This paper presents an under-appreciated way to conceptualize stationary black holes, which we call the river model. The river model is mathematically sound, yet simple enough that the basic picture can be understood by non-experts. %that can by understood by non-experts. In the river model, space itself 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. We show that the river model works also 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, as one might have anticipated, but rather falls inward with no azimuthal swirl at all. Instead, 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), not just three (velocity). 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

from the event horizon. Instead, it gets stuck at the event horizon. Since light moves faster than all others, matter can only move inward at the event horizon Gullstrand–Painlevé coordinates are a particular set of coordinates for the Schwarzschild metric – a solution to the Einstein field equations which describes the gravitational field in the vicinity of a spherical mass with no electric charge or angular momentum. The ingoing coordinates are such that the time coordinate follows the proper time of a free-falling observer who starts from far away at At places very far away from the black hole, r → ∞ , d r d t r = ± 1. {\displaystyle r\to \infty ,{\tfrac {dr}{dt_{r}}}=\pm 1.} The speed of light is 1, the same as in special relativity. At the event horizon, r = 2 M , {\displaystyle r=2M,} the speed of light shining outward away from the center of black hole is d r d t r = 0. {\displaystyle {\tfrac {dr}{dt_{r}}}=0.} It can not escape from the event horizon. Instead, it gets stuck at the event horizon. Since light moves faster than all others, matter can only move inward at the event horizon. Everything inside the event horizon is hidden from the outside world. Inside the event horizon, r < 2 M , {\displaystyle r<2M,} the rain observer measures that the light moves toward the center with speed greater than 2. This is plausible. Even in special relativity, the proper speed of a moving object is