# arXiv Jul 22nd-27th 2023

## A week on gr-qc

`2307.13939`A gravitating global monopole gan be generated by breaking \(SO(3)\) to \(U(1)\).`2307.13760`An opportunity to get a basic understanding of Carrollian geometry; we were not really successful in our discussion so this is left to another day!`2307.13803`This one potentially looked very interesting. As is well known, there are significant problems in constructing nonlinear completions of massive gravity. The authors of this paper propose a massive graviton without introducing the Boulware-Deser ghost, requiring Vainshtein screening or even modifying classical GR. The (effective?) model they are using for the gravitational sector is \(S_{\text{eff}}=\int\mathrm{d}^4x\sqrt{-g}\left(M_{Pl}^2R/2-i\gamma\text{tr}\log |g_{\mu\nu}|\right)\). The motivation for this follows from assuming a non-trivial functional measure, whose effects are preserved by selecting a Gaussian regularisation scheme (see`2102.10688`for more details). Phenomenologically, \(\gamma\) is derived from a Wilsonian coefficient and is proportional to the graviton mass, with GR being recovered in the limit \(\gamma\to 0\). A key feature of this approach is that the GR limit is free from the vDVZ discontinuity. This is supposedly because the model with the logarithm is*already*a nonlinear completion of the theory, and in the field equations following it can be seen that the dynamics have a smooth massless limit. Separately, if the model is linearised then the Fierz-Pauli mass term appears in proportion to \(\gamma\). This argument isn't too clear to me, since I'd understood vDVZ to appear at the linear level anyway. There are some other curious features here; the square is purely imaginary, so the particle has to be virtual, and due to its origin in the functional measure it vanishes in the \(\hbar\to 0\) limit. Finally, despite the correction appearing to violate diffeomorphism invariance, the symmetry is restored by the modifications needed to variations in the presence of a non-trivial measure. In the final section of the paper, applications to the Newtonian potential are considered: this is interesting, you would typically expect a Yukawa-type potential for a massive graviton, but the imaginary nature of the mass leads to an oscillatory potential modulated by Yukawa decay.`2307.13435`I was not aware that there was a Russian space VLBI mission.`2307.11151`By some excellent authors ;)