created an entry for *Lorentzian geometry*, prompted by this Physics.SE question

created *Einstein manifold*

(for the moment only to record the example of weak $G_2$-manifolds…)

]]>just to make links work, I have started a minimum at *gravitational wave*.

created a bare minimum at *associative submanifold*

added a paragraph on extremality and spinning black hole formation (taken from a Phyiscs.SE comment, linked to) to *Kerr spacetime*.

(Needs more formatting, but I have to run now.)

]]>created *hyperbolic manifold* in order to record a reference on the relation between volumes of hyperbolic 3-folds and their Chern-Simons/Dijkgraaf-Witten invariants by Zickert.

am starting a *special holonomy table*, have included it into relevant entries and created some of these entries, edited others.

Not really done yet and not really good yet. Hope to improve on it later.

]]>at *S-matrix* and elsewhere is reference to the “causal order“-relation, the relation saying that for a pair $(S_1,S_2)$ of subsets of a spacetime, $S_1$ does not intersect the past of $S_2$, or equivalently that $S_2$ does not intersect the future of $S_1$.

(Following a suggestion by Arnold Neumaier, a neat suggestive notation for this is $S_1 {\vee\!\!\!\wedge} S_2$, which I have been implementing now at *S-matrix*.)

I am starting to give this concept its own entry, currently titled “causal order”; but what’s good terminology?

This relation ${\vee\!\!\!\wedge}$ is not really an ordering, since it is not transitive. It would seem tempting to say “causal relation”, but googling for this term shows that has an different established meaning.

]]>I have touched the Idea-section at *first-order formulation of gravity*, trying to improve a little.

created *rapidity*, just enough to serve as a link from the computation of the *singular support of the causal propagator*

in the course of writing those notes on *A first idea of quantum field theory* I occasionally find the need to reference more field theory jargon. In this vein I just created a simple entry “relativistic quantum field theory” just with some highlighting of terminology.

(Similarly I had also created *locally variational quantum field theory* a while back, but did not find the leisure yet to give it substantial content.)

I have added to *causal complement* the actual definition of causal complements of subsets of Lorentzian manifolds.

The entry used to contain only a more abstract concept, now kept as the second subsection of the Definition section here.

]]>expanded the Idea- and the Definition section at *G2-manifold* (also further at *G2*). (Still not really complete, though.) Highlighted the relation to 2-plectic geometry and cross-linked there.

I have added something to *causal structure*, for the moment mainly so as to record references to definitions of causal manifolds and to proposals for axioms of local nets over these.

edits and edit discussion on the entry *conformal compactification* is going on here

am beginning to add some genuine content to *Ruelle zeta function* (which used to just redirect to *zeta function of a dynamical system* which in turn is no more that a stub)

not done yet

]]>I have finally added a little bit of substance to *Polyakov action* (with a little spill-over at *Nambu-Goto action*).

This is not polished yet, I need to run now and come back to it later.

]]>Have started some minimum at *calibration*.

created *celestial sphere*

am splitting off *complex volume* from *hyperbolic manifold*

created a bare minimum at *harmonic map* (for the moment just so as to have a place to record the reference given there)

I have been touching, adding references and little pointers, but otherwise nothing real substantial, the following entries:

superisometry group (new but stubby), Killing spinor, BPS state, M-brane, black brane, M9-brane, KK-monopole

and maybe others.

]]>The traditional concepts of asymptotically flat spacetime and asymptotically anti de Sitter spacetimes unify, at least naively, from the point of view of Cartan geometry: here both are Cartan geometries that approach their model Klein geometry “at infinity”.

Is there any discussion in the literature of what would be this general concept? Cartan geometries “approaching” their model Klein geometry “asymptotically” in some suitable sense?

]]>made the following table, which had been copy-and-pasted into the relevant entries, a standalong table for automatic inclusion: *local and global geometry - table*

created a stub for *hearing the shape of a drum* with just two paragraphs on the idea. Cross-linked with *spectral geometry* and *spectral triple*.