Related papers: Quasi-Topological Ricci Polynomial Gravities
In three spacetime dimensions, general relativity drastically simplifies, becoming a ``topological'' theory with no propagating local degrees of freedom. Nevertheless, many of the difficult conceptual problems of quantizing gravity are…
In this paper, I emphasize those features of the extended phase space approach to quantization of gravity that distinguish it among other approaches. First of all, it is the conjecture about non-trivial topology of the Universe which was…
We show that the system of vacuum Einstein equations (i.e., Ricci-flat metrics) with two hypersurface-orthogonal, commuting Killing vector fields in $d \ge 5$ dimensions is invariant under the action of a one-parameter Lie group, and the…
In this work we investigate Ricci flows of almost Kaehler structures on Lie algebroids when the fundamental geometric objects are completely determined by (semi) Riemannian metrics, or effective) regular generating Lagrange/ Finsler,…
Motivated by recent developments in the theory of gravitation, we revisit the idea of topological variations, originally introduced by Wheeler and Hawking, from a rigorous perspective. Starting from a localized version of the…
When tetrad (metric) fields are not invertible, the standard canonical formulation of gravity cannot be adopted as it is. Here we develop a Hamiltonian theory of gravity for non-invertible tetrad. In contrast to Einstein gravity, this phase…
We consider metric f(R) theories of gravity without mapping them to their scalar-tensor counterpart, but using the Ricci scalar itself as an "extra" degree of freedom. This approach avoids then the introduction of a scalar-field potential…
B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain diffeomorphism. We use this observation to…
We classify solutions to Einstein's equations in AdS with Ricci-flat boundary metric and with covariantly constant boundary stress tensor, which in general is not diagonalizable, i.e. it does not admit a reference frame. New solutions are…
The elliptic Einstein-DeTurck equation may be used to numerically find Einstein metrics on Riemannian manifolds. Static Lorentzian Einstein metrics are considered by analytically continuing to Euclidean time. Ricci-DeTurck flow is a…
We find that noncritical gravity, a special class of higher derivative gravity, is classically equivalent to Einstein gravity at the full nonlinear level. We obtain the viscosity-to-entropy ratio and the second order transport coefficients…
The possibility of the extension of spatial diffeomorphisms to a larger family of symmetries in a class of classical field theories is studied. The generator of the additional local symmetry contains a quadratic kinetic term and a potential…
We consider a concircularly semi-symmetric metric connection and its application. The Ricci tensors with respect to the concircularly semi-symmetric metric connection are symmetric, and they are used to define Einstein type manifolds. In…
The polynomial affine gravity is an alternative model of gravity whose fundamental field is the affine connection, and it is invariant under the complete group of diffeomorphisms. In 3+1 dimensions the field equations generalise those of…
In this paper, we mainly study left invariant pseudo-Riemannian Ricci-parallel metrics on connected Lie groups which are not Einstein. Following a result of Boubel and B\'{e}rard Bergery, there are two typical types of such metrics, which…
A $(3+1)$-dimensional Einstein-Gauss-Bonnet theory of gravity has been recently formulated in [D. Glavan and C. Lin, Phys. Rev. Lett. {\bf 124}, 081301 (2020)] which is different from the pure Einstein theory, i.e., bypasses the Lovelock's…
The topology change in quantum gravity is modeled by a Ricci flow. In this approach we offer to consider the Ricci flow as a statistical system. The metric in the Ricci flow enumerated by a parameter $\lambda$ is a microscopical statistical…
It is formulated a new 'anholonomic frame' method of constructing exact solutions of Einstein equations with off--diagonal metrics in 4D and 5D gravity. The previous approaches and results are summarized and generalized as three theorems…
As a contribution towards quantizing three-dimensional gravity, we show at the classical level that Euclidean three-dimensional Einstein gravity with a negative cosmological constant is uplifted to the $SU(2)$-invariant sector of…
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is…