Related papers: Gravitational Algebras with Two Areas
We study a physically motivated representation of an algebra of operators in gravitational and non gravitational theories called the covariant representation of an algebra. This is a representation where the symmetries of the operator…
Given two associative algebras A, C and a linear space V together with some linear maps R_1, R_2, R_3, E satisfying some conditions, we define an associative algebra structure on A\otimes V\otimes C called a two-sided crossed product.…
In this paper, we study gravitational symmetry algebras that live on 2-dimensional cuts $S$ of asymptotic infinity. We define a notion of wedge algebra $\mathcal{W}(S)$ which depends on the topology of $S$. For the cylinder $S=\mathbb{C}^*$…
We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings,…
In this paper, we analyze the variation of the gravitational action on a bounded region of spacetime whose boundary contains segments with various characters, including null. We develop a systematic approach to decompose the derivative of…
We study the threshold of gravitational collapse in spherically symmetric spacetimes governed by the Einstein-Maxwell-Vlasov equations. We numerically construct solutions describing a collapsing distribution of charged matter that either…
Recent work has highlighted the importance of crossed products in correctly elucidating the operator algebraic approach to quantum field theories. In the gravitational context, the crossed product simultaneously promotes von Neumann…
The w_\infty algebra is a particular generalization of the Virasoro algebra with generators of higher spin 2,3,...,\infty. It can be viewed as the algebra of a class of functions, relative to a Poisson bracket, on a suitably chosen surface.…
Geometric torsions are torsions of acyclic complexes of vector spaces which consist of differentials of geometric quantities assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a…
By working in a symplectically covariant real formulation of special K\"ahler geometry, we propose and give strong evidence for a canonical BPS partition function for AdS$_2 \times_w M_2$ near-horizon geometries with arbitrary rotation and…
We consider the algebra of observables of perturbative quantum gravity in the exterior of a stationary black hole or the static patch of de Sitter spacetime. It was previously argued that the backreaction of gravitons on the spacetime…
An extension of the General Coordinate Transformations algebra is constructed by means geometrical consistency conditions. An class of infinite invariants is derived. In particular we construct the consistent extension of the gravitational…
We analyse a variety of Euclidean saddles in the gravitational path integral, with asymptotic AdS boundary conditions, in a class of Einstein-Scalar-Maxwell models. These include single boundary solutions, usual and wineglass wormholes, as…
In this Master of Science Thesis I introduce geometric algebra both from the traditional geometric setting of vector spaces, and also from a more combinatorial view which simplifies common relations and operations. This view enables us to…
We introduce a new class of finite dimensional gentle algebras, the surface algebras, which are constructed from an unpunctured Riemann surface with boundary and marked points by introducing cuts in internal triangles of an arbitrary…
The purpose of this paper is to propose the implementation of some methods from algebraic geometry in the theory of gravitation, and more especially in the variational formalism. It has been assumed that the metric tensor depends on two…
In this thesis, we study the Hamiltonian and covariant phase space description of gravitational theories. The phase space represents the allowed field configurations and is accompanied by a closed nondegenerate 2 form- the symplectic form.…
We employ two-dimensional chiral algebra techniques to produce solutions of certain differential and integral equations which occur in the context of the Analytic Geometric Langlands Program.
We discuss black hole spacetimes with a geometrically defined quasi-local horizon on which the curvature tensor is algebraically special relative to the alignment classification. Based on many examples and analytical results, we conjecture…
The gravitational path integral suggests a striking result: the Hilbert space of closed universes in each superselection sector, a so-called $\alpha$-sector, is one-dimensional. We develop an abstract formalism encapsulating recent…