Related papers: Exact Bianchi Identity in Regge Gravity
A model for quantum gravity in one (time) dimension is discussed, based on Regge's discrete formulation of gravity. The nature of exact continuous lattice diffeomorphisms and the implications for a regularized gravitational measure are…
Metric-affine theories in which the gravity Lagrangian is built using (projectively invariant) contractions of the Ricci tensor with itself and with the metric (Ricci-Based Gravity theories, or RBGs for short) are reviewed. The goal is to…
We consider minisuperspace gravity system described by piecewise flat metric discontinuous on three-dimensional faces (tetrahedra). There are infinite terms in the Einstein action. However, starting from proper regularization, these terms…
We present a formulation of Regge Calculus where arbitrary coordinates are associated to each vertex of a simplicial complex and the degrees of freedom are given by the metric on each simplex. The lengths of the edges are thus determined…
We provide a step towards classifying Riemannian four-manifolds in which the curvature tensor has zero divergence, or -- equivalently -- the Ricci tensor Ric satisfies the Codazzi equation. Every known compact manifold of this type belongs…
We consider the possibility that, in the semiclassical Einstein equation for cosmological spacetimes, gravity is sourced by the amount of stress-energy that is above that of the instantaneous ground state. For this possibility to be…
In Parts I and II of the work (gr-qc/9405013, 9407032), we have shown that gravity is {\it sui generis} a Higgs field corresponding to spontaneous symmetry breaking when the fermion matter admits only the Lorentz subgroup of world…
We consider the effects of higher curvature terms on a holographic dual description of boundary conformal field theory. Specifically, we consider three-dimensional gravity with a specific combination of Ricci tensor square and curvature…
The Palatini formulation is used to develop a genuine connection theory for general relativity, in which the gravitational field is represented by a Lorentz-valued spin connection. The existence of a tetrad field, given by the Fock-Ivanenko…
With the theory of general relativity, Einstein abolished the interpretation of gravitation as a force and associated it to the curvature of spacetime. Tensorial calculus and differential geometry are the mathematical resources necessary to…
In this paper we define an orientation of a measured Gromov-Hausdorff limit space of Riemannian manifolds with uniform Ricci bounds from below. This is the first observation of orientability for metric measure spaces. Our orientability has…
I present a model of discrete gravity, which is formulated in terms of a topological gauge theory with defects. The theory has no local degrees of freedom and the gravitational field is trivial everywhere except at a number of colliding…
New general spherically symmetric solutions have been derived with a cosmological "constant" \Lambda as a source. This \Lambda field is not constant but it satisfies the properties of the asymptotically safe gravity at the ultraviolet fixed…
In general relativity, the contracted Bianchi identity makes the field equation compatible with the energy conservation, likewise in $f(R)$ theories of gravity. We show that this classical phenomenon is not guaranteed in the symmetric…
We derive some elliptic differential inequalities from the Weitzenb\"ock formulas for the traceless Ricci tensor of a K\"ahler manifold with constant scalar curvature and the Bochner tensor of a K\"ahler-Einstein manifold respectively.…
The Ricci curvature equations are a central subject of study in geometry. However, in the smooth real case, their linear analysis is often confined to settings in which the background metric is Einstein. In this paper, we establish…
The quantal algebra combines classical and quantum mechanics into an abstract structurally unified structure. The structure uses two products: one symmetric and one anti-symmetric. The local structure of spacetime is contained in the…
We prove a sharp gradient estimate for the natural Green's function of a closed manifold with positive Ricci curvature. We also show that this estimate is closely related to a family of monotonicity formulae. These results extend those…
In a recent paper \cite{1}, we have studied the vacuum solutions of Bianchi types I and V spacetimes in the framework of metric f(R) gravity. Here we extend this work to perfect fluid solutions. For this purpose, we take stiff matter to…
We prove some boundary rigidity results for the hemisphere under a lower bound for Ricci curvature. The main result can be viewed as the Ricci version of a conjecture of Min-Oo.