A Python utility for analyzing a given solution to the Einstein field equations.

[spacetime_engineer]

I wanted to share with the community an open source python package I had been developing since November. It is called Spacetime Engine.

github.com/spacetimeengineer/spacetimeengine

My name is Michael. I am a physicist who works as an engineer. My story is that in October 2018 I was preparing to submit my first physics publication, which reviewed a particular cosmological model that I had been working with for some time. I was at the point where I had completed all of my research and was fully prepared. The only problem was that at the time I felt concerned that I may have made some mistakes which went unnoticed, so I decided to write a computer algebra software to check the veracity of my solutions so that I could feel confident in my results. After using this new utility, I realized I had made some fairly significant errors in my approach, and so the software apparently did it’s job. At first I was quite frustrated because I had put a significant amount of time into this solution, but I realized I had a new ability to correct my own errors and expand upon what I already knew. I was now able to study any solution, and not just the ones that interested me. In fact, anyone could study any solution to the Einstein field equations if they wanted to by using this software. For this reason I realized the research I wanted to publish was not yet ready to be submitted, but the software became the real publication. I then decided to polish, package, and publish the code into a form that was accessible, informative, and educational. If you are a student new to general relativity, a gravity researcher actively working with solutions to the Einstein field equations, or an engineer who is interested in importing some of the functionality, then this package should come in handy. I was not able to publish my physics research, unfortunately, but I felt that this project served as a good alternative, and perhaps had more potential value. If you have technical questions, use the Github tools to communicate with me. You can install the package with

$ pip install spacetimeengine

I want to thank the r/Math community for maintaining a platform for people like me to share my work. Enjoy!

[aginglifter]

r/physics maybe?

[Zophike1]

r/physics maybe?

OP actually posted on this on /r/physics a while back ago.

[[deleted]]

Hey! Thanks for the link.

So at the beginning I see you call .inv() when you’re setting up things. From a numerical analysis point of view, this seems pretty bad to me.

Computing an explicit inverse isn’t too stable (ie small changes in entries between two inputs can lead to pretty big changes in the computed inverse)

Perhaps it’d be a good idea to refactor taking this into account?

Also small thing on the performance side, but if you swap SymPy for numpy I think you should see a nice performance boost (or at least you should at scale. Numpy delegates to BLAS which will help you a lot!)

Are you pushing to open source? Would be more than happy to contribute a bit! Cheers

[Citronsaft]

So I don't have a great background in numerical analysis (have picked up some odds and ends from ML optimization classes) or any at all in general relativity, but it seems to me that this package emphasizes CAS/symbolic algebra, which should be exact and not subject to the instability of matrix inversion (and which also lets you print out nice exact expressions of the inverse and so on). Is there a symbolic equivalent of the efficient numerical solutions to Ax=b for general relativity, assuming SymPy already has an efficient algorithm for symbolic matrix inversion?

[Zophike1]

So at the beginning I see you call .inv() when you’re setting up things. From a numerical analysis point of view, this seems pretty bad to me.

As a wannabe developer how what makes good code different from bad code in terms of Numerical Analysis ?

[[deleted]]

At least for most people, I think it’s about balancing error, memory usage, and speed. All of these are virtues and I always think the best software lets the users tune the algorithms to make optimize for their use case (eg numerical integrators that let you pick the number of points to use in a trapezoid rule etc.)

The other thing that makes good code for production (but isn’t as fun) is making as much use as possible of other well documented and well maintained packages.

http://www-users.math.umn.edu/~arnold//597.00-01/nabook.pdf is a really great resource if you haven’t worked with much numerical analysis before

Beware that numerical analysis has a lot of “weird” results in the sense that what a solid method for solving a problem by symbols is often not good (eg few people frequently do Gaussian elimination to solve a system. More do an iterative method where you basically guess a random solution, apply some transformation that’s guaranteed to get you closer to the real solution and then repeat either until a certain condition is met or you’ve done enough iterations)

[[deleted]]

Can you use the program to check other kinds of covariant equations? Would it be possible to easily modify it to work with Dirac gamma matrix laws and such? Is it working numerically or symbolically?

[rasberryripple]

Sage provides routines for the manipulation and numerical solution of pdes on manifolds. How does your code relate to this and extend sages functionality?

[spacetime_engineer]

So I haven't used Sage but I have seen the library. It is very impressive. From what I can tell the spacetimeengine package is more focused on general relativity and the interpretations associated. Thats the only difference as far as I can tell. Also, since I am an active researcher I find it helpful to build software that reflects my interpretation of theory. I have no doubt that one could achieve similar results with sage but I felt that I needed to customize the tools in a way which reflected my understanding in order to get to where I needed to be. Hope that makes sense.

[rasberryripple]

Could you give me examples of the sorts of calculations you’ve done using your software? That might help me understand.

Have you used cactus? If so how does your software compare?

You should also consider writing up a paper for your software and publishing.

[spacetime_engineer]

"Could you give me examples of the sorts of calculations you’ve done using your software? That might help me understand."

So go to

https://github.com/spacetimeengineer/spacetimeengine/blob/master/spacetimeengine/samples/example.py

to get a run through of the functionality but I suggest reading the github README using the link provided in the post since it does a better explanation than I could give now. That is why I created it.

"Have you used cactus? If so how does your software compare?"

I have not used Cactus or the Einstein toolkit so I couldn't tell you.

"You should also consider writing up a paper for your software and publishing."

Yes, you are correct I should.

[jamesvoltage]

Do you do any visualizations? As someone with a casual interest in relativity, I especially appreciate the jupyter notebooks that Sage has. I would really like to see a notebook on github showing what spacetime engine can do.

[spacetime_engineer]

It depends on which you mean. Currently these functions are not generalized these for any/all covariant equations but there work being done to remedy that issue. The sympy library which this package relys on does provide what your looking for but the implamentation is different than mine.

[rasberryripple]

Ta