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What is black holes made of?

At the core of the black hole is the singularity. A point in space-time where the density of a mass becomes infinite. This point is so massive that it bends the whole space-time around it which curvature so deep even the light can't escape it. Yes , the light, which doesn't actually have any mass isn't actually prevented from escaping the black hole due gravity itself, but the space itself being so twisted that the light is unable to find it's way out of there.

While it could be theoretically possible there to be a naked singularity as a result of the rest of the black hole evaporating over (really) long period of time via Hawking's radiation they are usually surrounded by the area most commonly recognized as a black hole. This is the area where nothing can escape and it's border is fittingly named the point of no return. The distance from the center of the black hole up to this border is called the Schwarzhchilds radius. This is also the border beyond where the normal laws of physics stop applying.

If there is enough loose matter available around the black hole it's usually surrounded by the accretion disk. This is formed by the unfortunate matter that has brought itself too close to the black holes gravitational pull and is eventually being sucked into the home itself. These discs can be one of the brightest things in the universe when the matter is accelerated around the black hole heated by friction. These "lighthouses of the universe" are called quasi-stellar objects or more commonly known just quasars.