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Marginally Trapped Surfaces and Kaluza-Klein Theory

Year 2009, Volume: 2 Issue: 1, 1 - 16, 30.04.2009

Bang-yen Chen

Abstract


Keywords

Trapped surface black hole Kaluza-Klein theory general relativity

References

  • [1] Aledo, J. A., Galvez, J. A. and Mira, P., Marginally trapped surfaces in L4 and an extended Weierstrass-Bryant representation. Ann. Global Anal. Geom. 28 (2005) , 395-415.
  • [2] Andersson, L., Mars, M. and Simon, E., Local existence of dynamical and trapping horizons, Phys. Rev. Letters 95 (2005), 111102-(1-4).
  • [3] Bray, H., Proof of the Riemannian Penrose inequality using the positive mass theorem, J. Di®erential Geom. 59 (2001), 177-267.
  • [4] Chen, B. Y., A report on submanifolds of finite type. Soochow J. Math. 22 (1996), 117-337.
  • [5] Chen, B. Y., Realizations of Robertson-Walker space-times as affine hypersurfaces, J. Phys. A, 40 (2007), 4241-4250.
  • [6] Chen B. Y., Classification of marginally trapped Lorentzian flat surfaces in E42 and its application to biharmonic surfaces. J. Math. Anal. Appl. 340 (2008), 861-875.
  • [7] Chen B. Y., δ-invariants, inequalities of submanifolds and their applications, Topics in Dif- ferential Geometry (edited by A. Mihai, I. Mihai and R. Miron), Editura Academiei Romane, Bucharest, 2008, pp. 29-155.
  • [8] Chen, B. Y. and Dillen, F., Classification of marginally trapped Lagrangian surfaces in Lorentzian complex space forms. J. Math. Phys. 48 (2007), 013509, 23 pp; Erratum, J. Math. Phys. 49 (2008), 059901.
  • [9] Chen, B. Y. and Ishikawa, S., Biharmonic surfaces in pseudo-Euclidean spaces. Memoirs Fac. Sci. Kyushu Univ. Ser. A, Math. 45 (1991), 325-349.
  • [10] Chen, B. Y. and Ishikawa, S., Biharmonic pseudo-Riemannian submanifolds in pseudo- Euclidean spaces. Kyushu J. Math. 52 (1998), 1-18.
  • [11] Chen, B. Y. and Mihai, I., Classification of quasi-minimal slant surfaces in Lorentzian complex space forms. Acta Math. Hungar. 122 (2009), 307-328.
  • [12] Chen, B. Y. and Van der Veken, J., Marginally trapped surfaces in Lorentzian space forms with positive relative nullity. Classical Quantum Gravity 24 (2007), 551-563.
  • [13] Chen, B. Y. and Van der Veken, J., Spatial and Lorentzian surfaces in Robertson-Walker space-times. J. Math. Phys. 48, no. 7, 073509, 12 pages, 2007.
  • [14] Chen, B. Y. and Van der Veken, J., Classification of marginally trapped surfaces with parallel mean curvature vector in Lorentzian space forms, Houston J. Math. (to appear).
  • [15] Chen, B. Y. and Van der Veken, J., Complete classi¯cation of parallel surfaces in Lorentzian space forms, Tohoku Math. J. 61 (2009), 1-40.
  • [16] Einstein, A., Grundlage der allgemeinen Relativittstheorie, Ann, Phys. (Ser. 4) 51 (1916), 769-822.
  • [17] Haesen, S. and Ortega, M., Boost invariant marginally trapped surfaces in Minkowski 4-space. Classical Quantum Gravity 24 (2007), 5441-5452.
  • [18] Haesen, S. and Verstraelen, L., Ideally embedded space-times, J. Math. Phys. 45 (2004), 1497-1510.
  • [19] Huisken, G. and Ilmanen, T., The Riemannian Penrose inequality, Internat. Math. Res. Notices, 1997, no. 20, 1045-1058.
  • [20] Kaluza, T., Zum Unitatsproblem der Physik, Sitz. Preuss. Akad. der Wiss. Phys. Math. Berlin, 1921, pp. 966-972.
  • [21] Klein, O., Quantentheorie und fnfdimensionale Relativittstheorie, Zeits. Phys. 37 (1926), 895-906.
  • [22] Krolak, A., Black holes and the weak cosmic censorship, Gen. Relativity Gravitation 16 (1984), 365{373, 1984.
  • [23] Mars, M. and Senovilla, J. M. M., Trapped surfaces and symmetries, Classical Quantum Gravity, 20 (2003), L293-L300
  • [24] Michell, J., On the means of discovering the distance, magnitude, etc. of the ¯xed stars, Phil. Trans. Royal Soc. (London), 74 (1784), 35-57.
  • [25] O'Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
  • [26] Overduin, J. M. and Wesson, P. S., Kaluza-Klein gravity, Phys. Rep. 283 (1997), 303-378.
  • [27] Penrose, R., Gravitational collapse and space-time singularities, Phys. Rev. Lett. 14 (1965), 57-59.
  • [28] Penrose, R., The question of cosmic censorship. In Black holes and relativistic stars 103{122, Univ. Chicago Press, Chicago, 1998.

