It would be a 2-spatial-dimensional oscillating (that's where the time dimension comes in) membrane around the black hole. Where? Super close to the horizon or super far from it? The answer varies, but the former is more popular. A better question, and I do not know a proper canonical answer in this particular case you've asked about, is: is the membrane or its oscillations tangible, or more precisely, how does one characterize (microscopically) the interaction with light and matter incident upon an oscillation?
Also not very clear in the article is the popularity of adding dimensions beyond the 3+1 spacetime and hiding them where gravitation isn't strong. For example, ADS/CFT comes up in the article but that's an equivalence between AdS_5 × S_5 and N = 4 supersymmetric Yang-Mills theory, or ADS5/CFT4. The value of N is essentially the number of (independent) operations that transform the spins of bosons and fermions; the subscripted 5 on AdS means an embedding of a higher-dimensional contracting, bounded space into 5 spacetime dimensions, and the subscripted 5 on S means there are five extra compact spacelike dimensions as well. There are other (less proven? I don't really pay attention to that area of string theory) correspondences with different numbers of extra dimensions and symmetries compared to our universe. In any of these a black hole (or something very like it) has some complete description on a membrane somewhere around it, and there's still some metaphysics about whether the CFT is outright sourced by the bulk or if ADS & CFT are just equivalent representations of the same bulk system.
"Holography" is a rough analogy - a 2-d film on a credit card looks like a 3-d image of e.g. a bird; a 4-dimensional conformal field's configuration can represent a 5-dimensional object (including a black hole), provided there are extra symmetries in the field theory and extra spatial dimensions available around the object into which one can shove some excess energy.
In these approaches the boundary of the collapsing spacetime and the membrane on which the CFT lives are very far away from everything (our universe doesn't appear to have a boundary or a membrane full of high-energy particles surrounding everything in the sky, after all), the anti-expansion is very slow (as the metric expansion of our universe is pretty obvious with all those redshifted supernovae, quasars, hot clouds of hydrogen, etc), the extra dimensions are made invisible by making them small and/or curled up, and so on.
Various flavours of the holographic principle have their adherents who believe their preferred form of holography say something important about gravitation in our universe, and might explain various features of collapsed stars and supermassive black holes.
A contrasting approach is to assume the Standard Model and 3+1 dimensional General Relativity and to use numerical simulations of gravitational collapses and black hole evaporations and so forth.
There is insufficient evidence from astronomy to really hint at which approach is better, although there are now limits from astronomy on the numbers and natures of possible extra spatial dimensions (they tend to leave imprints on the spectra of distant light sources, for example) and limits from particle physics on the minimum energy levels of extra symmetries beyond the Standard Model.