arXiv research

Mathematical general relativity reviewed.

Advanced mathematical relativity course for math and physics students.

For any finitely generated, non-elementary, torsion-free group $G$ that is hyperbolic relative to $\mathbb P$, we show that there exists a group $G^*$ containing $G$ such that $G^*$ is hyperbolic relative to $\mathbb P$ and $G$ is not relatively quasiconvex in $G^*$. This generalizes a result of I. Kapovich for hyperbo…

Homotopy momentum map extends Noether's theorem in general relativity.

We discuss some aspects about the computation of kinematic, spectroscopic, Fermi and astrometric relative velocities that are geometrically defined in general relativity. Mainly, we state that kinematic and spectroscopic relative velocities only depend on the 4-velocities of the observer and the test particle, unlike F…

Develops axiomatic framework for differential cohomology and constructs generalized Cheeger-Simons characters.

Characterizes geometric actions on graphs with flexible stabilizers.

Characterizes relative hyperbolicity using Morse and contracting boundaries.

Extends a theorem for first-order elliptic operators on manifolds.

Optimizes Einstein equations using optimal transport.

The set of Clifford bundles of bounded geometry over open manifolds can be endowed with a metrizable uniform structure. For one fixed bundle $E$ we define the generalized component $\gencomp (E)$ as the set of Clifford bundles $E'$ which have finite distance to $E$. If $D$, $D'$ are the associated generalized Dirac ope…

We generalize the Weinstein-Moser theorem on the existence of nonlinear normal modes near an equilibrium in a Hamiltonian system to a theorem on the existence of relative perodic orbits near a relative equilibrium in a Hamiltonian system with continuous symmetries. In particular we prove that under appropriate hypothes…

Explains Einstein's theory of gravity for mathematicians.

Researchers address the generation of differential invariants for geometric structures.

Study of endperiodic maps on infinite graphs, proving homotopy and eigenvalue properties.

CV inference can be invalid for relatively unstable model comparisons.

Mass in relativity linked to polyhedra geometry.

New method uses relative capacities of geodesic balls to determine scalar curvature.

New tool: relative Hopf invariant for Poincaré surgery.

Study Berwald spacetimes and their relation to very special relativity.

Study General Relativity using field theories and Poisson brackets.

We show the equivalence of several characterizations of relative hyperbolicity for metric spaces, and obtain extra information about geodesics in a relatively hyperbolic space. We apply this to characterize hyperbolically embedded subgroups in terms of nice actions on (relatively) hyperbolic spaces. We also study the d…

Combines relatively hyperbolic groups over a complex.

Finite index subgroups of relatively hyperbolic groups have equal index.

The paper generalizes Bayesian Cramér-Rao inequality using information geometry of relative α-entropy.

For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two relatively quasiconvex subgroups $Q_1$ and $Q_2$ is relatively quasiconvex and isomorphic to $Q_1 \ast_{Q_1 \cap Q_2} Q_2$. The main theorem extends results for quasiconvex subgroups of word-hyperbolic groups, an…

New definitions of center of mass and angular momentum in general relativity.

Two Pin groups fit fermions in gravity.

An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework of a classical result by Weinstein and Moser on the existence of periodic orbits …

New energy measure for isolated systems in general relativity.

Unique expanders found with vanishing entropy.

Study on singular values of Riemann curvature tensor in general relativity.

Solves characteristic problem in general relativity for null data.

The paper extends cyclic cocycles and proves relative index theorems for partitioned manifolds.

General Relativity can be reformulated as a diffeomorphism invariant SU(2) gauge theory. A new action principle for this "pure connection" formulation of GR is described.

We introduce a class of generalized relative entropies (inspired by the Bregman divergence in information theory) on the Wasserstein space over a weighted Riemannian or Finsler manifold. We prove that the convexity of all the entropies in this class is equivalent to the combination of the nonnegative weighted Ricci cur…

OGRePy simplifies tensor calculations in general relativity.

Article generalizes open book construction for 5D contact pairs.

The center of mass in General Relativity is hard to define due to coordinate freedom.

The paper introduces new invariants to detect hyperbolic parts in relatively hyperbolic groups.

Theory of relatively Anosov representations using flow methods.

In this paper, we prove a limit set intersection theorem in relatively hyperbolic groups. Our approach is based on a study of dynamical quasiconvexity of relatively quasiconvex subgroups. Using dynamical quasiconvexity, many well-known results on limit sets of geometrically finite Kleinian groups are derived in general…

We prove a criterion for stability of relative equilibria in symmetric Hamiltonian systems at singular points of the momentum map. This generalizes a theorem of G.W. Patrick. The method of the proof is also useful in studying the bifurcation of relative equilibria.

The paper extends cellular algebras with relative orderings and explores their properties.

Generalizes Doob's theorem for supermartingales relative to a convex set of measures.

The paper shows how local cut points imply group splittings in relatively hyperbolic groups.

Simple bounds for covariance and Gram matrices across various settings.

Sum formula for relative Seiberg-Witten invariants in 4-manifolds.