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In theoretical physics, Lovelock's theory of gravity (often referred to as Lovelock gravity) is a generalization of Einstein's theory of general relativity introduced by David Lovelock in 1971.〔D. Lovelock, The Einstein tensor and its generalizations, J. Math. Phys. 12 (1971) 498.〕 It is the most general metric theory of gravity yielding conserved second order equations of motion in arbitrary number of spacetime dimensions ''D''. In this sense, Lovelock's theory is the natural generalization of Einstein's General Relativity to higher dimensions. In three and four dimensions (''D'' = 3, 4), Lovelock's theory coincides with Einstein's theory, but in higher dimensions the theories are different. In fact, for ''D'' > 4 Einstein gravity can be thought of as a particular case of Lovelock gravity since the Einstein–Hilbert action is one of several terms that constitute the Lovelock action. ==Lagrangian density== The Lagrangian of the theory is given by a sum of dimensionally extended Euler densities, and it can be written as follows : where ''Rμναβ'' represents the Riemann tensor, and where the generalized Kronecker delta ''δ'' is defined as the antisymmetric product : in corresponds to the dimensional extension of the Euler density in 2''n'' dimensions, so that these only contribute to the equations of motion for ''n'' < ''D''/2. Consequently, without lack of generality, ''t'' in the equation above can be taken to be for even dimensions and for odd dimensions. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lovelock theory of gravity」の詳細全文を読む スポンサード リンク
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