Black Holes

I’m not going to go into too much depth on what black holes are or how they come into being. The concept itself is pretty basic. It’s a region of space in our universe that has so much mass that the escape velocity is greater than the speed of light. They are defined by the event horizon, the surface that surrounds them where the gravitational pull of what is inside the black hole equals the speed of light. In other words, if you are inside a black hole and shine a flashlight towards the inside surface of that event horizon the light will never escape out into the rest of the universe. Black holes, although they can not be observed directly, can be observed by the gravitational effect that they have on their surroundings. Astronomers have “observed” these effects, weighed their masses, and have generally proven that they exist. The radius of this event horizon (called the Schwarzschild radius) is defined by a simple formula that is a function of the mass and rotation. Most of the references for this article are to Wikipedia (5) where you can find lots of fascinating details.

Black holes have lots of interesting features. Because of the way that general relativity works the event horizon can also be described as the place that time stops. A clock at the surface of the earth runs a little slower than one in orbit around the earth. The stronger a gravitational field is the slower time passes. At the event horizon of a black hole it crawls to a complete stop. This of course depends on the observer. Here is the first of our thought experiments.

Let’s take a spaceship ride to the center of our galaxy where there exists a black hole of some 2.6 million solar masses. Once there we will go into orbit at a safe distance away. A volunteer puts on his spacesuit, straps on his jetpack, and with a flashlight in one hand, an alarm clock in the other, and a powerful portable telescope strapped to his back, exits the spacecraft for a one way trip to the event horizon. We watch through a very powerful telescope as he waves goodbye and fires the retrorockets on his jetpack and kills his orbital motion around the black hole. (By the way, this is a very special jetpack. It creates a very powerful beam of light from, well, nothing. I know, it’s impossible, but it is my story.)

As we watch him fall deeper into the gravity well we notice a number of curious effects. The light from his flashlight begins to redden and the clock in his hand is running slower than an identical clock in our spacecraft. As he gets ever closer to the black hole and his velocity relative to ours approaches the speed of light his clock slows to a crawl and his fall appears to slow. The light from his flashlight stretches past red and into the radio wave spectrum. From our point of view it is not possible to watch him go through the event horizon.

What does the falling astronaut see if he looks back at our spaceship with the telescope that he has strapped to his back? Oddly enough, he does not see the universe speed up. The speed of light as measured in his frame of reference is the same towards the black hole as it is away from the black hole. Only if he turns on his jetpack and tries to escape the black hole does he see the external universe speed up. If he was to find a way of accelerating away from the black hole just shy of the event horizon it would take a very long time to crawl out of the gravity well by our frame of reference but because of the time distortion effects of the gravity field a much shorter time would have passed by our astronauts clock. (6)

What would the astronaut experience as he went through the event horizon? If it is a sufficiently large black hole tidal forces will not rip him apart (as they are theorized to do as he approaches the singularity inside). Here is an interesting quote from reference (6).

“Finally, we might ask what an observer would find if he followed a path that leads across an event horizon and into a black hole. In truth, no one really knows how seriously to take the theoretical solutions of Einstein’s field equations for the interior of a black hole, even assuming an open infinite universe. For example, the “complete” Schwarzschild solution actually consists of two separate universes joined together at the black hole, but it isn’t clear that this topology would spontaneously arise from the collapse of a star, or from any other known process, so many people doubt that this complete solution is actually realized. It’s just one of many strange topologies that the field equations of general relativity would allow, but we aren’t required to believe something exists just because it’s a solution of the field equations. On the other hand, from a purely logical point of view, we can’t rule them out, because there aren’t any outright logical contradictions, just some interesting transfinite topologies.”

Does this mean that our universe disappears? It shouldn’t as there is still one way communication from outside of the event horizon to the inside. Light from the orbiting spacecraft can still pass through the event horizon but it will do so after our astronaut has passed through and it may not ever catch up to him. What is important is that our astronaut can no longer have an effect on the universe outside of the event horizon. Remember that special energy from nothing jetpack? If he points it out towards the event horizon and turns on that super powerful beam of light it will never cross that boundary. If the jetpack created that light from nothing, and energy and mass are equivalent, related by Einstein’s e=mc^2, the gravitational effects created by the jetpack will never be felt outside of the event horizon. Any mechanism that creates energy or mass in the interior of a black hole cannot have any effect on the universe outside of the event horizon. When we measure the mass of a black hole we can only see the effect of what has been contributed by our universe, not of what could be inside of the object.