Space-Time

Although black holes have a strong magnetic field, objects seem to get slower the nearer they get. In fact, many scientists believe time stops completely when they finally cross the event horizon. Of course that's from our perspective, and I bet that if we threw living beings in one of these objects, like in a spaceship, it might not seem like time is bending at all. The objects would then fade to an extreme shade of red, one out of our reach (like ultra-violet) and therefore they may seem like they're disappearing. Many argue that if we'd somehow be able to see those colors, we might be able to see all the stuff that ever got stuck in the black hole, including the star that formed it.

These strange speculations come from the theory of relativity of Einstein, our current best theory of gravity. Not only did it predict black holes and worm holes, but it also implies the existence of white holes, parallel universes and how to travel between them.

Everything started with a flaw in Newtonian Gravity F=M[(m1m2)/r^2], as Isaac Newton deduced from his observations that every object with mass attract one another. But himself wasn't convinced in his own theory: how could masses separated by such vast distances apply a force on each other?

"That one body may act upon another at a distance through a vacuum without the mediation of anything else, is to me so great of an absurdity that, I believe, no man that has a competent faculty of thinking could ever fall into it."  

- Isaac Newton

Two years later, Albert Einstein figured out how gravity is mediated: bodies don't exert force on each other directly, instead they curve space time in its immediate vicinity. For example, the Sun curves then curves the space time around it, so on all the way to Earth.

Einstein's field equations: {\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu }}

Aka: Resultant curvature of spacetime = Distribution of matter and energy

But it's not really a single line equation, more so a family of equations... they're coupled equations and they depend on each other. (And were only scraping the surface here)

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Let's say you're floating around in empty space, a flash of light goes off above your head and spreads out in all directions. Your entire future will remain contained and occur inside this bubble, as the only way to get out of it would be to travel faster than light. In 2d this bubble is just a growing circle. If we allow time in our simulation, and take snapshots at regular intervals, this light bubble traces out a cone... your 'future light cone', the only region of space-time you could ever hope to explore and influence.

By convention, when measured, the axis are scaled so that the lights always travels at 45°.

 

Now imagine that instead of a flash of light above your head, the photons actually were traveling in from all corners of the universe and they met at that instant and  then continued on in their separate directions. In that case, into the past these photons also reveal a light cone: your 'past light cone', only the events that ever occurred in it could affect you up to this moment.

We can simplify this further with what we call the 'Space-Time Diagram of Empty Space':

 

Einstein published his field equations in 1915 during WWI but couldn't find an exact solution. Schwarzchild decided to take on the challenge. He found a solution with the help of the most basic metrics, an empty space with only one mass that doesn't spin, and time: the Schwarzchild Metric.

 {\displaystyle {ds}^{2}=c^{2}\,{d\tau }^{2}=\left(1-{\frac {r_{\mathrm {s} }}{r}}\right)c^{2}\,dt^{2}-\left(1-{\frac {r_{\mathrm {s} }}{r}}\right)^{-1}\,dr^{2}-r^{2}{d\Omega }^{2},}

It describes how space-time curves outside of the mass. Far from the mass space-time is relatively flat, but the closer you get to it, the more it curves, attracts object it and time runs slower.

Schwarzchild sent his paper to Einstein.

"I have read your paper with the utmost interest. I had not expected that one could formulate the exact solution of the problem in such a simple way."

- Albert Einstein 

But people noticed two problem spots: at the center of the mass, where r=0, the term R(s)/r comes out as R(s) divided by 0, so it blows up to infinity (∞). And therefore this equation breaks down and cannot physically describe what is happening. This is what's called a 'singularity'. Then, at a special distance from the center (known at the Schwarzchild radius), the term 1/1-[R(s)/R(s)] comes out as 1/0 and creates a second singularity (∞).

What's going on here?

Well, at the Schwarzchild radius R(s), the space-time curvature becomes so steep that the escape velocity V(esc), aka the speed you would need to leave there, is the speed of light. That means that inside, nothing, not even light, would be able to escape. A black hole.

 

Black holes would require a lot of mass to collapse down into a tiny space, which is hard to believe.

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