Related papers: Geometric Obstructions on Gravity
Motivated by conventional gauge theories, we consider a theory of gravity in which the Einstein-Hilbert action is replaced by a term that is quadratic in the Riemann tensor. We focus on cosmological solutions to the field equations in flat,…
It is known that General Relativity ({\bf GR}) uses Lorentzian Manifold $(M_4;g)$ as a geometrical model of the physical space-time. $M_4$ means here a four-dimensional differentiable manifold endowed with Lorentzian metric $g$. The metric…
Riemannian geometry is a particular case of Hamiltonian mechanics: the orbits of the hamiltonian $H=\frac{1}{2}g^{ij}p_{i}p_{j}$ are the geodesics. Given a symplectic manifold (\Gamma,\omega), a hamiltonian $H:\Gamma\to\mathbb{R}$ and a…
Regularized Einstein-Gauss-Bonnet (EGB) theory of gravity in four dimensions is a new attempt to include nontrivial contributions of Gauss-Bonnet term. In this paper, we make a detailed analysis on possible constraints of the model…
We study the characteristic structure of the Einstein-Hilbert (EH) action when modifications of the form of $R^2,~ R_{\mu\nu}^2$, $R_{\mu\nu\rho\sigma}^2$ and $C_{\mu\nu\rho\sigma}^2$ are included. We show that when these quadratic terms…
The properties of the effective sigma-model for D-dimensional Einstein gravity based on multidimensional geometries is analyzed. Besides pure geometry, additional minimally coupled scalars and (p+2)-forms are considered which yield an…
Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ans\"atze. They therefore play no r\^ole in constructing these solutions, but can affect the…
Due to the presence of a gravitational anomaly in topologically massive gravity (TMG), the geometric entropy is no longer simply the Hubeny-Rangamani-Takayanagi (HRT) area; instead, it is given by the HRT area plus an anomalous…
In a former paper we proposed a model for the quantization of gravity by working in a bundle $E$ where we realized the Hamilton constraint as the Wheeler-DeWitt equation. However, the corresponding operator only acts in the fibers and not…
We consider the embedding theory, the approach to gravity proposed by Regge and Teitelboim, in which 4D space-time is treated as a surface in high-dimensional flat ambient space. In its general form, which does not contain artificially…
In four dimensions complexified General Relativity (GR) can be non-trivially deformed: There exists an (infinite-parameter) set of modifications all having the same count of degrees of freedom. It is trivial to impose reality conditions…
In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main…
In the tetrad formulation of gravity, the so-called simplicity constraints play a central role. They appear in the Hamiltonian analysis of the theory, and in the Lagrangian path integral when constructing the gravity partition function from…
We discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and develop ideas of Weyl, Eddington, and Einstein, in particular, Einstein's proposal to specify the space - time…
We show that that four dimensional conformal gravity plus a simple Neumann boundary condition can be used to get the semiclassical (or tree level) wavefunction of the universe of four dimensional asymptotically de-Sitter or Euclidean…
Valiant's famous determinant versus permanent problem is the flagship problem in algebraic complexity theory. Mulmuley and Sohoni (Siam J Comput 2001, 2008) introduced geometric complexity theory, an approach to study this and related…
We propose an exact Hamiltonian lattice theory for (2+1)-dimensional spacetimes with homogeneous curvature. By gauging away the lattice we find a generalization of the ``polygon representation'' of (2+1)-dimensional gravity. We compute the…
Certain peculiar features of Einstein-Hilbert (EH) action provide clues towards a holographic approach to gravity which is independent of the detailed microstructure of spacetime. These features of the EH action include: (a) the existence…
The Einsteinian Theory of Gravitation ("General Theory of Relativity") is founded essentially; on the reception that the geometrical properties of the 4-dimensional space-time continuum are defined from the matter in it. Contrary to this,…
This is the first paper in a series devoted to understanding the classical and quantum nature of edge modes and symmetries in gravitational systems. The goal of this analysis is to: i) achieve a clear understanding of how different…