标题： 关于标量-张量引力理论中标量场的能量-动量张量 显示英文标题

标题： On the Energy-Momentum Tensor of the Scalar Field in Scalar--Tensor Theories of Gravity

摘要： 我们研究引力的动力学描述、标量场能量-动量张量的适当定义以及它们之间的相互关系在标量-张量引力理论中。 我们表明，人们会天真地认为是标量场的能量-动量张量的量并不合适，因为它被引力的动力学描述的一部分所破坏。 可以定义一个新的联络，通过它，引力的完整动力学描述是明确的，并且可以立即识别正确的标量场能量-动量张量。 必须对定义特定标量-张量理论的两个自由函数（耦合函数和势能）施加某些不等式，以确保标量场能量密度永远不会为负。 正确的动力学描述自然导致标量-张量引力的爱因斯坦框架表述，这也被详细研究。 显示英文摘要

摘要： We study the dynamical description of gravity, the appropriate definition of the scalar field energy-momentum tensor, and the interrelation between them in scalar-tensor theories of gravity. We show that the quantity which one would naively identify as the energy-momentum tensor of the scalar field is not appropriate because it is spoiled by a part of the dynamical description of gravity. A new connection can be defined in terms of which the full dynamical description of gravity is explicit, and the correct scalar field energy-momentum tensor can be immediately identified. Certain inequalities must be imposed on the two free functions (the coupling function and the potential) that define a particular scalar-tensor theory, to ensure that the scalar field energy density never becomes negative. The correct dynamical description leads naturally to the Einstein frame formulation of scalar-tensor gravity which is also studied in detail.