Visualizing GR Geometry: Software for Einstein Field Equations

[mieral]

General Relativity is just geometry with 20 numbers corresponding to Weyl and Ricci curvature. It's possible to write software that can let you input say the mass or stress energy or whether it's Sitter or de Sitter space and other variables.. then it can input the corresponding 3D graphic representation of the equivalent 4D geometry to visualize whether it collapses into black hole or other solutions to the Einstein Field Equations.

Are there such software? What's it called.. and if impossible to write the software, why impossible?

 

[pervect]

There are 20 numbers at every point in space-time. So it's not just 20 numbers, it's a system of partial differential equations.

There is software that people use for calculating the gravitational wave emission from binary inspirals (for comparison with experimens, such as Ligo), but I don't know a whole lot about it, except that it was a tricky problem to get it all working and converging. As with any numerical integrator, there are issues of stability, convergence, and accuracy of the numerical integration algorithims. I believe the programs that are used for this are typically run on supercomputers, so don't expect one on your PC soon.

There is also some software out there (GRTensor, for instance, though I wouldn't necessarily recommend that particular package nowadays that will aid in the algebraic manipulation of the various tensors GR uses. Some of these are free, they're basically built on top of symbolic algebra programs, programs that can manipulate and solve equations algebraically like Maple, Mathlab, and Macsyma. The last is free, and does have some GR software, but it's not terribly user friendly to say the least.

 

[m4r35n357]

General Relativity is just geometry with 20 numbers corresponding to Weyl and Ricci curvature. It's possible to write software that can let you input say the mass or stress energy or whether it's Sitter or de Sitter space and other variables.. then it can input the corresponding 3D graphic representation of the equivalent 4D geometry to visualize whether it collapses into black hole or other solutions to the Einstein Field Equations.

Are there such software? What's it called.. and if impossible to write the software, why impossible?

Oh it is possible all right, and you even can have it for nothing. Beware though, it's one thing having it, but quite another to know what to do with it!

 

[mieral]

There are 20 numbers at every point in space-time. So it's not just 20 numbers, it's a system of partial differential equations.

There is software that people use for calculating the gravitational wave emission from binary inspirals (for comparison with experimens, such as Ligo), but I don't know a whole lot about it, except that it was a tricky problem to get it all working and converging. As with any numerical integrator, there are issues of stability, convergence, and accuracy of the numerical integration algorithims. I believe the programs that are used for this are typically run on supercomputers, so don't expect one on your PC soon.

If you are manually solving for the Einstein Field Equations for say a typical black hole. How long does it usually take? is it one week? one month? a year?

Do you know how fast our PC are these days. They can compute for you what you could manually do in a week or two.. why do we need Supercomputers to compute for the Einstein Field Equations??

There is also some software out there (GRTensor, for instance, though I wouldn't necessarily recommend that particular package nowadays that will aid in the algebraic manipulation of the various tensors GR uses. Some of these are free, they're basically built on top of symbolic algebra programs, programs that can manipulate and solve equations algebraically like Maple, Mathlab, and Macsyma. The last is free, and does have some GR software, but it's not terribly user friendly to say the least.