Year 2009, Volume: 2 Issue: 1, 1 - 16, 30.04.2009

Bang-yen Chen

Abstract

References

  • [1] Aledo, J. A., Galvez, J. A. and Mira, P., Marginally trapped surfaces in L4 and an extended Weierstrass-Bryant representation. Ann. Global Anal. Geom. 28 (2005) , 395-415.
  • [2] Andersson, L., Mars, M. and Simon, E., Local existence of dynamical and trapping horizons, Phys. Rev. Letters 95 (2005), 111102-(1-4).
  • [3] Bray, H., Proof of the Riemannian Penrose inequality using the positive mass theorem, J. Di®erential Geom. 59 (2001), 177-267.
  • [4] Chen, B. Y., A report on submanifolds of finite type. Soochow J. Math. 22 (1996), 117-337.
  • [5] Chen, B. Y., Realizations of Robertson-Walker space-times as affine hypersurfaces, J. Phys. A, 40 (2007), 4241-4250.
  • [6] Chen B. Y., Classification of marginally trapped Lorentzian flat surfaces in E42 and its application to biharmonic surfaces. J. Math. Anal. Appl. 340 (2008), 861-875.
  • [7] Chen B. Y., δ-invariants, inequalities of submanifolds and their applications, Topics in Dif- ferential Geometry (edited by A. Mihai, I. Mihai and R. Miron), Editura Academiei Romane, Bucharest, 2008, pp. 29-155.
  • [8] Chen, B. Y. and Dillen, F., Classification of marginally trapped Lagrangian surfaces in Lorentzian complex space forms. J. Math. Phys. 48 (2007), 013509, 23 pp; Erratum, J. Math. Phys. 49 (2008), 059901.
  • [9] Chen, B. Y. and Ishikawa, S., Biharmonic surfaces in pseudo-Euclidean spaces. Memoirs Fac. Sci. Kyushu Univ. Ser. A, Math. 45 (1991), 325-349.
  • [10] Chen, B. Y. and Ishikawa, S., Biharmonic pseudo-Riemannian submanifolds in pseudo- Euclidean spaces. Kyushu J. Math. 52 (1998), 1-18.
  • [11] Chen, B. Y. and Mihai, I., Classification of quasi-minimal slant surfaces in Lorentzian complex space forms. Acta Math. Hungar. 122 (2009), 307-328.
  • [12] Chen, B. Y. and Van der Veken, J., Marginally trapped surfaces in Lorentzian space forms with positive relative nullity. Classical Quantum Gravity 24 (2007), 551-563.
  • [13] Chen, B. Y. and Van der Veken, J., Spatial and Lorentzian surfaces in Robertson-Walker space-times. J. Math. Phys. 48, no. 7, 073509, 12 pages, 2007.
  • [14] Chen, B. Y. and Van der Veken, J., Classification of marginally trapped surfaces with parallel mean curvature vector in Lorentzian space forms, Houston J. Math. (to appear).
  • [15] Chen, B. Y. and Van der Veken, J., Complete classi¯cation of parallel surfaces in Lorentzian space forms, Tohoku Math. J. 61 (2009), 1-40.
  • [16] Einstein, A., Grundlage der allgemeinen Relativittstheorie, Ann, Phys. (Ser. 4) 51 (1916), 769-822.
  • [17] Haesen, S. and Ortega, M., Boost invariant marginally trapped surfaces in Minkowski 4-space. Classical Quantum Gravity 24 (2007), 5441-5452.
  • [18] Haesen, S. and Verstraelen, L., Ideally embedded space-times, J. Math. Phys. 45 (2004), 1497-1510.
  • [19] Huisken, G. and Ilmanen, T., The Riemannian Penrose inequality, Internat. Math. Res. Notices, 1997, no. 20, 1045-1058.
  • [20] Kaluza, T., Zum Unitatsproblem der Physik, Sitz. Preuss. Akad. der Wiss. Phys. Math. Berlin, 1921, pp. 966-972.
  • [21] Klein, O., Quantentheorie und fnfdimensionale Relativittstheorie, Zeits. Phys. 37 (1926), 895-906.
  • [22] Krolak, A., Black holes and the weak cosmic censorship, Gen. Relativity Gravitation 16 (1984), 365{373, 1984.
  • [23] Mars, M. and Senovilla, J. M. M., Trapped surfaces and symmetries, Classical Quantum Gravity, 20 (2003), L293-L300
  • [24] Michell, J., On the means of discovering the distance, magnitude, etc. of the ¯xed stars, Phil. Trans. Royal Soc. (London), 74 (1784), 35-57.
  • [25] O'Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York, 1983.
  • [26] Overduin, J. M. and Wesson, P. S., Kaluza-Klein gravity, Phys. Rep. 283 (1997), 303-378.
  • [27] Penrose, R., Gravitational collapse and space-time singularities, Phys. Rev. Lett. 14 (1965), 57-59.
  • [28] Penrose, R., The question of cosmic censorship. In Black holes and relativistic stars 103{122, Univ. Chicago Press, Chicago, 1998.
There are 28 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Bang-yen Chen

