Outside the black hole, it depends on what form the matter takes.If it happens to be in the form of gas that has been orbiting the black hole in a so-called accretion disk, the matter gets heated to very high temperatures as the individual atoms collide with higher and higher speed producing friction and heat. The closer the gas is to the black hole and its Event Horizon, the more of the gravitational energy of the gas gets converted to kinetic energy and heat. Eventually the atoms collide so violently that they get stripped of their electrons and you then have a plasma. All along, the gas emits light at higher and higher energies, first as optical radiation, then ultraviolet, then X-rays and finally, just before it passes across the Event Horizon, gamma rays. Here is what a model of such a disk looks like based on a typical calculation, in this case by physicist Kovak Zoltan (Phys Rev D84, 2011, pp 24018) for a 2 million solar mass black hole accreting mass at a rate of 2.5 solar masses every million years. Even around massive black holes, temperatures run very hot. The event horizon for this black hole is at a distance of 6 million kilometers. The first mark on the horizontal axis is '5' meaning 5 times the horizon radius or a distance of 30 million km from the center of the black hole. This is about the distance from our sun to mercury!

If the matter is inside a star that has been gravitationally captured by the black hole, the orbit of the star may decrease due to the emission of gravitational radiation over the course of billions of years. Eventually, the star will pass so close to the black hole that its fate is decided by the mass of the black hole. If it is a stellar-mass black hole, the tidal gravitational forces of the black hole will deform the star from a spherical ball, into a football-shaped object, and then eventually the difference in the gravitational force between the side nearest the black hole, and the back side of the star, will be so large that the star can no longer hold itself together. It will be gravitationally shredded by the black hole, with the bulk of the star's mass going into an accretion disk around the black hole. If the black hole has a mass of more than a billion times that of the sun, the tidal gravitational forces of the black hole are weak enough that the star may pass across the Event Horizon without being shredded. The star is, essentially, eaten whole and the matter in the star does not produce a dramatic increase in radiation before it enters the black hole. Here is an artist version of such a tidal encounter.

Once inside a black hole, beyond the Event Horizon, we can only speculate what the fate of captured matter is. General relativity tells us that there are two kinds of black holes; the kind that do not rotate, and the kind that do. Each of these kinds has a different anatomy inside the Event Horizon.For the non-rotating 'Schwarzschild black hole', there is no way for matter to avoid colliding with the Singularity. In terms of the time registered by a clock moving with this matter, it reaches the Singularity within a few micro seconds for a solar-massed black hole, and a few hours for a supermassive black hole. We can't predict what happens at the Singularity because the theory says we reach a condition of infinite gravitational force.

For the rotating ' Kerr Black holes', the internal structure is more complex, and for some ingoing trajectories for matter, you could in principle avoid colliding with the Singularity and possibly reemerge from the black hole somewhere else, or at some very different future time thousands or billions of years after you entered.

Some exotic theories say that you reemerge in another universe entirely, but physicists now don't believe that interpretation is accurate. The problem is that for black holes created by real physical events, the interior of a black hole is awash with gravitational radiation which makes the geometry of space-time very unstable, preventing just these kinds of trips.

For the simplist non-rotating Schwarschild black holes, even they offer a mind-numbing prospect. The mathematics says that outside the event horizon, a particle will experience space and time normally. The particle (and you!) can travel freely in space along the R, radial coordinate, but have no control over your progression in time along the T coordinate. You can speed it up or slow it down a bit through the time dilation effect of high-sped travel, but you can not travel backwards in time. At the event horizon, something amazing happens. The mathematical variables we have been using for time and space, that is R and T, reverse their rolls in the equations that define the separation between points in spacetime. What this means is that the space coordinate, R, behaves like a time coordinate so that you have no freedom to maneuver and not be crushed at the Singularity at R=0. Meanwhile you have some freedom to move along the T coordinate as though it acted like the old familiar space coordinate out side the event horizon.

For Schwarschild black holes that form from supernovae, you have another problem. The event horizon in the mathematics only appears a LONG time after the implosion of matter. In fact it is what mathematicians call an asymptotic feature of the collapsing spacetime. What this means is that if you fell into the black hole long after the supernova created it, the collapse is still going on in the frame of someone far away with the surface of the star trying to pass inside the horizon, but this process has not yet completed. For you falling in, the bulk of the star is still outside the horizon and the black hole has not yet formed! The time dilation effect is so extreme at the horizon that the star literally freezes its motion from the standpoint of the distant observer and becomes a frozen-in-time, black star. As seen from the outside, it will take an eternity for you to actually reach the horizon, but from your frame of reference, it will only take an hour or less depending on where you start! Once you pass inside the horizon, the time to arriving at the singularity is approximately the gravitational free-fall time from the horizon distance. For a supermassive black hole this could take hours, but for a solar mass black hole this takes about 10 microseconds!

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