Conformal invariance and the conformal-traceless decomposition of the gravitational field

被引:20
作者
Brown, JD [1 ]
机构
[1] N Carolina State Univ, Dept Phys, Raleigh, NC 27695 USA
来源
PHYSICAL REVIEW D | 2005年 / 71卷 / 10期
关键词
D O I
10.1103/PhysRevD.71.104011
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
Einstein's theory of general relativity is written in terms of the variables obtained from a conformal-traceless decomposition of the spatial metric and extrinsic curvature. The determinant of the conformal metric is not restricted, so the action functional and equations of motion are invariant under conformal transformations. With this approach the conformal-traceless variables remain free of density weights. The conformal invariance of the equations of motion can be broken by imposing an evolution equation for the determinant of the conformal metric g. Two conditions are considered, one in which g is constant in time and one in which g is constant along the unit normal to the spacelike hypersurfaces. This approach is used to write the Baumgarte-Shapiro-Shibata-Nakamura system of evolution equations in conformally invariant form. The presentation includes a discussion of the conformal thin sandwich construction of gravitational initial data, and the conformal flatness condition as an approximation to the evolution equations.
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页数:12
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共 21 条
[1]   Gauge conditions for long-term numerical black hole evolutions without excision -: art. no. 084023 [J].
Alcubierre, M ;
Brügmann, B ;
Diener, P ;
Koppitz, M ;
Pollney, D ;
Seidel, E ;
Takahashi, R .
PHYSICAL REVIEW D, 2003, 67 (08)
[2]   Hamiltonian time evolution for general relativity [J].
Anderson, A ;
York, JW .
PHYSICAL REVIEW LETTERS, 1998, 81 (06) :1154-1157
[3]  
[Anonymous], 2004, FINITE ELEMENT METHO
[4]  
ARNOWITT R, GRQC0405109
[5]   3-DIMENSIONAL GEOMETRY AS CARRIER OF INFORMATION ABOUT TIME [J].
BAIERLEIN, RF ;
SHARP, DH ;
WHEELER, JA .
PHYSICAL REVIEW, 1962, 126 (05) :1864-&
[6]   Numerical integration of Einstein's field equations [J].
Baumgarte, TW ;
Shapiro, SL .
PHYSICAL REVIEW D, 1999, 59 (02)
[7]   Testing a simplified version of Einstein's equations for numerical relativity [J].
Cook, GB ;
Shapiro, SL ;
Teukolsky, SA .
PHYSICAL REVIEW D, 1996, 53 (10) :5533-5540
[8]   Initial data for numerical relativity [J].
Cook G.B. .
Living Reviews in Relativity, 2000, 3 (1)
[9]   Combining spectral and shock-capturing methods:: A new numerical approach for 3D relativistic core collapse simulations -: art. no. 064023 [J].
Dimmelmeier, H ;
Novak, J ;
Font, JA ;
Ibáñez, JM ;
Müller, E .
PHYSICAL REVIEW D, 2005, 71 (06) :1-30
[10]   Relativistic simulations of rotational core collapse -: I.: Methods, initial models, and code tests [J].
Dimmelmeier, H ;
Font, JA ;
Müller, E .
ASTRONOMY & ASTROPHYSICS, 2002, 388 (03) :917-935