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A black hole is a region of spacetime from which nothing can escape. More formally, the future light cone of any observer within the black hole is completely contained in the black hole, and the black hole region is not within the past light cone of any observer that goes to spatial infinity in an infinite amount of time.
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Is there an expression for a black hole in global deSitter coordinates?
The usual deSitter-Schwartzchild black hole is expressed in terms of the static patch, is there a coordinate patch and metric that describes global deSitter with a black hole?
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Can I change the speed of light in vacuum?
A gravitational source will bend the path of the photons, but it doesn't change its speed. So even if you shine it right at a black hole, its speed will remain c.