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In the vicinity of a Schwarzchild black hole, spacetime looks like this (at least according to a quick google search). Here, the centre of the black hole is supposed to be at $x=0$ and the event horizon at $x=3$. And outside the event horizon, the future light cones look pretty normal, except they kind of bend upwards. enter image description here

But what would a diagram like this look like if we swapped the black hole for a white hole? Which way would the light cones bend?

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The maximal extension of Schwarzschild spacetime geometry is the Kruskal spacetime. It has both the Schwarzschild black hole in the future (that is, essentially everything eventually falls in) and a white hole in the past. The white hole has exactly the form of a time-inverted black hole. So the light cones in the vicinity of the white hole look exactly the same as those in the vicinity of the black hole, except with the past and future reversed. While the black hole features trapped surfaces for which all directions point down the neck of the black hole, toward the singularity, the white hole has "anti-trapped" surfaces, for which all future-directed timelines point away from the singularity.

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