In general relativity, finding out the geodesics of a given spacetime manifold is an important task because it determines which classical processes are dynamically forbidden. Conserved quantities play an important role in solving the geodesic equations of a general spacetime manifold. Furthermore, knowing all possible conserved quantities of a system gives information about the hidden symmetries of that system since conserved quantities are deeply connected with the symmetries of the system. These are very important in their own right. Conserved quantities are also useful to capture certain features of spacetime manifold for an asymptotic observer. In this article, we show the existence of these conserved charges and their algebra in a generic curved spacetime for a class of dynamical systems with the Hamiltonians quadratic and linear in momentum and spin.

中文翻译：

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弯曲时空中守恒量及其代数的存在

在广义相对论中，找出给定时空流形的测地线是一项重要任务，因为它决定了哪些经典过程是动态禁止的。守恒量在求解一般时空流形的测地线方程中起着重要作用。此外，知道系统的所有可能守恒量可以提供有关该系统隐藏对称性的信息，因为守恒量与系统的对称性密切相关。这些本身就非常重要。守恒量对于为渐近观察者捕捉时空流形的某些特征也很有用。在本文中，