Black Holes Made Simple

Advanced Physics Made Simple

Black Holes, White Holes, and Worm Holes

The Schwarzschild Solution Shortly after Einstein developed the general theory of relativity, Karl Schwarzschild found a solution for the equations of general relativity in empty space. He started by assuming only that the solution was SPHERICALLY SYMMETRIC. This means that no matter how the system is rotated about its center, it remains the same. He then applied the required mathematical conditions to general relativity, and came up with a solution that approximates the behaviour of planets around the sun. In fact, one of the first tests of general relativity was the prediction of the motion of Mercury using the Schwarzschild solution. Another benefit of the solution is that it is static. This means that a star can pulse and evolve in any spherically symmetric way, and there is no way of measuring the effect on gravity.

Unfortunately, there is a problem with the Schwarzschild solution. When the distance from the center of the system is equal to a constant multiplied by the total mass of the body, the Schwarzschild metric (recall that this is the function used to measure distance in general relativity) becomes infinite, and has no time dependence. Although it cannot be proved here, this corresponds to light being trapped at this distance. Even worse, when the distance is smaller, time and space swap properties, so that ordinary distance acts like time and time acts like distance.

Black Holes

The Schwarzschild solution has a problem at a certain distance, called the Schwarzschild radius or the Event Horizion, at which light cannot escape. Because no light escapes from the event horizon, the object would appear black, and thus was dubbed a black hole. However it is very rare to have a high enough mass density, and usually the Schwarzschild radius lies within the body where the Schwarzschild solution doesn't apply. It is still debated if such high density objects could exist.

According to a person who falls into a Black Hole, the event horizon does not exist (this is shown by transforming to other solutions for spherically symmetric bodies) but when they cross it, they can no longer send messages to the outside world. The person then continues to fall towards the center.

According to a person a stays at a constant distance from the black hole, the person who falls in never reaches the event horizon. They appear to slow down forever, and messages sent from the person seem to slow down.

White Holes

The black hole is not the only interpretation of the Schwarzschild solution. There is another possibility which instead of trapping everything in the event horizon, continuosly emits stuff. They would emit so much light, that the would be very bright white objects. In theory, anything could come out of a white hole, from dust particles to a stream of toasters. More than likely, only fundamental particles would be emitted, but there is no reason to assume this.

The problem with white holes is that they violate the SECOND LAW OF THERMODYNAMICS. (This will be covered in a later section) Basically it states that any ordered system becomes more disorganized (like if you drop an egg, it will become a disordered mess, but a disordered mess will never spontaneously form a perfect egg), and so a system which produces adds order to a system is not possible. This is why many believe that a white hole can not exist.

Worm Holes

If a white hole and a black hole could be linked somehow, then stuff which falls into the black hole could suddenly appear coming out of a white hole elsewhere in the universe. In science fiction, such a phenomena allows people to travel across large amounts of space, faster than normal travel through space will ever allow.

However in the real world, there are many problems with travelling through a worm hole. The first problem is that the black hole and white hole would have to be very similar, and so even a small particle could break the symmetry and destroy the worm hole. This may be possible to resolve by using exotic matter which is not currently known about and which could stabilize a worm hole. The second problem is surviving such a trip. The gravity around black and white holes is so large and varies so much in space that anything in the region of a black hole would be ripped apart. ( For example if the space shuttle approached a black hole, the front would be pulled in faster than the back of the ship and probably break it)

Naked Singularities and the Cosmic Censorship Hypothesis

It has been hypothesized that a black hole would collapse to a single point, and at this point, called a SINGULARITY, the laws of physics do not apply. For a true black hole, this does not cause any problems, since the event horizon hides the singularity and so nothing outside the black holes is affected.

However there is a lot of research which indicates the possibility of NAKED SINGULARITIES. These are similar to black holes in that the center of the system is a singularity where the laws of physics fail, but differ dramatically because light can escape from them. Therefore the singularity can be observed and studies, and some research indicates time travel may occur at the singularity.

The problems which accompany a naked singularity made some physicists decide there must be a COSMIC CENSORSHIP HYPOTHESIS. This rule, which as yet has no proof, states that nature abhors a naked singularity (thus its title) and so, if it can ever be proved, everything works without problems from a singularity.