Gravitational Waves - Little Commission Pendant

Sorry, I deleted that comment about R because it didn't really take into consideration that there was more than one black hole. Kind of a dumb error, sorry.

In any case, I think it's time to write some code to see what these things actually look like. I'll go for 3D and use Marching Cubes to generate the isosurface.

I got the basic code complete...

According to the software, the mass (and radius) is conserved when two black holes merge (assuming no major energy loss via gravitational waves). This is to be expected.

The metaball function that I used was:

2*mass / sqrt(pow(location.x - v.x, 2.0) + pow(location.y - v.y, 2.0) + pow(location.z - v.z, 2.0)),

which is based on mass and distance, where v is a metaball centre and location is the sample location.

If one removes the sqrt function from the metaball function, then the surface area is conserved, like on the Wikipedia Metaball page. Just pointing this out for the sake of fun.

The code can be downloaded from https://github.com/sjhalayka/bhmerger

I would expect a percentage of mass to be converted to energy in the form of gravitational waves. Perhaps a few percent at least.


Found this.
https://www.shapeways.com/product/2...-nonpolar-diatomic-molecule?optionId=55934905

You're probably right about the loss of mass-energy due to gravitational waves... I'm just simplifying things to make the calculations possible. My next step is to merge a giant black hole with a tiny black hole, to see if it produces the same bridge as those in the images you shared earlier.

Nice diatomic molecule. I wonder if they used metaballs and Marching Cubes.

It doesn't look like it replicates the bridge shown in the images you shared earlier. Attached is an image of a black hole of unit mass merging with a black hole of mass = 1000. The bridge should be pointy, not blobby like in the attached image. Oh well, next time I'll be right.

Well you're almost done. Now you just need to include the increasing velocities as the black holes approach each other prior to and during the merge, and how this affects the bridge shape and ringing after the merge. Since this is the simpler case of black holes heading straight towards each other you could probably calculate the maximum possible velocities they would be heading towards each other based on the initial condition of how much potential energy is present in the system when the two binary holes are separated by a great distance. Not sure if they would end up approaching each other at relativistic speeds for most of the approach but I wouldn't be surprised if they do so very close to the point of impact or during the merge. And after that you could model the approaches at ever increasing increasing angles that would end up causing the black holes to end up in the eventual orbiting merger scenario.

At that leads to another thought. If you flung one black hole or something else like a neutron star straight into a black hole would it ever be possible to end up with multiple black holes? In other words would it ever be possible for momentum to be transferred to the internal mass distributions of a black hole to split it into two or more smaller black holes? Might it also be possible to liberate some energy and mass from the inside of a black hole to normal space in such a collision?

Integrating gravitation (acceleration) and velocity into the mix is something beyond my skill level when it comes to general relativity, sorry.

I don't know if it's possible to split a black hole into two black holes. Something about how the change in entropy over the change in time is dS/dt >= 0, and how no loss of information can occur (barring Hawking radiation and the Penrose process). That is, take a radius = 4 black hole and convert it to two black holes each of radius = 2; roughly half of the information would be lost (where S = total_surface_area/4). I think this involves the second law of black hole thermodynamics.

I only mention the velocity of merging because it would be a very significant factor, particularly if the relative velocities end up being a good fraction of the speed of the light.. It's the orbiting scenario that actually slows down and delays the merger!

Did you want to help writing a small paper about modelling black holes using metaballs?

I think this is like modelling global warming. There are way too many variables, both known and unknown, to pull it out of the domain of physicists. As an electrical engineer I would only get side tracked by wondering what's inside a black hole!

The paper can be found at http://vixra.org/abs/1701.0614

Attached is Jim Blinn's original paper on metaballs, where he uses them to visualize electron density. It seems that in my code, we are visualizing graviton density.

I found the shape that describes the black hole merger. It's called the Cassini oval:

http://paulbourke.net/geometry/egg/
https://en.wikipedia.org/wiki/Cassini_oval
http://mathworld.wolfram.com/CassiniOvals.html

I do not follow your thread but I think I can help you to see a womhole from close!

It is available here: http://shpws.me/NPzj





Maybe you would be inetrsted to know that in a paper I did in 1997 for an international physics research competition "prooves" that in a microscopic level matter may have a way out through the event horizon! I'm not talking about Hawking's radiation of course...

Thanks Nickola! Do you have a copy of that paper you did?

yes but do not expect a very accurate project cause the paper was for an international physics competition for lyceum students. So my paper (I was then 19 years old) is not a mathematically correct paper but is more an idea. I do not have the backround (i'm not a physicist) to mathematically describe correct the whole idea

I can sent you a copy to an email if you like!

OK... my email is sjhalayka@gmail.com