广义 Vaidya 黑洞的阴影
Shadow of the generalized Vaidya black hole
AI总结：
研究广义 Vaidya 黑洞阴影，通过假设正压状态方程，确定自相似类并转换几何形状，推导有效势等。表明参数α影响阴影大小，还得出真正随时间变化时阴影增长或收缩由局部有效流入量决定，对类电荷分支有判断标准。
AI中文摘要：
在本文中，我们研究了由 Husain 解描述的广义 Vaidya 黑洞的阴影。假设额外物质部分的正压状态方程，我们首先确定承认一个同位相似 Killing 向量的自相似类，并将几何形状转换为共形静态形式。这使我们能够在共形静态表示中推导零测地线的有效势，确定相应的同位相似光子表面，然后将结果转换回原始的广义 Vaidya 坐标。我们表明，在弱能量条件分支内，控制状态方程的参数α决定了相对于 Vaidya 情况阴影是增大还是减小：分支0≤α<1/2增加光子球和阴影半径，而分支1/2<α≤1减小它们。然后我们转向真正随时间变化的 Husain 度规，并推导瞬时光子表面和临界碰撞参数 的准静态慢演化方程。特别是，我们表明阴影的增长或收缩由光子区域中的局部有效流入量决定，而不是分别由M和N的符号决定。对于类电荷分支，这产生了一个清晰的标准，用于判断吸积何时会扩大阴影，以及何时快速电荷增长反而会导致阴影缩小。
英文摘要：
In this paper, we investigate the shadow of the generalized Vaidya black hole described by the Husain solution. Assuming a barotropic equation of state for the additional matter sector, we first identify the self-similar class admitting a homothetic Killing vector and transform the geometry to a conformally static form. This allows us to derive the effective potential for null geodesics in the conformally static representative, determine the corresponding homothetic photon surface, and then transform the result back to the original generalized Vaidya coordinates. We show that, within the weak-energy-condition branches, the parameter $α$ controlling the equation of state determines whether the shadow is enlarged or reduced relative to the Vaidya case: the branch $0\leqα<1/2$ increases the photon-sphere and shadow radii, whereas the branch $1/2<α\leq 1$ decreases them. We then turn to the genuinely time-dependent Husain metric and derive quasistatic slow-evolution equations for the instantaneous photon surface and critical impact parameter. In particular, we show that the growth or contraction of the shadow is governed by the local effective influx in the photon region rather than by the signs of $\dot M$ and $\dot N$ separately. For the charge-like branch, this yields a transparent criterion for when accretion enlarges the shadow and when rapid charge growth instead causes it to shrink.
