标题： 完整的布兰斯-迪克理论 显示英文标题

标题： The complete Brans-Dicke theory

摘要： 在标量场与普通物质之间以一种唯一定义的方式交换能量时，得到了Brans-Dicke引力理论的最一般完成形式。 该理论包含一个新的参数（来自积分过程的积分常数），当这个参数被关闭时，Brans-Dicke理论就会出现。 通常情况下，当物质的能量-动量张量为零时，可以从完整的Brans-Dicke理论中定义真空理论。 然而，此外还找到了与标量场的自由波方程一致的完整真空理论族。 该族中的一个子类具有恒定协变守恒的能量-动量张量，并且因此可以补充任何标量场的运动方程。 显示英文摘要

摘要： The most general completion of Brans-Dicke gravity is found when energy is exchanged in a uniquely defined way between the scalar field and ordinary matter. The theory contains a new parameter (integration constant from the integration procedure) and when this is switched off, Brans-Dicke theory emerges. As usually, the vacuum theory can be defined from the complete Brans-Dicke theory when the matter energy-momentum tensor vanishes. However, additionally, the complete family of vacuum theories is found, consistent with the free wave equation for the scalar field. The subclass of this family with identically covariantly conserved energy-momentum tensor is identified and, thus, can be supplemented by any equation of motion for the scalar field.