The river model of black holes

Abstract

We present a lesser known way to conceptualize stationary black holes, which we call the river model. In this model, space flows like a river through a flat background, while objects move through the river according to the rules of special relativity. In a spherical black hole, the river of space falls into the black hole at the Newtonian escape velocity, hitting the speed of light at the horizon. Inside the horizon, the river flows inward faster than light, carrying everything with it. The river model also works for rotating (Kerr–Newman) black holes, though with a surprising twist. As in the spherical case, the river of space can be regarded as moving through a flat background. However, the river does not spiral inward, but falls inward with no azimuthal swirl. The river has at each point not only a velocity but also a rotation or twist. That is, the river has a Lorentz structure, characterized by six numbers (velocity and rotation). As an object moves through the river, it changes its velocity and rotation in response to tidal changes in the velocity and twist of the river along its path. An explicit expression is given for the river field, a six-component bivector field that encodes the velocity and twist of the river at each point and encapsulates all the properties of a stationary rotating black hole.