-type and -type four dimensional plane wave solutions of Einstein's field

ABSTRACT: In the present paper, we have studied ( ) ] 2 1 [ y  z  t - type and [t 2 ( y  z)]-type plane wave solutions of Einstein’s field equations in general theory of relativity in the case where the zero mass scalar field coupled with gravitational field and zero mass scalar field coupled with gravitational & electromagnetic field and established the existence of these two types of plane wave solutions in V4 . Furthermore we have considered the case of massive scalar field and shown that the non-existence of these two types of plane wave solutions in GR theory. Keywords : Einstein’s field equations in general relativity in case where the zero mass scalar field coupled with gravitational field and zero mass scalar field coupled with gravitational & electromagnetic field, four dimensional space-time, etc.

摘要：本文研究了广义相对论（General Theory of Relativity）中爱因斯坦场方程（Einstein’s Field Equations）在零质量标量场（Zero Mass Scalar Field）与引力场（Gravitational Field）耦合、零质量标量场与引力及电磁场（Electromagnetic Field）耦合情形下的$rac{1}{2}(y+z-t)$型与$[t^2(y+z)]$型平面波解，并确立了这两类平面波解在四维空间$V_4$中的存在性。此外，本文还探讨了有质量标量场（Massive Scalar Field）的情形，并证明了在广义相对论（GR）框架下这两类平面波解不存在。
关键词：广义相对论中零质量标量场与引力场耦合、零质量标量场与引力及电磁场耦合情形下的爱因斯坦场方程，四维时空（Four Dimensional Space-Time）等。