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It is shown that Ashtekar and Hansenss Universal Structure at Spatial Infinity (SPI), which has recently be used to establish the conservation of supercharges from past null infity to future null infinity, is an example of a (pseudo-) Carollian structure. The relation to Kinematic Algebras is clarified.
Following the recent work of Henneaux and Troessaert, which revisits the problem of spacetime symmetries at spatial infinity, we analyze this problem using the Bondi metric without determinant condition as our starting point. It turns out that in thi
The Hamilton-Jacobi analysis of three dimensional gravity defined in terms of Ashtekar-like variables is performed. We report a detailed analysis where the complete set of Hamilton-Jacobi constraints, the characteristic equations and the gauge transf
Weakly nonlinear dynamics in anti-de Sitter (AdS) spacetimes is reviewed, keeping an eye on the AdS instability conjecture and focusing on the resonant approximation that accurately captures in a simplified form the long-term evolution of small initi
Four-dimensional random geometries can be generated by statistical models with rank-4 tensors as random variables. These are dual to discrete building blocks of random geometries. We discover a potential candidate for a continuum limit in such a mode
For a plane gravitational wave whose profile is given, in Brinkmann coordinates, by a $2times2$ symmetric traceless matrix $K(U)$, the matrix Sturm-Liouville equation $ddot{P}=KP$ plays a multiple and central r^ole: (i) it determines the isometries,