Relativistic Gravity

Posted in: Gravity Simulator, Lesson Time! | June 4, 2014 | No Comments

Thought I’d keep you all apprised of the latest addition I’m working on:

RELATIVITY IN THE GRAVITY SIMULATOR.

At least, *mostly* relativity.  You see, we’d talked about adding in Black Holes… which would be awesome.  But not just *nom*nom*nom* generic sci-fi ‘sucks-stuff-in’ Black Holes.  This is TestTubeGames, after all.  So I wanted to at least get stuff approximately right.  Maybe so ‘orbits’ become something like this:

Orbits around (into?) a black hole, taken from helpful, helpful wikipedia: http://bit.ly/1p7N7Qo

A while back, in an earlier chat in the forums, we found a General Relativistic formula for the attraction between two objects.  Seems reasonable that we could plug in that force law (after all, we’ve got change-able force laws already).  It won’t be precisely right (there won’t be gravity waves…), but it’ll get us close.

Simple, then, slap on a GR Force Law and call it a day!  Well, nope.  Because Black Holes have this neat feature where once something gets too close — ~~inside the event horizon ~~ — it’ll *never* come back out.  Mwahahaha.

Never, that is, unless it travels faster than light.  Which, in the real world (as far as we know) nothing does.  But in the Gravity Simulator, you can launch stuff at any speed!  Black Holes would lose all meaning, objects could escape at will.  They’d become just ‘really strong stars’ instead of ‘points of no return.’  Boo, hiss.

That means I need to add more relativity in the sim, to make objects obey the speed limit of light.  Now when something accelerates, it can get close to, but never reach the speed of light. And, lo and behold, we get neat orbits like this:

Look Familiar?  (Drawn with an unreleased version of Gravity Simulator)

Great.  Can we just paint that star black and stop there?

NO!

Because once you have objects traveling near the speed of light, well, then E=mc^2 becomes important.  Namely, mass is energy, energy is mass.  So what?  So EVERYTHING.  Imagine two stars colliding.  They rush inwards to meet one another, then *boom* they combine to form a single, stationary star.

Whaaa??? (Drawn in an unreleased version of Gravity Simulator)

The total energy has to remain the same, which means that Kinetic Energy had to go somewhere.  In our sim, there’s only one place that energy can go: into rest mass.  Just as two subatomic particles can combine to form something massive (wee protons crashing into each other to make the Higgs boson, anyone?), two stars can combine to make one *huge* star.

What other parts of relativity will come into play down the line?  Well, the Schwartzschild radius is important. And relativistically slowed clocks are awesomely fun…

Where does this all end?  With a bang?  With a whimper?  Will the simulation collapse into a singularity under all the weight of the new code?  Stay tuned to find out!

-Andy