论文标题
角度动量的局部连续性和对总体相对论物质的noether电荷
Local Continuity of Angular Momentum and Noether Charge for Matter in General Relativity
论文作者
论文摘要
保护法在数值相对论中有许多应用。但是，由于缺乏坐标翻译对称性，定义一般动态空间的局部保护定律并不直接。在平坦的空间中，有限间距体积内能量摩托车的变化速率相当于在该体积的表面上集成的通量。对于一般的空间，有必要包括由时空曲率引起的源项组成的体积积分。在这项工作中，对总体相对论的物质连续性进行了一项研究，以包括物质的角动量和与仪表对称性相关的Noether电流。使用这种形式主义发现了复杂标量场和复杂Proca场的NOETHE电荷和通量的表达式。还得出了角动量密度，通量和源的表达式，然后将其应用于3D中的玻色子恒星的数值相对性碰撞，该恒星具有非零撞击参数，以说明了方法。
Conservation laws have many applications in numerical relativity. However, it is not straightforward to define local conservation laws for general dynamic spacetimes due the lack of coordinate translation symmetries. In flat space, the rate of change of energy-momentum within a finite spacelike volume is equivalent to the flux integrated over the surface of this volume; for general spacetimes it is necessary to include a volume integral of a source term arising from spacetime curvature. In this work a study of continuity of matter in general relativity is extended to include angular momentum of matter and Noether currents associated with gauge symmetries. Expressions for the Noether charge and flux of complex scalar fields and complex Proca fields are found using this formalism. Expressions for the angular momentum density, flux and source are also derived which are then applied to a numerical relativity collision of boson stars in 3D with non-zero impact parameter as an illustration of the methods.
