Lagrange multipliers and gravitational theory
Lagrange multipliers and gravitational theory
复制标题
拉格朗日乘子和引力理论
DOI：
10.1063/1.523076
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发表时间：
1976
期刊：
影响因子：
--
通讯作者：
F. Elston
中科院分区：
文献类型：
--
作者：
J. Safko;F. Elston
的拉格朗日乘子版本的Palatini变分原理扩展到非线性拉格朗日，它是在二次拉格朗日的情况下，如预期的那样，这个版本的Palatini方法是等价的希尔伯特变分方法。二次拉格朗日量的（非零）拉格朗日乘子，然后明确地得到协变形式。然后指出，在Arnowitt、Deser和Misner发展的（3+1）形式语言中的拉格朗日乘子方法如何允许将二次和一般高阶拉格朗日量的运动方程重铸为ADM正则形式。一般情况下，如果没有拉格朗日乘子方法，高阶ADM问题无法解决。以最简单的二次拉格朗日量（g1/2 R2）为例，这是明确完成的。
The Lagrange multiplier version of the Palatini variational principle is extended to nonlinear Lagrangians, where it is shown in the case of the quadratic Lagrangians, as expected, that this version of the Palatini approach is equivalent to the Hilbert variational method. The (nonvanishing) Lagrange multipliers for the quadratic Lagrangians are then explicitly obtained in covariant form. It is then pointed out how the Lagrange multiplier approach in the language of the (3+1) ‐formalism developed by Arnowitt, Deser, and Misner permits the recasting of the equations of motion for quadratic and general higher‐order Lagrangians into the ADM canonical formalism. In general without the Lagrange multiplier approach, the higher order ADM problem could not be solved. This is done explicitly for the simplest quadratic Lagrangian (g1/2R2) as an example.