标题： 诺特荷，布朗-约克准局部能量及相关主题 显示英文标题

标题： Noether Charges, Brown-York Quasilocal Energy and Related Topics

摘要： 由York等人提出的拉格朗日量和广义相对论的协变一阶拉格朗日量被引入以处理参考背景上的（真空）引力场。这两个拉格朗日量进行了比较，并表明在适当的假设下，第一个拉格朗日量可以从后者得到。也对所诱导的变分原理进行了比较和讨论。还建立了诺特定量、准局部能量和通过3+1分解得到的标准哈密顿量之间的条件对应关系。结果表明，当需要考虑参考背景场时，协变一阶拉格朗日量更为合适，这在非渐近平直时空中的守恒量处理中是普遍接受的。作为使用协变一阶拉格朗日量的进一步优势，我们证明了所有计算出的量都是明显协变的，这在广义相对论中是合适的。 显示英文摘要

摘要： The Lagrangian proposed by York et al. and the covariant first order Lagrangian for General Relativity are introduced to deal with the (vacuum) gravitational field on a reference background. The two Lagrangians are compared and we show that the first one can be obtained from the latter under suitable hypotheses. The induced variational principles are also compared and discussed. A conditioned correspondence among Noether conserved quantities, quasilocal energy and the standard Hamiltonian obtained by 3+1 decomposition is also established. As a result, it turns out that the covariant first order Lagrangian is better suited whenever a reference background field has to be taken into account, as it is commonly accepted when dealing with conserved quantities in non-asymptotically flat spacetimes. As a further advantage of the use of a covariant first order Lagrangian, we show that all the quantities computed are manifestly covariant, as it is appropriate in General Relativity.