On the shape of bodies in general relativistic regimes
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- 作者：Martin Reiris (1)
1. Max Planck Institute f眉r Gravitationsphysik ; Am Mhlenberg 1 ; 14476 ; Golm ; Germany - 关键词：General relativity ; Radius ; Shape ; Angular momentum ; Rotating stars
- 刊名：General Relativity and Gravitation
- 出版年：2014
- 出版时间：September 2014
- 年：2014
- 卷：46
- 期：9
- 全文大小：365 KB
- 参考文献：1. Bizon, P, Malec, E, O鈥橫urchadha, N (1989) Trapped surfaces due to concentration of matter in spherically symmetric geometries. Class. Quantum Grav. 6: pp. 961-976 f="http://dx.doi.org/10.1088/0264-9381/6/7/004" target="_blank" title="It opens in new window">CrossRef
2. Bray, H, Hayward, S, Mars, M, Simon, W (2007) Generalized inverse mean curvature flows in spacetime. Commun. Math. Phys. 272: pp. 119-138 f="http://dx.doi.org/10.1007/s00220-007-0203-9" target="_blank" title="It opens in new window">CrossRef
3. Castillon, P (2006) An inverse spectral problem on surfaces. Comment. Math. Helvetici 81: pp. 271-286 f="http://dx.doi.org/10.4171/CMH/52" target="_blank" title="It opens in new window">CrossRef
4. Chandrasekhar, S (1967) Ellipsoidal figures of equilibrium鈥揳n historical account. Commun. Pure Appl. Math. 20: pp. 251-265 f="http://dx.doi.org/10.1002/cpa.3160200203" target="_blank" title="It opens in new window">CrossRef
5. Christodoulou, D., Yau, S.-T.: Some remarks on the quasi-local mass. In: Mathematics and General Relativity (Santa Cruz, CA, 1986), volume 71 of Contemp. Math., pp. 9鈥?4. Am. Math. Soc., Providence, RI (1988)
6. Colding, TH, Minicozzi, WP (2002) Estimates for parametric elliptic integrands. Int. Math. Res. Not. 6: pp. 291-297 f="http://dx.doi.org/10.1155/S1073792802106106" target="_blank" title="It opens in new window">CrossRef
7. Dain, S (2008) Axisymmetric evolution of Einstein equations and mass conservation. Class. Quantum Gravity 25: pp. 145021 f="http://dx.doi.org/10.1088/0264-9381/25/14/145021" target="_blank" title="It opens in new window">CrossRef
8. Dain, S (2014) Inequality between size and angular momentum for bodies. Phys. Rev. Lett. 112: pp. 041101 f="http://dx.doi.org/10.1103/PhysRevLett.112.041101" target="_blank" title="It opens in new window">CrossRef
9. Fischer-Colbrie, D (1985) On complete minimal surfaces with finite Morse index in three-manifolds. Invent. Math. 82: pp. 121-132 f="http://dx.doi.org/10.1007/BF01394782" target="_blank" title="It opens in new window">CrossRef
10. Gromov, M., Lawson, Jr., H.B.: Positive scalar curvature and the Dirac operator on complete Riemannian manifolds. Inst. Hautes 脡tudes Sci. Publ. Math., 58:83鈥?96 (1983)
11. Kawai, S (1988) Operator $$\Delta -aK$$ 螖 - a K on surfaces. Hokkaido Math. J. 17: pp. 147-150 f="http://dx.doi.org/10.14492/hokmj/1381517802" target="_blank" title="It opens in new window">CrossRef
12. Khuri, MA (2009) The hoop conjecture in spherically symmetric spacetimes. Phys. Rev. D 80: pp. 124025 f="http://dx.doi.org/10.1103/PhysRevD.80.124025" target="_blank" title="It opens in new window">CrossRef
13. Klenk, J (1998) Geometric properties of rotating stars in general relativity. Class. Quantum Gravity 15: pp. 3203 f="http://dx.doi.org/10.1088/0264-9381/15/10/021" target="_blank" title="It opens in new window">CrossRef
14. Meeks, III, W.H., P茅rez, J., Ros, A.: Stable constant mean curvature surfaces. In: Handbook of Geometric Analysis. no. 1, volume 7 of Adv. Lect. Math. (ALM), pp. 301鈥?80. Int. Press, Somerville, MA (2008)
15. Meinel, R, Ansorg, M, Kleinw盲chter, A, Neugebauer, G, Petroff, D (2008) Relativistic Figures of Equilibrium. Cambridge University Press, Cambridge f="http://dx.doi.org/10.1017/CBO9780511535154" target="_blank" title="It opens in new window">CrossRef
16. O鈥橫urchadha, N (1986) How large can a star be?. Phys. Rev. Lett. 57: pp. 2466-2469 f="http://dx.doi.org/10.1103/PhysRevLett.57.2466" target="_blank" title="It opens in new window">CrossRef
17. Pogorelov, AV (1981) On the stability of minimal surfaces. Dokl. Akad. Nauk SSSR 260: pp. 293-295
18. Reiris, M, Clement, MEG (2013) On the shape of rotating black-holes. Phys. Rev. D 88: pp. 044031 f="http://dx.doi.org/10.1103/PhysRevD.88.044031" target="_blank" title="It opens in new window">CrossRef
19. Schoen, R, Yau, ST (1983) The existence of a black hole due to condensation of matter. Commun. Math. Phys 90: pp. 575-579 f="http://dx.doi.org/10.1007/BF01216187" target="_blank" title="It opens in new window">CrossRef
20. Shiohama, K, Shioya, T, Tanaka, M (2003) The Geometry of Total Curvature on Complete Open Surfaces, volume 159 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge f="http://dx.doi.org/10.1017/CBO9780511543159" target="_blank" title="It opens in new window">CrossRef
21. Stephani, H, Kramer, D, MacCallum, M, Hoenselaers, C, Herlt, E (2003) Exact Solutions of Einstein鈥檚 Field Equations. Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge f="http://dx.doi.org/10.1017/CBO9780511535185" target="_blank" title="It opens in new window">CrossRef
22. Stergioulas, N (2003) Rotating stars in relativity. Living Rev. Rel. 6: pp. 3 - 刊物类别：Physics and Astronomy
- 刊物主题：Physics
Mathematical and Computational Physics
Relativity and Cosmology
Differential Geometry
Quantum Physics
Astronomy, Astrophysics and Cosmology - 出版者：Springer Netherlands
- ISSN：1572-9532
文摘
The analysis of axisymmetric spacetimes, dynamical or stationary, is usually made in the reduced space. We prove here a stability property of the quotient space and use it together with minimal surface techniques to constraint the shape of General Relativistic bodies in terms of their energy and rotation. These constraints are different in nature to the mechanical limitations that a particular material body can have and which can forbid, for instance, rotation faster than a certain rate, (after which the body falls apart). The relations we are describing instead are fundamental and hold for all bodies, albeit they are useful only in General Relativistic regimes. For Neutron stars they are close to be optimal, and, although precise models for these stars display tighter constraints, our results are significative in that they do not depend on the equation of state.