arXiv research

Contravariant gravity on Poisson manifolds is linked to Einstein gravity.

A novel gravity theory based on Poisson Generalized Geometry is investigated. A gravity theory on a Poisson manifold equipped with a Riemannian metric is constructed from a contravariant version of the Levi-Civita connection, which is based on the Lie algebroid of a Poisson manifold. Then, we show that in Poisson Gener…

Study of contravariant pseudo-Hessian manifolds and their Poisson structures.

Examines scalar curvature results via covariant and contravariant methods.

Classifies contravariant matrix-valued valuations on polytopes without continuity assumptions.

Using Fedosov's approach we give a geometric construction of a formal symplectic groupoid over any Poisson manifold endowed with a torsion-free Poisson contravariant connection. In the case of Kaehler-Poisson manifolds this construction provides, in particular, the formal symplectic groupoids with separation of variabl…

A complete classification of all continuous GL(n) contravariant Minkowski valuations is established. As an application we present a family of sharp isoperimetric inequalities for such valuations which generalize the classical Petty projection inequality.

We discuss contravariant connections on Poisson manifolds. For vector bundles, the corresponding operational notion of a contravariant derivative had been introduced by Izu Vaisman. We show that these connections play an important role in the study of global properties of Poisson manifolds and we use them to define Poi…

The abstract semiclassicalises quantum group principal bundles to Poisson geometry.

Study Poisson algebras for Hamiltonian systems linearization.

This paper is based on the author's talk at 1997 Taniguchi Symposium ``Integrable Systems and Algebraic Geometry''. We consider an approach to the theory of Frobenius manifolds based on the geometry of flat pencils of contravariant metrics. It is shown that, under certain homogeneity assumptions, these two objects are …

In this paper, I will show that, if a Lie algebra $\G$ acts on a manifold $P$, any solution of the classical Yang-Baxter equation on $\G$ gives arise to a Poisson tensor on $P$ and a torsion-free and flat contravariant connection (with respect to the Poisson tensor). Moreover, if the action is locally free, the matacur…

Let $M$ be either a projective manifold $(M,Pi)$ or a pseudo-Riemannian manifold $(M,g).$ We extend, intrinsically, the projective/conformal Schwarzian derivatives that we have introduced recently, to the space of differential operators acting on symmetric contravariant tensor fields of any degree on $M.$ As operators,…

Let $(M,π,\mathcal{D})$ be a Poisson manifold endowed with a flat, torsion-free contravariant connection. We show that if $\mathcal{D}$ is an $\mathcal{F}$-connection then there exists a tensor $\mathbf{T}$ such that $\mathcal{D}\mathbf{T}$ is the metacurvature tensor introduced by E. Hawkins in his work on noncommutat…

The paper calculates curvatures in a specific type of warped product space.

Introduces a new relation between BF theory and gravity.

Study invariant Poisson structures on homogeneous manifolds, algebraically and geometrically.

Proposes new conformal parametrizations for modified Einstein gravity.

PhD dissertation on Finsler geometry and gravity, focusing on Berwald spaces and exact solutions.

We present new classes of exact solutions with noncommutative symmetries constructed in vacuum Einstein gravity (in general, with nonzero cosmological constant), five dimensional (5D) gravity and (anti) de Sitter gauge gravity. Such solutions are generated by anholonomic frame transforms and parametrized by generic off…

We will introduce two notions of compatibility bettwen pseudo-Riemannian metric and Poisson structure using the notion of contravariant connection introduced by Fernandes R. L., we will study some proprities of manifold endowed with such compatible structures an we will give some examples.

A differential calculus, differential geometry and the E-R Gravity theory are studied on noncommutative spaces. Noncommutativity is formulated in the star product formalism. The basis for the gravity theory is the infinitesimal algebra of diffeomorphisms. Considering the corresponding Hopf algebra we find that the defo…

We argue that Horava-Lifshitz (HL) gravity provides the minimal holographic dual for Lifshitz-type field theories with anisotropic scaling and dynamical exponent z. First we show that Lifshitz spacetimes are vacuum solutions of HL gravity, without need for additional matter. Then we perform holographic renormalization …

The space of Minkowski valuations on an m-dimensional complex vector space which are continuous, translation invariant and contravariant under the complex special linear group is explicitly described. Each valuation with these properties is shown to satisfy geometric inequalities of Brunn-Minkowski, Aleksandrov-Fenchel…

We use conformal, but ghostful, Weyl gravity to study its ghost-free, second derivative, partially massless (PM) spin 2 component in presence of Einstein gravity with positive cosmological constant. Specifically, we consider both gravitational- and self- interactions of PM via the fully non-linear factorization of conf…

A theory of gravitation is proposed, modeled after the notion of a Ricci flow. In addition to the metric an independent volume enters as a fundamental geometric structure. Einstein gravity is included as a limiting case. Despite being a scalar-tensor theory the coupling to matter is different from Jordan-Brans-Dicke gr…

De Donder form for gravity is globally defined.

We simplify and extend a 6D conformal gravity theory to 8D, linking it to Q-curvature.

Analyzing static solutions in Finsler gravity, extending known results.

Identifies null hypersurfaces with constant surface gravity.

Fine shape of local compacta represented by ordinary maps.

Explains non-lorentzian theories and their dynamics.

New generalized Poisson structures are introduced by using suitable skew-symmetric contravariant tensors of even order. The corresponding `Jacobi identities' are provided by conditions on these tensors, which may be understood as cocycle conditions. As an example, we provide the linear generalized Poisson structures wh…

HR in 8D encodes unique conformal gravity with negative curvature.

Special issue honors Stanley Deser, focusing on advanced physics topics.

Projective connection explains gravity dynamics in 2D.

Study Codazzi tensors in space-times, linking to Cotton gravity.

Prominent approaches to quantum gravity struggle when it comes to incorporating a positive cosmological constant in their models. Using quantization of a complex $\mathrm{SL}(2,\mathbb{C})$ Chern-Simons theory we include a cosmological constant, of either sign, into a model of quantum gravity.

We developed a perturbation model for affine gravity theories.

The study characterizes spacetimes with specific solitons in $f(\mathcal{R})$-gravity.

The $(2k)$-th Gauss-Bonnet curvature is a generalization to higher dimensions of the $(2k)$-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for $k=1$. The Gauss-Bonnet curvatures are used in theoretical physics to describe gravity in higher dimensional space times where they are known a…

Shielding gravity fields using special potentials.

The paper explores generalizations of Mirzakhani's recursion and computes volumes for physical gravity models.

We show that 3D gravity, in its pure connection formulation, admits a natural 6D interpretation. The 3D field equations for the connection are equivalent to 6D Hitchin equations for the Chern-Simons 3-form in the total space of the principal bundle over the 3-dimensional base. Turning this construction around one gets …

CNN outperforms other methods in gravity inversion.

Study of Randers spacetimes and their Finsler gravity solutions.

Theory for gravity coupled with fields on manifolds with null-boundary.

New models predict mobility flows as well as complex machine learning but are simpler and interpretable.