arXiv research

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

Using the results and techniques of a previous paper where we proved the quantization of gravity we extend the former result by adding a Yang-Mills functional and a Higgs term to the Einstein-Hilbert action.

3d gauge theories encode 4d simplicial geometries, with quantum blocks approximating gravity.

Contravariant gravity on Poisson manifolds is linked to Einstein gravity.

A first-order formulation of gravity is developed in which the fundamental fields consist of an SL(2,C) connection and two spinor-valued 1-forms. It is shown that the first term of an expansion of the Einstein-Hilbert action leads to an action for these fields which consists of dynamic L2 inner products of their covari…

Novel gravity theory on Poisson manifolds with R-flux.

The study finds geometric obstructions for Einstein-Hilbert-Palatini theories.

Quantizes area of surfaces in loop quantum gravity.

This paper quantizes geometry using SL(2,C) Chern-Simons theory and flat connections.

In this paper we study the spectral asymmetry of (possibly nonselfadjoint) elliptic PsiDO's in terms of the difference of zeta functions coming from different cuttings. Refining previous formulas of Wodzicki in the case of odd class elliptic PsiDO's, our main results have several consequence concerning the local indepe…

Study $p$-brane Galilean and Carrollian geometries via intrinsic torsion.

Geometric obstructions prevent gravity in high dimensions.

This paper is two-fold. At first we will discuss the generation of source terms in the Einstein-Hilbert action by using (topologically complicated) compact 3-manifolds. There is a large class of compact 3-manifolds with boundary: a torus given as the complement of a (thickened) knot admitting a hyperbolic geometry, den…

Defines and computes a generalized spectral action for Lorentz warped products.

Extends Einstein-Hilbert action to higher-order spectral triples.

The paper explores Einstein manifolds with torsion and nonmetricity.

Extends Einstein-Hilbert functional definition for stable manifolds.

Study connects Einstein-Hilbert actions to Courant algebroid connections.

The paper calculates variations of Einstein-Hilbert action on CR manifolds.

Study of Einstein-Hilbert actions with non-symmetric metrics and torsion.

The paper studies Einstein-Hilbert action on complex manifolds.

Study shows non-positivity of Einstein-Hilbert action for certain metrics.

The Einstein-Hilbert functional detects vanishing Sasaki-Futaki invariant, providing curvature obstructions.

The double tetrahedron is the triangulation of the three-sphere gotten by gluing together two congruent tetrahedra along their boundaries. As a piecewise flat manifold, its geometry is determined by its six edge lengths, giving a notion of a metric on the double tetrahedron. We study notions of Einstein metrics, consta…

Study stability of non-Kähler Calabi-Yau metrics using critical points of generalized Einstein Hilbert action.

Computes Wilson Loop observable using Einstein-Hilbert and Chern-Simons path integrals.

We apply the ADM approach to obtain a Hamiltonian description of the Einstein-Hilbert action. In doing so we add four new ingredients: (i) We eliminate the diffeomorphism constraints. (ii) We replace the densities $\sqrt g$ by a function $\f(x,g_{ij})$ with the help of a fixed metric $χ$ such that the Lagrangian and he…

In this paper, we investigate the behavior of ADM mass and Einstein-Hilbert functional under the Yamabe flow. Through studying the Yamabe flow by weighted spaces, we show that ADM mass and Einstein-Hilbert functional are well-defined and monotone non-increasing under the Yamabe flow on $n$-dimensional, $n\geq 3$, asymp…

The paper studies Einstein-Hilbert functional and its relation to K-semistability.

New formula for Lichnerowicz Laplacian on homogeneous spaces.

Introduces a restricted Chen-Nagano variational principle for the Einstein-Hilbert functional.

Paper proves convergence of MDL to Einstein-Hilbert with boundary term.

A new framework for Einstein-Hilbert action with topological variations.

Study of Einstein-Hilbert action on metric-affine spaces with connections.

The paper studies variations of metrics on foliated manifolds and finds solutions to specific actions.

A first-order Lagrangian $L^\nabla$ variationally equivalent to the second-order Einstein-Hilbert Lagrangian is introduced. Such a Lagrangian depends on a symmetric linear connection, but the dependence is covariant under diffeomorphisms. The variational problem defined by $L^\nabla$ is proved to be regular and its H…

The paper calculates volumes and curvatures in Sasaki geometry using localization formulas.

New stable metric found on a complex space.

The study examines stability of specific geometric flows.

Paper studies stability of generalized Ricci solitons with mathematical rigor.

By means of a Kaluza-Klein type argument we show that the Perelman's F-functional is the Einstein-Hilbert action in a space with extra ``phantom'' dimensions. In this way, we try to interpret some remarks of Perelman in the introduction and at the end of the first section in his first famous paper. As a consequence the…

Develops Palatini formalism for pseudo-Finsler metrics, recovering classical results.

New method measures deviation from static spacetime.

Study on stability of Einstein metrics on symmetric spaces.

Introduces a new relation between BF theory and gravity.

Quantum gravity model includes cosmological constant using Chern-Simons theory.

Proposes new conformal parametrizations for modified Einstein gravity.

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