标题： 电荷守恒，熵流和引力 显示英文标题

标题： Charge Conservation, Entropy Current, and Gravitation

摘要： 我们提出了一类新的矢量场，用于在能量动量张量协变守恒的一般场论中构造一个守恒电荷。 我们表明，在给定的场论中，即使没有全局对称性，也总是存在这样的矢量场。 我们还认为，从(渐近)时间类矢量场构造的守恒电流可以被识别为系统的熵流。 作为证据，我们证明了由此定义的守恒电荷在温度有适当定义的情况下，满足各向同性系统的热力学第一定律。 我们将该公式应用于几个引力系统，如膨胀的宇宙、Schwarzschild 黑洞和 BTZ 黑洞以及引力平面波。 我们分别确认了在宇宙任何均匀和各向同性膨胀下，所提出的熵密度的守恒性，准确再现结合热力学第一定律的Bekenstein-Hawking 熵，以及存在不携带电荷的引力平面波。 我们还对简单模型中的引力塌缩期间的能量守恒进行了评论。 显示英文摘要

摘要： We propose a new class of vector fields to construct a conserved charge in a general field theory whose energy momentum tensor is covariantly conserved. We show that there always exists such a vector field in a given field theory even without global symmetry. We also argue that the conserved current constructed from the (asymptotically) time-like vector field can be identified with the entropy current of the system. As a piece of evidence we show that the conserved charge defined therefrom satisfies the first law of thermodynamics for an isotropic system with a suitable definition of temperature. We apply our formulation to several gravitational systems such as the expanding universe, Schwarzschild and BTZ black holes, and gravitational plane waves. We confirm the conservation of the proposed entropy density under any homogeneous and isotropic expansion of the universe, the precise reproduction of the Bekenstein-Hawking entropy incorporating the first law of thermodynamics, and the existence of gravitational plane wave carrying no charge, respectively. We also comment on the energy conservation during gravitational collapse in simple models.