In this paper, we describe the process of general relativistic gravitational induction in spherically symmetric spacetimes by defining an energy momentum tensor for the induction process, which is divergence-free and hence conserved. The aforementioned tensor explicitly describes how the matter-free gravity, as measured by the geometrical Weyl curvature, interacts with the matter. This tensor is clearly different from the energy momentum tensor of the standard matter and we transparently show that in spherical symmetry, the Bianchi identities reduce to the conservation laws for these two such energy momentum tensors. Working with a semitetrad covariant formalism in spherically symmetric spacetimes, we then demonstrate the process of constructing a consistent causal thermodynamical picture for the free gravity and matter interaction via the general non-truncated Israel-Stewart heat transport equation. As an illustrative example, we consider the Lemaitre-Tolman-Bondi spacetime to highlight the relationship between the shear and the Weyl curvature in determining the inductive heat flux.

中文翻译：

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广义相对论引力感应和因果温度


在本文中，我们通过定义感应过程的能量动量张量来描述球对称时空中广义相对论引力感应的过程，该张量是无发散的，因此是守恒的。上述张量明确描述了由几何 Weyl 曲率测量的无物质引力如何与物质相互作用。这个张量与标准物质的能量动量张量明显不同，我们透明地表明，在球对称性中，Bianchi 恒等式简化为这两个能量动量张量的守恒定律。在球对称时空中使用半四元协变形式，然后我们演示了通过一般非截断 Israel-Stewart 热传递方程为自由引力和物质相互作用构建一致的因果热力学图的过程。作为一个说明性的例子，我们考虑 Lemaitre-Tolman-Bondi 时空来突出剪切和 Weyl 曲率在确定感应热通量时的关系。