三维AdS宇宙中的点粒子模型
Models of a point particle in a three-dimensional AdS universe
AI总结：
本研究在2+1维引力中，通过将奇异物质源近似为规则能量分布并研究其可忽略尺寸的极限，得出点粒子质量由渐近几何角亏缺给出，且该极限质量与BTZ质量参数不同的结论。
AI中文摘要：
在2+1维引力中，锥形亏缺通常被解释为点状粒子。由于爱因斯坦方程是非线性的，对这类源的分布描述存在问题。此外，具有非平凡渐近行为的时空的总质量因遥远区域中无限的背景能量而变得模糊。在本研究中，我们支持点粒子的质量由渐近几何的角亏缺给出这一标准主张。我们将奇异物质源近似为足够规则的能量分布，并研究该分布尺寸可忽略的极限，同时保持渐近几何不变。比较具有相同渐近行为的时空可确保我们正确识别并移除宇宙学物质。我们发现，所得锥形时空的角亏缺由物体局部质量的极限给出，其中局部质量是2+1引力中自然的可加质量概念。令人惊讶的是，该极限质量与BTZ质量参数不同，尽管这两种质量密切相关。
英文摘要：
In 2+1-dimensional gravity, a conical deficit is commonly interpreted as a point-like particle. A distributional description of such a source is problematic since the Einstein equations are non- linear. Moreover, the total mass of the spacetime with nontrivial asymptotics is obfuscated by the infinite amount of background energy in the distant regions. In this work, we support the standard claim that the mass of a point particle is given by the angular deficit of the asymptotic geometry. We approximate the singular matter source by a sufficiently regular energy distribution, and we study the limit of negligible size for such a distribution while keeping the asymptotic geometry intact. Comparing spacetimes with equal asymptotics ensures that we correctly identify and remove the cosmological matter. We find that the angular deficit of the resulting conical spacetime is given by a limit of the local mass of the object, where the local mass is a natural concept of additive mass in 2+1 gravity. Surprisingly, the limiting mass is different from the BTZ mass parameter, although both masses are closely related.
