论文标题
量规不变的二次近似准本地质量及其与哈密顿的重力场的关系
Gauge-invariant quadratic approximation of quasi-local mass and its relation with Hamiltonian for gravitational field
论文作者
论文摘要
量规不变，在紧凑型区域内的hamiltonian表述，$ \ partialσ$在紧凑型区域$σ$中，用于通过Kottler Metric线性化的重力场。讨论了使系统自主群体的边界条件，并计算了相应的哈密顿功能$ \ MATHCAL {H} _ \ text {不变} $。结果表明，在特定的边界条件下，Quasi-local Geroch-高质量$ \ Mathcal {h} _ \ text {hawking} $在弱字段近似中将$降低至$ \ MATHCAL {h} _ \ text {h} _ \ text {noffariant} $。该观察结果是经典Brill-deser结果的准本地版本。
Gauge invariant, Hamiltonian formulation of field dynamics within a compact region $Σ$ with boundary $\partial Σ$ is given for the gravitational field linearized over a Kottler metric. The boundary conditions which make the system autonomous are discussed and the corresponding Hamiltonian functional $\mathcal{H}_\text{Invariant}$ is calculated. It is shown that, under specific boundary conditions, the quasi-local Geroch--Hawking mass $\mathcal{H}_\text{Hawking}$ reduces to $\mathcal{H}_\text{Invariant}$ in the weak field approximation. This observation is a quasi-local version of the classical Brill--Deser result.
