雷乔杜里方程

在广义相对论中，雷乔杜里方程（），或朗道–雷乔杜里方程（）Spacetime as a deformable solid, M. O. Tahim, R. R. Landim, and C. A. S. Almeida, .是描述邻近物质运动的基本方程。

它不仅是彭罗斯-霍金奇点定理和广义相对论的精确解研究的基本引理，还具有独特之处，即它指出引力应该是广义相对论中任意质量-能量之间的普遍存在的吸引力，正如在牛顿引力理论中那样。

这一方程由印度物理学家和苏联物理学家列夫·朗道各自独立发现。The large scale structure of space-time by Stephen W. Hawking and G. F. R. Ellis, Cambridge University Press, 1973, p. 84, .

 数学表述 
考虑一个类时的单位矢量场 （可理解为不相交的世界线的）, 雷乔杜里方程可写为



式中



是剪切张量



和涡度张量



的二次不变量。这里



是扩张张量，是它的迹，称为扩张标量。



是正交于的超平面上的投影张量。另外，圆点表示对固有时的微分。的迹可写为

  +1

这个量有时也称为雷乔杜里标量。

 参见 

 引力奇点
 彭罗斯-霍金奇点定理

 注释 

 参考资料 
  See chapter 2 for an excellent discussion of Raychaudhuri's equation for both timelike and null geodesics, as well as the focusing theorem.
  See appendix F.
  See chapter 6 for a very detailed introduction to geodesic congruences, including the general form of Raychaudhuri's equation.
   See section 4.1 for a discussion of the general form of Raychaudhuri's equation.
   Raychaudhuri's paper introducing his equation.
  See section IV  for derivation of the general form of Raychaudhuri equations for three kinematical quantities (namely expansion scalar, shear and rotation).
  See for a review on Raychaudhuri equations.

 外部链接 
 The Meaning of Einstein's Field Equation  by John C. Baez and Emory F. Bunn.  Raychaudhuri's equation takes center stage in this well known (and highly recommended) semi-technical exposition of what Einstein's equation says.

Category:广义相对论