    • 0000699811 scopus 로고
    • The existence of a black hole due to condensation of matter
    • [SY5] Schoen, R., Yau, S.-T.: The existence of a black hole due to condensation of matter. Commun. Math. Phys. 90, 575-579 (1983)
    • (1983) Commun. Math. Phys. , vol.90 , pp. 575-579
    • Schoen, R.1    Yau, S.-T.2
  • 47
    • 0001738480 scopus 로고
    • Complete surface of constant mean curvature-1 in the hyperbolic 3-space
    • [UY] Umehara, M., Yamada, K.: Complete surface of constant mean curvature-1 in the hyperbolic 3-space. Ann. Math. 137, 611-638 (1993)
    • (1993) Ann. Math. , vol.137 , pp. 611-638
    • Umehara, M.1    Yamada, K.2
  • 48
    • 0039843578 scopus 로고    scopus 로고
    • Mass for asymptotically hyperbolic manifolds
    • [Wa] Wang, X.: Mass for asymptotically hyperbolic manifolds. J. Diff. Geom. 57, 273-299 (2001)
    • (2001) J. Diff. Geom. , vol.57 , pp. 273-299
    • Wang, X.1
  • 49
    • 33744727108 scopus 로고
    • A new proof of the positive energy theorem
    • [Wi] Witten, E.: A new proof of the positive energy theorem. Commun. Math. Phys. 80, 381-402 (1981)
    • (1981) Commun. Math. Phys. , vol.80 , pp. 381-402
    • Witten, E.1
  • 50
    • 79551488820 scopus 로고    scopus 로고
    • Geometry of three manifolds and existence of black hole due to boundary effect
    • [Ya] Yau, S.-T.: Geometry of three manifolds and existence of black hole due to boundary effect. Adv. Theor. Math. Phys. 5, 755-767 (2001)
    • (2001) Adv. Theor. Math. Phys. , vol.5 , pp. 755-767
    • Yau, S.-T.1
  • 51
    • 0842294295 scopus 로고
    • Energy and momentum of the gravitational field
    • ed. F.J. Tipler, New York: Academic Press
    • [Yo] York, J.: Energy and momentum of the gravitational field. In: Essays in General Relativity, ed. F.J. Tipler, New York: Academic Press, 1980
    • (1980) Essays in General Relativity
    • York, J.1
  • 52
    • 0033239067 scopus 로고    scopus 로고
    • Angular momentum and positive mass theorem
    • [Z1] Zhang, X.: Angular momentum and positive mass theorem. Commun. Math. Phys. 206, 137-155 (1999)
    • (1999) Commun. Math. Phys. , vol.206 , pp. 137-155
    • Zhang, X.1
  • 53
    • 0034348711 scopus 로고    scopus 로고
    • Strongly asymptotically hyperbolic spin manifolds
    • [Z2] Zhang, X.: Strongly asymptotically hyperbolic spin manifolds. Math. Res. Lett. 7, 719-728 (2000)
    • (2000) Math. Res. Lett. , vol.7 , pp. 719-728
    • Zhang, X.1
  • 54
    • 0037833673 scopus 로고    scopus 로고
    • Remarks on the total angular momentum in general relativity
    • [Z3] Zhang, X.: Remarks on the total angular momentum in general relativity. Commun. Theor. Phys. 39, 521-524 (2003)
    • (2003) Commun. Theor. Phys. , vol.39 , pp. 521-524
    • Zhang, X.1
  • 55
    • 4544256346 scopus 로고    scopus 로고
    • In preparation
    • [Z4] Zhang, X.: In preparation
    • Zhang, X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.