General relativity and conjugate ordinary differential equations
General relativity and conjugate ordinary differential equations
复制标题
广义相对论和共轭常微分方程
DOI：
10.1016/0022-0396(78)90012-8
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发表时间：
1978
影响因子：
2.4
通讯作者：
F. Tipler
中科院分区：
文献类型：
--
作者：
F. Tipler
本文主要研究常微分方程理论中的一个非常重要的问题：方程d2 x-p + F（t）Jc = 0中的函数F（t）有在区间I中至少有两个零点的解的充分条件是什么？然而，这里导出的充分条件在一个方面是不寻常的：定理的动机来自引力场的物理学--广义相对论--而不是数学美学。广义相对论中的方程和概念的符号和约定与[1]相同;参见[2]以获得对广义相对论的更基本的介绍。广义相对论的研究对象是一个时空，它是一个四维无边界的Hausdorff流形，具有非退化的Lorentz度规g。A.类时向量V是满足g（V，V）< 0的向量，满足g（V，V）= 0的零向量，以及满足g（V，V）> 0的类空向量。拉丁索引标记空间和时间维度，从1到4;希腊索引仅标记空间维度，从1到3。
This paper will essentially be concerned with a very aid problem in the theory of ordinary differential equations: what are sufficient conditions on the function F (t) in the equation d2x-p+ F (t) Jc;= 0 such that (I) has a solution with at least two zeros in an interval I? However, the sufficient conditions derived here are unusual in one respect: the motivation for the theorems comes from the physics of the gravitational field--General Relativity-and not from mathematical aesthetics. The notation and conventions of the equations and concepts from General Relativity theory will be the same as in [I]; see [2] for a more elementary introduction to General Relativity. Kecall that the object of study in Generai Relativity is a spacetime, which is a four-dimensional boundaryless Hausdorff manifold with a non-degenerate Lorentz metric g. A. timelike vector V is a vector satisfying g (V, V)< 0, a null vector satisfk g (V, V)=: 0 and a spacelike vector satisfies g (V, V)> 0. Latin indices label space and time dimensions and run from 1 to 4; Greek indices label space dimensions only and run from I to 3.