Related papers: Partial Orderings of Curvature Invariants
We define new higher-order Alexander modules $\mathcal{A}_n(C)$ and higher-order degrees $\delta_n(C)$ which are invariants of the algebraic planar curve $C$. These come from analyzing the module structure of the homology of certain…
We construct matter field theories in ``theory space'' that are fractal, and invariant under geometrical renormalization group (RG) transformations. We treat in detail complex scalars, and discuss issues related to fermions, chirality, and…
This paper deals with locally constrained inverse curvature flows in a broad class of Riemannian warped spaces. For a certain class of such flows we prove long time existence and smooth convergence to a radial coordinate slice. In the case…
The main aim of this article is to investigate a spacetime of quasi-constant sectional curvature. At first, the existence of such a spacetime is established by several examples. We have shown that a spacetime of quasi-constant sectional…
We consider the evolution of perturbed cosmological spacetime with multiple fluids and fields in Einstein gravity. Equations are presented in gauge-ready forms, and are presented in various forms using the curvature (\Phi or \phi_\chi) and…
Motivated by recent studies of nonlinear perturbations of asymptotically anti-de Sitter spacetimes, we study gravitational perturbations of $(n+2)$ dimensional Minkowski spacetime with a spherical Dirichlet wall. By considering the tensor,…
We analyse the stability of the vector and axial sectors of Poincar\'e gauge theory around general backgrounds in the presence of cubic order invariants defined from the curvature and torsion tensors, showing how the latter can in fact…
We prove that a compact stratied space satises the Riemannian curvature-dimension condition RCD(K, N) if and only if its Ricci tensor is bounded below by K $\in$ R on the regular set, the cone angle along the stratum of codimension two is…
We study disformal transformations of the metric in the cosmological context. We first consider the disformal transformation generated by a scalar field $\phi$ and show that the curvature and tensor perturbations on the uniform $\phi$…
Quantum fields are investigated in the (2+1)-open-universes with non-trivial topologies by the method of images. The universes are locally de Sitter spacetime and anti-de Sitter spacetime. In the present article we study spacetimes whose…
In this paper we find the first and second order perturbations of the induced metric and the extrinsic curvature of a non-degenerate hypersurface $\Sigma$ in a spacetime $(M,g)$, when the metric $g$ is perturbed arbitrarily to second order…
We discuss linearized gravitational perturbations of higher dimensional spacetimes. For algebraically special spacetimes (e.g. Myers-Perry black holes), we show that there exist local gauge invariant quantities linear in the metric…
We consider generic static spacetimes with Killing horizons and study properties of curvature tensors in the horizon limit. It is determined that the Weyl, Ricci, Riemann and Einstein tensors are algebraically special and mutually aligned…
Semi-Riemannian manifolds that satisfy (homogeneous) linear differential conditions of arbitrary order on the curvature are analyzed. They include, in particular, the spaces with (higher-order) recurrent curvature, (higher-order) symmetric…
The curvature of a spacetime, either in a topological sense, or averaged over super-horizon-sized patches, is often equated with the global curvature term that appears in Friedmann's equation. In general, however, the Universe is…
The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order theories of gravity. We can define effective pressure and energy density directly connected to the Ricci scalar of curvature of a generic…
We discuss the structure of microcanonical ensembles in inertial and non-inertial frames attached to a confined system of positive energy particles in curved spacetime. Under certain physically reasonable assumptions that ensure the…
An alternative approach introducing a 3 dimensional Ricci scalar curvature quantum operator given in terms of volume and area as well as new edge length operators is proposed. An example of monochromatic 4-valent node intertwiner state…
The Minkowski tensors are valuations on the space of convex bodies in ${\mathbb R}^n$ with values in a space of symmetric tensors, having additional covariance and continuity properties. They are extensions of the intrinsic volumes, and as…
The goal of the paper is to give an optimal transport characterization of sectional curvature lower (and upper) bounds for smooth $n$-dimensional Riemannian manifolds. More generally we characterize, via optimal transport, lower bounds on…