广义相对论中Shock Waves的碰撞
Collisions of Shock Waves in General Relativity
摘要：
我们表明，Nariai-Bertotti彼得罗夫D型，爱因斯坦的真空场方程的均匀解与宇宙学常数描述的空间-时间的相互作用区域的两个均匀的，平面的引力冲击波，每个最初在真空中不包含宇宙学常数的迎面碰撞。在这种情况下，冲击波具有阶跃函数轮廓，而脉冲波具有δ函数轮廓。碰撞后，两个类光信号，每个组成的平面，均匀的类光壳的物质和平面，均匀的脉冲引力波，旅行远离对方和宇宙学常数中产生的相互作用区域。此外，一个平面，光的信号组成的电磁冲击波伴随着引力冲击波描述的帮助下，两个真正的参数，一个波。两个这样的类光信号的迎面碰撞的检查，我们表明，如果一个简单的代数关系是满足两对参数与每个传入的类光信号，然后在相互作用区域的碰撞后的时空是一个Bertotti时空，这是一个均匀的解决方案的真空爱因斯坦-麦克斯韦场方程组的宇宙学常数。
英文摘要：
We show that the Nariai-Bertotti Petrov type D, homogeneous solution of Einstein's vacuum field equations with a cosmological constant describes the space-time in the interaction region following the head-on collision of two homogeneous, plane gravitational shock waves each initially traveling in a vacuum containing no cosmological constant. A shock wave in this context has a step function profile in contrast to an impulsive wave which has a delta function profile. Following the collision two light-like signals, each composed of a plane, homogeneous light-like shell of matter and a plane, homogeneous impulsive gravitational wave, travel away from each other and a cosmological constant is generated in the interaction region. Furthermore a plane, light-like signal consisting of an electromagnetic shock wave accompanying a gravitational shock wave is described with the help of two real parameters, one for each wave. The head-on collision of two such light-like signals is examined and we show that if a simple algebraic relation is satisfied between the two pairs of parameters associated with each incoming light-like signal then the space-time in the interaction region following the collision is a Bertotti space-time which is a homogeneous solution of the vacuum Einstein-Maxwell field equations with a cosmological constant.
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