Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

被引:86
作者
Krtous, Pavel [1 ]
Kubiznak, David
Page, Don N.
Frolov, Valeri P.
机构
[1] Charles Univ Prague, Inst Theoret Phys, V Holesovickach 2, CR-11636 Prague 1, Czech Republic
[2] Univ Alberta, Inst Theoret Phys, Edmonton, AB T6G 2G7, Canada
来源
JOURNAL OF HIGH ENERGY PHYSICS | 2007年 / 02期
关键词
large extra dimensions; classical theories of gravity; black holes; II SUPERCONDUCTORS; HARMONIC SUSCEPTIBILITIES; MAGNETIZATION CURVES; MODEL; LOSSES; AC; HYSTERESIS; FIELD;
D O I
10.1088/1126-6708/2007/02/004
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D + 1)/2] Killing-Yano tensors, of rank D-2j for all 0 <= j <= k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245).
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页数:15
相关论文
共 35 条
[1]   REMARKS ON CERTAIN SEPARABILITY STRUCTURES AND THEIR APPLICATIONS TO GENERAL RELATIVITY [J].
BENENTI, S ;
FRANCAVIGLIA, M .
GENERAL RELATIVITY AND GRAVITATION, 1979, 10 (01) :79-92
[3]  
Carter B., 1968, Communications in Mathematical Physics, V10, P280
[4]   SOLUTION OF DIRACS EQUATION IN KERR GEOMETRY [J].
CHANDRASEKHAR, S .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1976, 349 (1659) :571-575
[5]   General Kerr-NUT-AdS metrics in all dimensions [J].
Chen, W. ;
Lu, H. ;
Pope, C. N. .
CLASSICAL AND QUANTUM GRAVITY, 2006, 23 (17) :5323-5340
[6]   Separability and Killing tensors in Kerr-Taub-NUT-de Sitter metrics in higher dimensions [J].
Chong, ZW ;
Gibbons, GW ;
Hü, L ;
Pope, CN .
PHYSICS LETTERS B, 2005, 609 (1-2) :124-132
[7]   COMMENT ON SYMMETRIES OF KERR BLACK-HOLES [J].
COLLINSON, CD ;
SMITH, PN .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1977, 56 (03) :277-279
[8]   SEPARABILITY STRUCTURES AND KILLING-YANO TENSORS IN VACUUM TYPE-D SPACE-TIMES WITHOUT ACCELERATION [J].
DEMIANSKI, M ;
FRANCAVIGLIA, M .
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 1980, 19 (09) :675-680
[9]   SPACE-TIMES ADMITTING KILLING-YANO TENSORS .1. [J].
DIETZ, W ;
RUDIGER, R .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1981, 375 (1762) :361-378
[10]  
Floyd R.M., 1973, Ph.D. Thesis