标题： 自由下落的2维曲面与准局域能量 显示英文标题

标题： Freely falling 2-surfaces and the quasi-local energy

摘要： 我们推导出任意闭合类空2-曲面的有效引力质量表达式。 这一有效引力能量直接通过自由下落2-曲面的几何量定义，因此很好地符合了引力质量应由测试物体在引力场中的运动决定的直观预期。 我们发现，对于非真空时空中的小球，这一有效引力质量具有合理的正值，而在真空情况下可以为负值。 此外，我们将这一有效引力能量与基于广义相对论的$(2+2)$形式化的准局域能进行了比较。 尽管存在一些规范自由度，但真空情况下的准局域能解析表达式与有效引力质量相同。 特别是，我们看到宇宙常数的贡献在一般情况下是相同的。 显示英文摘要

摘要： We derive an expression for effective gravitational mass for any closed spacelike 2-surface. This effective gravitational energy is defined directly through the geometrical quantity of the freely falling 2-surface and thus is well adapted to intuitive expectation that the gravitational mass should be determined by the motion of test body moving freely in gravitational field. We find that this effective gravitational mass has reasonable positive value for a small sphere in the non-vacuum space-times and can be negative for vacuum case. Further, this effective gravitational energy is compared with the quasi-local energy based on the $(2+2)$ formalism of the General Relativity. Although some gauge freedoms exist, analytic expressions of the quasi-local energy for vacuum cases are same as the effective gravitational mass. Especially, we see that the contribution from the cosmological constant is the same in general cases.