We obtain approximate analytical solutions of the Einstein equations close to the trapping horizon for a dynamical spherically symmetric black hole in the presence of a minimally coupled self-interacting scalar field. This is made possible by a new parametrization of the metric, in which the displacement from the horizon as well as its expansion rate feature explicitly. Our results are valid in a neighborhood of the horizon and hold for any scalar field potential and spacetime asymptotics. An exact equation for the accretion rate is also obtained, which generalizes the standard Bondi formula. We also develop a dynamical system approach to study near-equilibrium black holes; using this formalism, we focus on a simple model to show that the near-equilibrium dynamics is characterized by scaling relations among dynamical variables. Moreover, we show that solutions with purely ingoing energy-momentum flux never reach equilibrium.

中文翻译：

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具有标量场吸积的演化黑洞

在存在最小耦合自相互作用标量场的情况下，我们获得了接近动态球对称黑洞陷阱视界的爱因斯坦方程的近似解析解。这是通过度量的新参数化实现的，其中从地平线的位移及其膨胀率明确地表征。我们的结果在视界附近有效，并且适用于任何标量场势和时空渐近。还获得了吸积率的精确方程，它推广了标准的邦迪公式。我们还开发了一种动力系统方法来研究近平衡黑洞；使用这种形式，我们专注于一个简单的模型，以表明近平衡动力学的特征在于动力学变量之间的比例关系。而且，