In Yong Wang's Multiply Twisted Products article, general definitions for so-called *deformed* Y *twisted* Products are delivered. The notion of *deformed* The products seem to be a fairly standard definition, first presented by O & # 39; Neill. I wonder if the definition of twisted products (and the generalizations of distorted and twisted products) in the previous document is also standard. Many theoretical physics articles sometimes talk about *deformed* Y *twisted* Space times in a fairly manual way, so I am never really sure if they are talking about a mathematical definition or if they simply want to sound elegant.

For example, Compère speaks in a general document about the Kerr / CFT correspondence about the following metric

begin {align}

mathrm {d} s ^ 2 = J left (1+ cos ^ 2 theta right) left (-r ^ 2dt ^ 2 + frac {dr ^ 2} {r ^ 2} + d theta ^ 2 right) + frac {4 sin ^ 2 theta} {1+ cos ^ 2 theta} left (d phi + rdt right) ^ 2 ,,

end {align}

be a "deformed and twisted product of $ AdS_2 times S ^ 2 $ "(J is only scaling the metric.) This seems to be a different definition of a twisted product, since in the role of twisted Wang it is a generalization of deformation. Also, I cannot understand that the previous metric is $ AdS_2 times S ^ 2 $, not even for $ theta = frac { pi} {2} $ a "twisted product of $ AdS_2 $ and a circle of constant radius ", since the suggested geometry should not have terms outside the diagonal such as $ mathrm {d} phi mathrm {d} t $ in the metric Are I missing coordinate transformations that make it obvious? What is a standard definition for a twisted product of Pseudo-Riemannian varieties?