I wonder if you could model this in Universe Sandbox [0]? (I live in Seattle so I've met the author Dan Dixon a few times at meetups but have no other relationship to it)
My question would be more about whether the simulation has sufficient granularity to avoid the star flying away due to the time step being too large, rather than concerns about relativity. And of course Universe Sandbox won't be simulating the black hole tearing away bits of the star, or at least, so I'd presume.
http://strainer.github.io/fancy#10
The two objects are the size of our sun, the green one represents the black hole. I put in the orbital distance as 2.5 times the Earth to Moon distance as stated in the article, and just tweaked the mass of the black hole (green orb) until the star orbits once every 30 minutes. The mass of the star will hardly matter. The mass of the black hole in this model is 60 solar masses.
The model timestep is here is 1 minute, five or ten minutes should still work for this engines integration scheme. Its a Newtonian model, at 0.01 lightspeed there will be innaccuracy but I guess just a few percent in measurements.
Does it account for relativity?
No, the physics in Universe Sandbox ² is currently only
Newtonian.
Why?
The short answer is that you need a supercomputer to
accurately simulate general relativity.
Jenn, astrophysicist and Universe Sandbox ² developer,
explains more in a blog post: "General relativity
requires simulating the spacetime itself. That is,
taking your simulation space, discretizing it to a
hi-res 3-D grid and checking the effect that each and
every point in that grid has on all neighboring points
at every timestep. Instead of simulating N number of
bodies, you are simulating a huge number of points.
You start with some initial data of the shape of your
spacetime and then see how it evolves according to the
Einstein equations, which are 10 highly non-linear
partial differential equations."
We are, however, interested in adding in a few features
which would address some effects of relativity. One
example is setting gravity to travel at the speed of
light, instead of instantaneously taking effect as it
currently does. You can read more about these in
Jenn's blog post: Gravitational Waves & Universe
Sandbox ².Furthermore calculating the whole theory runs into interesting challenges where the coordinate system is twisted and and distorted but underlying space-time is not. For a well-known example, a black hole can be described with both Schwarzschild coordinates and Kruskal–Szekeres coordinates. The first coordinate system blows up at the event horizon, the second doesn't. The fact that it blows up is due to a bad choice of coordinate system there, and not due to local space time being particularly bizarre at that spot.