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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeDec 7th 2015
• (edited Dec 7th 2015)

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.

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeDec 7th 2015
• (edited Dec 7th 2015)

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.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeDec 7th 2015

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”).

• CommentRowNumber4.
• CommentAuthorNikolajK
• CommentTimeDec 8th 2015
• (edited Dec 8th 2015)

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.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeDec 8th 2015

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.

• CommentRowNumber6.
• CommentAuthorNikolajK
• CommentTimeDec 8th 2015
• (edited Dec 8th 2015)

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.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeDec 8th 2015

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)

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeSep 8th 2016
• (edited Sep 8th 2016)

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).

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeDec 13th 2020

added (here) the Penrose diagram (from Hawking-Ellis 73)

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeDec 16th 2020