Real black holes probably spin, but probably have almost no electric charge, because our Universe appears to be electrically neutral, and a charged black hole would quickly neutralize by attracting charge of the opposite sign. Nevertheless, the internal geometry of an electrically charged black hole resembles mathematically that of a rotating black hole. For this reason the behavior inside a charged black hole is often taken as a surrogate for that inside a rotating black hole.
The big difference between a charged (Reissner-Nordström) and an uncharged (Schwarzschild) black hole is that the mathematical solution to the charged black hole has, inside its horizon, a one-way wormhole that connects to a white hole that propels you to another space and time. Sadly, the wormhole is violently unstable, and would not occur in reality. Click on Waterfall to learn more about why the charged black hole has a wormhole. Click on Realistic to see what happens in reality, and to learn more about the mass inflation instability that in reality prevents any wormhole from forming.
The background to the movie is again Axel Mellinger's All-Sky Milky Way Panorama (by permission).
As might be imagined from the long time it took to discover black hole solutions with spin, the Kerr-Newman geometry is technically much more complicated than the comparatively simple Reissner-Nordström geometry. It is for this reason that (as of 2009) I have yet to implement rotating black holes in the Black Hole Flight Simulator, and instead I have used the Reissner-Nordström geometry as a surrogate for the Kerr geometry in the visualizations on this website. You can be sure that one day I hope to have the opportunity to implement the Kerr-Newman geometry in the BHFS, but it will not be easy, and it will take time.
The Reissner-Nordström (mass plus charge) and Kerr-Newman (mass plus charge plus spin) geometries assume that the black hole is empty except at its singularity (which forms a ring in the Kerr-Newman geometry). Empty here means empty of energy-momentum — such as that produced by matter or light — aside from the energy-momentum of the electric field produced by an electric charge located at the singularity.
It may come as a surprise to learn that a Reissner-Nordström or Kerr-Newman black hole is gravitationally repulsive in its core. Indeed, the singularity is infinitely gravitationally repulsive.
In the case of a charged black hole, the gravitational repulsion of the core comes from the tension, or negative pressure, of the radial electric field. In relativity, mass is a form of energy (E = m c^{2}), so it is not surprising to learn that not only mass, but also energy in any form, including photons, which have energy but no rest mass, gravitate.
In a rotating black hole, the gravitational repulsion of the core can be explained more simply: it's produced by the centrifugal force.
Color | Zone |
---|---|
Green | Stable circular orbits |
Yellow | Unstable circular orbits |
Orange | No circular orbits |
Red lines | Horizons |
Red | Between horizons |
But whereas the uncharged black hole had a single horizon, the charged black hole has two horizons, an outer horizon and an inner horizon.
You follow a real free-fall trajectory into and through the charged black hole. The blue line inside the inner horizon marks the periapsis of your trajectory, the radius of your closest approach to the center of the black hole.
The time is in seconds if the black hole's mass equals that of the supermassive black hole at the center of our Galaxy, 5 million suns. On your trajectory, it takes 20 seconds to fall from the outer horizon to the inner horizon.
As you pass through the outer horizon, the horizon splits in two, the same as for a Schwarzschild black hole.
Without the horizon grids (right image), there is no sign that you have crossed the horizon.
At the inner horizon, you are hit by an infinitely bright, infinitely energetic burst of light. The bright point of light is an image of the outside universe reflected by the gravitationally repulsive singularity. The burst of light contains, infinitely speeded up, the entire history of the universe.
The infinitely bright burst of light signals the breakdown of the Reissner-Nordström geometry. The Reissner-Nordström geometry assumes that all matter and charge inside the black hole is concentrated at the central singularity. The assumption leads to the prediction that light from the outside universe concentrates infinitely at the inner horizon, which contradicts the assumption that the black hole is empty except at its singularity.
In reality, if there were such a thing as a charged black hole, as you approached very close to its inner horizon, you would see a rapidly growing explosion of light from the outside universe. The light triggers the mass inflation instability.
From the inner horizon on, the Reissner-Nordström geometry is not physically realistic, despite being an exact mathematical solution to Einstein's equations.
The horizon grids are colored with the blackbody color that you would see if the objects emitting at the horizon had a temperature of 4096 K and were free-falling radially from zero velocity at infinity.
As you fall inward through the inner horizon, a new grid appears, marking the ingoing inner horizon. The dark red grid marking the antihorizon becomes temporarily invisible as you turn around inside the wormhole, but then reappears as you approach the inner horizon going outwards.
As you pass back outward through the inner horizon, a third grid appears, the outgoing inner horizon, or inner antihorizon. As its Penrose diagram shows, the (outgoing) inner antihorizon is not the same as the (ingoing) inner horizon.
As the white hole catapults you outward into a new universe, a fourth grid appears, marking the white hole's outer horizon.
The movie at left is an excerpt, the wormhole part, of the longer movie linked at top of this page. In the movie, the camera is initially pointed inwards, towards the black hole, but as space turns and accelerates back out, the camera turns around and points outwards, away from the black hole.
Movie not quite what you expected? No, it does not look much like any Hollywood depiction you may have seen. But how could anyone draw a cameleopard before they saw what it actually looked like?
Of course, I have to surround this movie with caveats. As I keep repeating, in reality the wormhole would be prevented from forming by the mass inflation instability. If you fell into a real black hole, you would not go through a wormhole.
As you pass once again through the inner horizon, this time going outward rather than inward, you see a second infinitely bright, infinitely energetic burst of light. Whereas on your inward passage through the inner horizon you saw the entire history of the universe go by, this time, on your outward passage, you see the entire future of the universe go by.
The fact that you see the outside universe infinitely bright and blueshifted as you pass outward through the inner horizon was first pointed out by Roger Penrose in 1968.
You might have thought that, since you originally fell through the inner horizon from a black hole, when you passed back out through the inner horizon you would rejoin the black hole, but this is not true. It cannot be true, because space cannot simultaneously fall inward and outward faster than light. The white hole is actually a completely separate piece of spacetime, as is apparent in the Penrose diagram of the Reissner-Nordström geometry.
The white hole continuation of the Reissner-Nordström geometry is an exact mathematical solution, but it is no more realistic than a waterfall that falls down one side of a ravine, and then climbs smoothly up the other side.
As you pass outward through the outer horizon of the white hole, for the third time you see an infinitely bright, energetic burst of light. This time the light is from a new universe into which you have been deposited by the white hole. The burst of light contains the entire past history of the new universe.
As long as you were inside the white hole, light from the new universe could not penetrate into the white hole, since space in the white hole falls outward faster than light. Only when you reach the outer horizon of the white hole, where the outflow of space has slowed to the speed of light, do you get to see light from the new universe.
Since the Reissner-Nordström geometry is just a mathematical solution, it does not specify who or where or when the new universe is. If you like, you can imagine that the new universe might be another place and time in our own Universe. But in reality, the Reissner-Nordström geometry is not a physically consistent solution for a real black hole. In reality, there is no new universe.
In the movie, the new universe is another image of our own Milky Way Galaxy, from the 2-Micron All Sky Survey (2MASS).
You see light from your original Universe. The light has traversed the same journey as you, through the black hole, through the wormhole, through the white hole, into a new universe.