How do scientists make sophisticated calculations in general relativity?

[Starship]

How do professional scientists make sophisticated calculations, e.g the http://arxiv.org/PS_cache/math-ph/pdf/0412/0412064.pdf in general relativity? Are there any special algorithms for this?

I'd really like to solve these equations but it's almost impossible without computer help.

 

[dextercioby]

Using calculators...?The equations in physics are usually nonintegrable analytically,many of them are quasi/nonlinear (starting with Newton's gravity law,for example) and therefore the dynamics is found either intuitively or using a computer...

There are fortunate exceptions...The Schwarzschild solution is one of them.

Daniel.

 

[Starship]

Using calculators...?The equations in physics are usually nonintegrable analytically,many of them are quasi/nonlinear (starting with Newton's gravity law,for example) and therefore the dynamics is found either intuitively or using a computer...

There are fortunate exceptions...The Schwarzschild solution is one of them.

Daniel.

Thanks dexter. Do i need to develop my own algorithms?

The Einstein equations are nonlinear, therefore are very difficult to solve without a computer.

 

[robphy]

How do professional scientists make sophisticated calculations, e.g the http://arxiv.org/PS_cache/math-ph/pdf/0412/0412064.pdf in general relativity? Are there any special algorithms for this?

I'd really like to solve these equations but it's almost impossible without computer help.

The symbolic tensorial and spinorial calculations in the paper above are probably done by hand.
One can use tools like GRTensor and others to symbolically verify some calculations or evaluate tensor components [given component functions of the metric, for example].

To go beyond symbolic calculations, you'll need to find or write specialized software to solve systems of nonlinear PDEs. For these, you might start here
http://jean-luc.aei.mpg.de/
http://numrel.aei.mpg.de/
http://bh0.physics.ubc.ca/People/matt/555/
and the Numerical Relativity articles at
http://relativity.livingreviews.org/Articles/subject.html

 

[Starship]

The symbolic tensorial and spinorial calculations in the paper above are probably done by hand.
One can use tools like GRTensor and others to symbolically verify some calculations or evaluate tensor components [given component functions of the metric, for example].

To go beyond symbolic calculations, you'll need to find or write specialized software to solve systems of nonlinear PDEs. For these, you might start here
http://jean-luc.aei.mpg.de/
http://numrel.aei.mpg.de/
http://bh0.physics.ubc.ca/People/matt/555/
and the Numerical Relativity articles at
http://relativity.livingreviews.org/Articles/subject.html

Thanks robphy. This was a great help.

Most of these calculations are indeed symbolic but in order to really solve it, one either needs a strong software or a small supercomputer with a quite simple algorithm.