Related papers: Real null coframes in general relativity and GPS t…
It is well-known that General Relativity with positive cosmological constant can be formulated as a gauge theory with a broken SO(1,4) symmetry. This symmetry is broken by the presence of an internal space-like vector $V^A$, $A=0,...,4$,…
Exact categories are a natural generalisation of abelian categories and provide a fertile ground to develop relative homological algebra. In this paper, starting from a class of relative Gorenstein projective objects in an exact category…
We give a complete derived equivalence classification of all symmetric algebras of domestic representation type over an algebraically closed field. This completes previous work by R. Bocian and the authors, where in this paper we solve the…
When spacetime torsion is present, geodesics and autoparallels generically do not coincide. In this work, the well-known method that uses Killing vectors to solve the geodesic equations is generalized for autoparallels. The main definition…
The aim of this paper is to clarify the relation between the following objects: $ (a) $ rank 1 projective modules (ideals) over the first Weyl algebra $ A_1(\C)$; $ (b) $ simple modules over deformed preprojective algebras $…
The concept of sharpness has been successfully applied to traditional architectures like MLPs and CNNs to predict their generalization. For transformers, however, recent work reported weak correlation between flatness and generalization. We…
In this paper, we find all the Conformal Killing Vectors (CKVs) and their Lie Algebra for the recently reported [cqg1] spherically symmetric, shear-free separable metric spacetimes with non-vanishing energy or heat flux. We also solve the…
Let $G_k$ be a connected reductive group over an algebraically closed field $k$ of char $\neq 2$. Let $\theta_k$ be an algebraic group involution of $G_k$ and denote the fixed point subgroup by $K_k$. We construct an integral model for the…
This paper investigates intrinsic Killing symmetries of null hypersurfaces $\mathcal{N}_3$ within the framework of general relativity. To this end we consider $\mathcal{N}_3$ as detached from the embedding spacetime and equipped with a…
The recently introduced manifestly covariant canonical quantization scheme is applied to gravity. New diffeomorphism anomalies generating a multi-dimensional generalization of the Virasoro algebra arise. This does not contradict theorems…
This paper is a review of the relationship between the metric formulation of (2+1)-dimensional gravity and the loop observables of Rovelli and Smolin. I emphasize the possibility of reconstructing the geometry, via the theory of geometric…
In this paper we excavate, for the first time, the most general class of conformal Killing vectors, that lies in the two dimensional subspace described by the null and radial co-ordinates, that are admitted by the generalised Vaidya…
Nondegenerate plane congruences in the four-dimensional complex projective space with degenerate general focal conic are classified by using the focal method due to Corrado Segre.
According to Belinsky, Khalatnikov and Lifshitz, gravity near a space-like singularity reduces to a set of decoupled one-dimensional mechanical models at each point in space. We point out that these models fall into a class of conformal…
We study the notion of optical geometry, defined to be a Lorentzian manifold equipped with a null line distribution, from the perspective of intrinsic torsion. This is an instance of a non-integrable version of holonomy reduction in…
In this paper we will classify the finite spectral triples with KO-dimension six, following the classification found in [1,2,3,4], with up to four summands in the matrix algebra. Again, heavy use is made of Kra jewski diagrams [5].…
A complete and explicit classification of generalized, or local, symmetries of massless free fields of spin $s \geq 1/2$ is carried out. Up to equivalence, these are found to consists of the conformal symmetries and their duals, new chiral…
For any sequence of matrix algebras that converge to a coadjoint orbit we give explicit formulas that show that the distances between the matrix algebras (viewed as quantum metric spaces) converges to 0. In the process we develop a general…
We classify complete curvature homogeneous metrics on simply connected four dimensional manifolds which are invariant under a cohomogeneity one action. We show that they are either isometric to a symmetric space with one of its…
In this paper we extend some previous results for a new proposal for gravity and place them into overall context. The basic fields of this proposal provide an off-shell realization of symmetry with respect to SO(3,C) gauge transformations…