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have created Reissner-Nordström spacetime with some minimum content.
Nothing non-standard here for the moment, I just wanted the entry to exist in order to be able to point to it. But eventually I’d like to have a linked table that matches extremal black brane solutions to fundamental particles/branes. Not today though.
Hmm,
$r_{\pm} \coloneqq \tfrac{G}{2}\left( M \pm \sqrt{M^2 - 4 (P^2 + Q^2)} \right)$doesn’t look right as solutions to
$1 - G \frac{M}{r} + G \frac{Q^2 + P^2}{r^2} = 0.$OK, had there been $G^2$ in the last term.
Right. And it’s worse, if I display powers of the gravitational constant $G$ at all, I should also display powers of the speed of light. So I am lazy for the moment and put all these units to 1 (“natural units”).
Just because you have it of coordinates here: At one point I was searching for emergent physical metrics from Poisson structures in matrix models (I could actually tweak parameters to get the Reissner-Nordström spacetime) and in a small survey I found two very good papers on all the coordinate of the Robertson-Walker’esk metrics
http://arxiv.org/abs/0704.2788
http://arxiv.org/abs/0704.3265
At the end of the papers (p. 21 resp. p.10) you have tables with the metrics. Just in case you happen to stumble upon a reasonable metric one time and you want to check if it’s some simple universe you deal with here.
What kind of matrix models were you thinking of?
By the way, if you feel like adding some more explicit expressions for various spacetimes to the $n$Lab, please feel invited to do so.
I think my Masters advisor is still doing
http://arxiv.org/abs/1401.2020
Semiclassically, the commutator of the $X$’s is some Possion tensor $\theta$ (2.7) and it’s square gives a metric, $g\propto\theta^T\eta\theta$ (2.10). I was to look for solutions $\theta$ of the equations of motion which are also known solutions for $g$ of the Einstein equations. It was a look at symplectic geometrical concepts in the not so much studied case where a Pseudo-Riemannian metric is also lingering around. The tensor relation $\theta\sim\sqrt{g}$ is more ugly if $g$ has positive and negative components at the same time. An electro-statics like case for the equations of motion of $\theta$ made the Reissner-Nördstrom metric pop out. But the thesis looked solely on the metric geometry, and if anything apriori prevents known-gravity-like solutions within the model. Fermionic fields arising/living on that spacetime was not a concern. There is a paper version of the thesis
http://arxiv.org/abs/1111.2732
I looked for a Robertson-Walker entry on the nLab for the references, but there wasn’t one. I didn’t make one because I’m not dealing with this atm.
So the matrix model you mean is the IKKT matrix model.
We do have an entry FRW model.
Hyperlinks on the nForum are coded as
[link name](url)
I have added a commented survey of the literature on interior solutions of RN-spacetimes here (i.e. solutions where the singular point charge/mass is replaced by a finite mass/charge distribution, resolving the BH singularity).
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