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White holes are described by the time reversed Schwarzschild metric. A test particle which is gravitationally attracted to the black hole's event horizon in the Schwarzschild metric is also gravitationally attracted to the white hole's event horizon in time reversed Schwarzchild metric.

Still, white holes are described as a region of "outward-flowing space time".

How are both compatible?

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    $\begingroup$ How are both compatible?” - Your question is based on a bad assumption that the statements you quote are “correct”. They are not. First, “flowing spacetime” is a very bad, if not outright wrong, parallel to describe gravity. Second, black and white holes have the same metric outside the horizon, so, if you want to describe them as “flowing spacetime”, then the direction of the “flow” would be the same for both outside (but not inside) the horizon. Can you provide a reference for the “flowing spacetime” claim? $\endgroup$
    – safesphere
    Commented Nov 26, 2023 at 4:41
  • $\begingroup$ References: pbs.org/video/white-holes-7gg7ck , issuu.com/journalofyoungphysicists/docs/jypissuu , quora.com/… $\endgroup$ Commented Nov 26, 2023 at 11:38
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    $\begingroup$ The first link states, “a black hole is defined as a region of inward flowing spacetime”. No. There is no “flowing spacetime” in the definition of a black hole. In “PBS”, “P” doesn’t stand for “Physics” and “S” doesn’t stand for “Science”. The video targets a layman audience and is not very rigorous with numerous incorrect statements throughout. The second link is just a post of a random person who makes other wrong statements as well. $\endgroup$
    – safesphere
    Commented Nov 27, 2023 at 5:21

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There is no contradiction. “Attractive gravity” is about acceleration, which is directed toward the massive body. While “inward-flowing spacetime” in the river model of black hole (or “outward-flowing spacetime” for a white hole) is about the direction of velocity.

Under time reversal velocities reverse direction, while accelerations stay the same. If you play a movie depicting an object falling toward Earth backwards, you will see an object “jumping” upwards, but acceleration would still be directed downwards.

And it is best to always remember that how “space flows” is dependent on how one decomposes spacetime into “space” and “time” and this can be done in many ways, so one such representation does not preclude another from being equally true.

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  • $\begingroup$ What do you mean by "direction of velocity"? $\endgroup$ Commented Nov 26, 2023 at 11:40
  • $\begingroup$ @Manuel Direction of movement. $\endgroup$
    – safesphere
    Commented Nov 26, 2023 at 20:51
  • $\begingroup$ @safesphere What is direction of movement? $\endgroup$ Commented Nov 26, 2023 at 22:35
  • $\begingroup$ @Manuel If you drive from Kansas City to St. Louis, your “direction of velocity” or “direction of movement” points from Kansas City to St Louis. The distance from you to Kansas City increases while the distance from you to St. Louis decreases with time. $\endgroup$
    – safesphere
    Commented Nov 27, 2023 at 4:43
  • $\begingroup$ Good explanation of the time reversal +1. However there is a caveat essential to this question - an astrophysical white hole (the one, to which we could throw a rock) is not the exact time reversal of a black hole. The geodesic (and proper time) of the rock falling to such a white hole ends at the anti-horizon and for this reason has no time reversal counterpart (not physically at least). This is why no one can draw a Penrose diagram for a classical astrophysical white hole (without geodesics ending at the anti-horizon): physics.stackexchange.com/questions/740527 $\endgroup$
    – safesphere
    Commented Nov 27, 2023 at 4:46

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