Of Collapsing Bodies, Event Horizons, and Singularity

It is rather interesting that in the very year my interest in astronomy was really awakened, the world saw the image of a black hole for the first time. Even though others had postulated about the possible presence of black holes in the 18th century, it was really the work of Einstein that set the ball rolling. It all started with Newton, Einstein, and gravity.

Now Isaac Newton saw gravity as the result of the force between masses. Einstein saw it as the result of the curvature of spacetime.

To help understand the Einstein position without using the really hard-to-understand tensor calculus, let us do an exercise:

Imagine the universe is a large sheet of Spandex stretched and attached to several poles to keep it taut. Now imagine dropping a bowling ball into the sheet. It will dent or warp it, right? Good! Now drop a marble into the sheet with the bowling ball still on it. The marble will roll towards the bowling ball, wouldn’t it? If you drop smaller and lighter balls with different sizes and weights on the sheet, they will all follow the curvature induced by the bowling bowl and rotate around it before finally sinking into the depression it creates.

The curvature induced by the bowling bowl in the sheet of spandex is what causes the smaller bowls to rotate around it. (If one paid attention, one would notice that the path charted by the rotating balls is not a perfect circle but an ellipse).

In the same way, all the other balls will warp the sheet to a degree and cause their own curves. The biggest ball will cause the other balls to rotate around it – in this case, the bowling ball. The phenomenon whereby a body warps the sheet and thus induces other bodies to move along the created curve is what is similar to what happens in the universe. That is what we call gravity.

Whereas Newton saw the universe as being static, with everything having its place, Einstein saw the universe as being more dynamic. In Einstein’s view, space combined with time to form a universal “sheet” called spacetime with three spatial dimensions – backwards-forwards, left-right and up-down – and one-time dimension. Celestial bodies travel through spacetime and in the process, bend, warp or even curve it. The more massive an object is, the greater the warping. The planets orbiting the sun do so not because of a force exerted by the Sun but because they are following its induced curve in the spacetime fabric. 

These bends and curves can even affect the path that light takes as it travels from a star. Newton saw light as a corpuscle with mass. Thus he thought that a star could affect its path through gravitational force. By the time Einstein came around, we knew light was a wave. Its path is bent because of gravity alright but not the Newtonian version but rather the Einstein relativity one – through the curves induced by celestial bodies. This phenomenon is called gravitational lensing and was proven elegantly by Arthur Eddington during a solar eclipse in 1919. 

Thus gravity is not a force but the curvature induced in the spacetime fabric by celestial bodies causing them to move and rotate.

Einstein discussed his concept of gravity under what he termed “the Theory of General Relativity”, in four seminal papers that he published in November of 1915. A year later, a German theoretical physicist named Karl Schwarzschild published a paper that drew on Einstein’s work and made postulations that were at the time even more esoteric than Einstein’s. It would be years before the import of Schwarzschild’s work would be appreciated.

The paper was titled “Über das Gravitationsfeld eines Massenpunktes nach der Einstein’schen Theorie” (On the Field of Gravity of a Point Mass in the Theory of Einstein). In it, he delved into escape velocity – that is the velocity a smaller object needs to have to pull away from the gravitational curvature of a bigger body. This escape velocity is directly proportional to the mass but inversely proportional to the radius of the bigger body. So a rocket headed to the moon from the earth needs an escape velocity of 11.2 km/s.

Now imagine a scenario where a celestial body got smaller but kept its mass. The escape velocity from that body would increase. If the body kept getting smaller, it would reach a point where the escape velocity became equal to the speed of light – 300,000 km/s or 186,000 miles/s. At that point, nothing – matter, radiation, light, nothing – can escape from that body. It also becomes impossible for the body to stay intact and thus it disintegrates into a minuscule point whose only presence in the universe is a dark bottomless, infinitesimal entity called a “singularity”. Since no light escapes this point, it is invisible. However, this “singularity” induces a boundary called the “event horizon”. If another body goes over the event horizon, it vanishes into oblivion. Schwarzschild even presented a formula to calculate the size of an event horizon (the Schwarzschild radius).

At that time, physicists found Schwarzschild’s postulations quite arcane then most did not look beyond our planet. Yet if one considered the stars as the bodies being escaped from, his work made a lot of sense. Remember a star is really a collection of really hot gases or plasma and hot gases can get smaller as they burn out.

It would be years before the scientific community would understand it’s importance. His work joins that of Einstein and others in becoming the buttress for the concept and now the reality of black holes, a name coined disdainfully by the American physicist, John A. Wheeler, in 1967. Earlier this week, the world was treated to the first picture of the event horizon a black hole in M87.

According to theory, there might be three types of black holes: stellar, supermassive, and miniature black holes – depending on their mass. These black holes formed in different ways.

Stellar black holes form when a massive star collapses. 

Supermassive black holes, which can have a mass equivalent to billions of suns, are found in the centers of most galaxies and are likely the byproduct of galaxy formation. 

Miniature black holes could have formed shortly after the “Big Bang,” which is thought to have started the universe 13.7 billion years ago. They may be the result of faster moving matter causing slower ones to contract into black holes.

As noted above black holes may have been instrumental in how our universe formed billions of years ago. As mentioned earlier, stars are just a collection of hot gases fueled by intense radiation. As the universe formed, these massive initial stars burnt out creating massive black holes and pulling in other stars. They also emitted jets of high-velocity radiation that led to the formation of other stellar bodies. In a way, they are like the volcanoes of the universe – creators as well as destroyers. One massive one lies in the center of every galaxy. Like volcanoes, they are dormant most of the time. When they do get active, it is disastrous.

Schwarzschild was not the first person to think of the concept of a back hole.

Interestingly, back in 1783, an English priest, philosopher and scientist called John Michell, a man once described as “a little short man, of black complexion, and fat” would touch on this same claim in a presentation to the Royal Society. A few years later, in 1796, the French scientist, Laplace would make the same claim in his book, “Exposition du Système du Monde.”

In a letter to Einstein from November of 1924, the Austrian physicist wrote:

“Einstein, my upset stomach hates your theory of General Relativity—it almost hates you yourself! How am I to provide for my students? What am I to answer to the philosophers?!!”

I guess for us laymen, trying to understand the theories of Einstein and all it has spawned can lead to upset stomachs and even headaches. However, they definitely help us better understand our universe and our place in it. Moreover, they show how brilliant we humans can be. 

On the other hand, the presence of these black holes points out the fallibility of the universe we live in and by extension the fallibility of us humans. Scattered around us are places where we can vanish into oblivion. Places where the laws we think control our universe and our lives do not work. Maybe the time has come to probe into these black holes and with that, face our very fallibility. How excitingly scary is that!