Thursday, July 24, 2014

Numerical Relativity: Black Holes and Gravity - Part 2

Einstein's Theory of General Relativity


You have probably heard about Einstein's Theory of Relativity. His work on special relativity was published in 1905. This introduced a new framework in physics. He showed that the laws of physics are the same in all non-accelerating reference frame and that the speed of light is constant. This revolutionized different branches of physics and led to his 1915 Theory of General Relativity, or his theory of gravity. Einstein's view was that space and time could be distorted by objects with mass. This spacetime would be able to be stretched and bent. A classic example of this is to imagine a heavy object in the middle of a trampoline. Spacetime is distorted just like the fabric of the trampoline. This would change the way we perceive space and time. Perhaps the most outstanding predictions of this theory are black holes and gravitational waves.

Black Holes (BHs)


In the media, black holes are erroneously described as giant vacuum cleaners in space. Black holes do not suck in things in the way vacuum cleaners do. Physicist instead think of black holes as regions in space with extreme curvature. Black holes warp space and time in such an extreme manner that nothing - not even light - can escape once it is caught into orbit. Since light can't escape it, we cannot look up at the sky and actually point at a black hole. Instead we use different methods to find them. For example, we look for an object orbiting some dark region of space. We will discuss this further in a future post.

Black Hole Anatomy


Let's look at the anatomy of a black hole. Although a black hole is not an actual object we can touch, let's think of it as a black sphere; we choose black since we can't see black holes in the sky. First, let's call the surface of the sphere the event horizon. Once anything passes this point, it cannot return outside. In fact, we don't even know what happens inside the event horizon. All that we know is that there is a point inside which we call a singularity. A singularity is when the gravitational field is at infinity. This is where physics breaks down.

How Do Black Holes Form?


There are three main ways in which black holes form: implosion, high-energy collision, and binary black hole (BBH) collisions. Implosion, or gravitational collapse, is perhaps the most talked about way of black hole formation. This occurs when a star that is a few times larger than the size of our sun collapse onto itself due to a greater gravitation (or inward) force and smaller internal pressure (outward force). I will mention that for a star to implode, there is a minimum size, which is about 3 solar masses. This Tolman-Oppenheimer-Volkoff limit, however, is not well known because it depends on the equations of state for matter this dense, i.e. the relationship between the volume, pressure, temperature, and internal energy of a star.

Diagram of gravitational force vs. internal pressure on a star .
I won't go into details on the formation by high-energy collisions, since this could only happen in very special conditions. This type of event has never been detected, so it is purely theoretical. If it actually ever happened, the black hole would be so small that it would evaporate extremely fast.

Formation by binary black hole collisions is in a way the "easiest" to understand. Unlike implosion where there is an actual birth of a black hole, this type of collisions involve two already formed black holes that collide in order to form a bigger black hole. A very cool thing about this is that the final mass of this black hole is not equal to that of the sum of the two initial black holes. You might be wondering why! The next section gives us the answer.

Gravitational Waves (GWs)


Fantastic! So in the paragraph above we asked why the mass of the final black hole is not the sum of the two initial black holes that collided. This is actually my research area now, so I will try to explain it very thoroughly.

Gravitational waves, or gravitational radiation, are a result of acceleration; it is like light only in the sense that both types of radiation carry energy away. A great example of this is a system of two black holes. When two massive bodies orbit around each other, they accelerate. Because our system must conserve energy, gravitational radiation must be given off as our BHs accelerate, and this draws our BHs closer together which causes them to orbit faster. This radiation distorts spacetime, which is why you might have heard of the definition "Gravitational waves are ripples in spacetime." The closer they are, the more strongly radiate.

Binary neutron stars orbiting each other and radiating. Photo taken from NASA.

Below, you can see a picture of this radiation as the black holes get closer to each other and eventually collide. The height is the amplitude of the gravitational waves. the length shows the passing of time. Evidently, gravitational waves are given off as the BHs orbit each other. As they get closer the radiation increases by large factor. The highest point you see in the wave above, shows the time at which the black holes collided to become one. This releases an incredible amount of energy, making a BBH collision the most energetic phenomena in space. After they collide, the final BH will ring like a bell (radiating more) and eventually dying down to a quiescent state. When a black hole is not moving or "eating" anything, it will not radiate. 

Gravitational wave from a BBH.


I will go into more detail on how to detect this waves and what we can learn about them in a future post.
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