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When Cooper and his spaceship first get to the wormhole / black-hole Gargantua from Earth, they see it is spherical and dark on the outside.

But when they look at the same Gargantua from the "other side" (the other galaxy), they see it as a shining, Saturn-like object.

Is it the same Gargantua? If so, why does it look so different from two different sides?

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You are a bit confused. Gargantua is not the wormhole, but is on the far side of it.

As to why the black hole Gargantua looked the way it did (with a seeming ring and a seeming halo) is a function of gravitational lensing of light: the accretion disk crossing the near side of Gargantua's event horizon is the bright horizontal band, whereas the light from the accretion disk on the far side of the black hold is bent around it to form the halo.

By contrast the wormhole does not have an apparent event horizon, as we observed when they passed through: the geometry of the universe ripples and distorts, but there's not any sharp surface from Cooper &Co.'s frame of reference.

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    I loved how they depicted the black hole reasonably accurately, at least in terms of the visuals. – Lightness Races with Monica Nov 28 '14 at 23:31
  • @LightnessRacesinOrbit I am trying not gush over that... I really enjoyed the visuals in this film. – Lexible Nov 29 '14 at 3:40
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    Just to add to this, the glowing Saturn-like ring is meant to be the black hole's accretion disk, and as Lexible says, gravitational lensing makes the part of the ring on the opposite side as the viewer look like a "halo" rather than being obscured by the event horizon (the black circle). – Hypnosifl Nov 29 '14 at 4:09
  • @Lexible: Was just adding :) – Lightness Races with Monica Nov 29 '14 at 15:06
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    @Hypnosifl That is actually a really good point that I neglected: the halo is also an image of the accretion disk. Gonna update my answer. – Lexible Nov 29 '14 at 19:50

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