A generalized Momentum/Complexity correspondence

Holographic complexity, in the guise of the Complexity = Volume prescription, comes equipped with a natural correspondence between its rate of growth and the average infall momentum of matter in the bulk. This Momentum/Complexity correspondence can be related to an integrated version of the momentum constraint of general relativity. In this paper we propose a generalization, using the full Codazzi equations as a starting point, which successfully accounts for purely gravitational contributions to infall momentum. The proposed formula is explicitly checked in an exact pp-wave solution of the vacuum Einstein equations.

“Twisted” black holes are unphysical

So-called “twisted” black holes were recently proposed by [H. Zhang, arXiv:1609.09721 ], and were further considered by [S. Chen and J. Jing, arXiv:1610.00886 ]. More recently, they were severely criticized by [Y. C. Ong, J. Cosmol. Astropart. Phys. 1701, 001 (2017)]. While these spacetimes are certainly Ricci-flat, and so mathematically satisfy the vacuum Einstein equations, they are also merely minor variants on Taub–NUT spacetimes. Consequently, they exhibit several unphysical features that make them quite unreasonable as realistic astrophysical objects. Specifically, these “twisted” black holes are not (globally) asymptotically flat. Furthermore, they contain closed time-like curves that are not hidden behind any event horizon — the most obvious of these closed time-like curves are small azimuthal circles around the rotation axis, but the effect is more general. The entire region outside the horizon is infested with closed time-like curves.