# arXiv Jul 17th-21st 2023

## A week on gr-qc

`2307.10399`We opened this just to learn that an anisotropic star is one in which the matter stress energy tensor is anisotropic, the spacetime is still spherically symmetric.`2307.10199`I'd heard of Einstein-Maxwell and Einstein-Proca, but who is working on Einstein-Yang-Mills? I had some vague notion that people would not be interested in this, because there is no meaningful classical limit in QCD. Actually \(SU(3)\) is not the issue, there is a big community of interest for \(SU(2)\). After some discussion, I learned that this is about gravitating exact solutions, not connected to sphalerons. We did not explore the paper very thoroughly, but there is some nice discussion of black hole-like solutions.`2307.10899`For the cosmologists. This looks somewhat like an extension of the `early dark energy' paradigm that was floating around a few years back. The authors propose to modify the cosmological constant by \(\Lambda\to\Lambda_{\text{s}}\equiv\Lambda_{\text{s0}}\ \text{sgn}[z_\dagger-z]\). Well, I think the conclusion we drew is that the approach might be useful in the functional parameterisation of \(w(z)\) reconstruction, but apart from that the physical origin of the model is not really clear...`2307.10126`So, what is a `Polish doughnut'? It is a thick accretion disk.`2307.07743`Personally the most interesting article this week, a letter. The authors are considering some simple toy models, for which there are UV and EFT versions. On the UV side, they consider the complex scalar with a mass and a quartic potential, with overall \(U(1)\) symmetry, and also the extension of this with a vector field to give Abelian Higgs. The EFT counterparts are then quite interesting, though the initial formulation is pretty textbook. For the scalar theory, the heavy radial dynamics are integrated out, and it turns out that the resulting Lagrangian for the azimuthal mode \((\partial\Theta)^2(1-(\partial\Theta)^2/M^2)\) is what the cosmologists have been calling \(K\)-esssence theory (I heard this term being thrown around since forever). In particular, the nomenclature requires the function \(K(X)\propto X-X^2/M^2\) to encode the kinetic structure. This doesn't look healthy, and it isn't: the Cauchy problem breaks down as \(K'\to 0\), which you can in principle reach on a physical phase trajectory. Up to a change of variables, the same effect can be seen when the radial mode is integrated out of the Abelian Higgs model, but the resulting EFT can be shown to be the nonlinear Proca model. To solve the Cauchy problem, there was previously proposed an approach of*fixing*the equations of motion. This seems an arbitrary approach, but the idea is to shift the field equations by introducing alternative variables which approximate the originals due to some suitable*driving*condition. The dynamical evolution can then be guided through the singular regions whilst remaining roughly faithful to the EFT. It seems there is a lot of work needed to make this robust. The letter itself makes some attempts at numerical implementation, showing that*fixing*is not satisfactory in many cases, and that the breakdown of the EFT dynamics seems to coincide with high-frequency modes in the corresponding UV model (I feel there is probably something interesting to say about that). This is all nice on its own, but for me the most interesting feature is that this letter is a goldmine of references for the dynamical failures of the nonlinear Proca model.`2307.07668`For fun, and only four pages or so! I learned that there is such a thing as`hist-ph`.