Publication Date April 30, 2009
Published in Issue Year 2009 Volume: 2 Issue: 1

Cite

APA Chen, B.-y. (2009). Marginally Trapped Surfaces and Kaluza-Klein Theory. International Electronic Journal of Geometry, 2(1), 1-16.
AMA Chen By. Marginally Trapped Surfaces and Kaluza-Klein Theory. Int. Electron. J. Geom. April 2009;2(1):1-16.
Chicago Chen, Bang-yen. “Marginally Trapped Surfaces and Kaluza-Klein Theory”. International Electronic Journal of Geometry 2, no. 1 (April 2009): 1-16.
EndNote Chen B-y (April 1, 2009) Marginally Trapped Surfaces and Kaluza-Klein Theory. International Electronic Journal of Geometry 2 1 1–16.
IEEE B.-y. Chen, “Marginally Trapped Surfaces and Kaluza-Klein Theory”, Int. Electron. J. Geom., vol. 2, no. 1, pp. 1–16, 2009.
ISNAD Chen, Bang-yen. “Marginally Trapped Surfaces and Kaluza-Klein Theory”. International Electronic Journal of Geometry 2/1 (April 2009), 1-16.
JAMA Chen B-y. Marginally Trapped Surfaces and Kaluza-Klein Theory. Int. Electron. J. Geom. 2009;2:1–16.
MLA Chen, Bang-yen. “Marginally Trapped Surfaces and Kaluza-Klein Theory”. International Electronic Journal of Geometry, vol. 2, no. 1, 2009, pp. 1-16.
Vancouver Chen B-y. Marginally Trapped Surfaces and Kaluza-Klein Theory. Int. Electron. J. Geom. 2009;2(1):1-16.