Related papers: A fresh look at boundary terms in Einstein-Hilbert…
The Weiss variational principle in mechanics and classical field theory is a variational principle which allows displacements of the boundary. We review the Weiss variation in mechanics and classical field theory, and present a novel…
An earlier proposed theory with linear-gonihedhic action for quantum gravity is reviewed. One can consider this theory as a "square root" of classical gravity with a new fundamental constant of dimension one. We demonstrate also, that the…
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,…
A nonpertubative approach to quantum gravity using precanonical field quantization originating from the covariant De Donder-Weyl Hamiltonian formulation which treats space and time variables on equal footing is presented. A generally…
A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant…
The two surprising features of gravity are (a) the principle of equivalence and (b) the connection between gravity and thermodynamics. Using principle of equivalence and special relativity in the {\it local inertial frame}, one could obtain…
Gravity is derived from an entropic action coupling matter fields with geometry. The fundamental idea is to relate the metric of Lorentzian spacetime to a quantum operator, playing the role of an renormalizable effective density matrix and…
A well-defined variational principle for gravitational actions typically requires to cancel boundary terms produced by the variation of the bulk action with a suitable set of boundary counterterms. This can be achieved by carefully…
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 shown that in a quadratic gravity based on Weyl's conformal geometry, not only the Einstein-Hilbert action emerges but also a Weyl gauge field becomes massive in the Weyl gauge condition, $\tilde R = k$, for a Weyl gauge symmetry…
We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincar\'e group, taken as…
In the derivation of the Einstein field equations via Hamilton's principle, the inclusion of a boundary term is essential to render the variational problem well-posed, as it addresses variations that do not vanish at the boundary of the…
We briefly discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and generalize Einstein's proposal to specify the space-time geometry by use of the Hamilton principle to…
In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a…
We study the semiclassical Einstein field equations with a Klein-Gordon field in ultrastatic and static spacetimes. In both cases, the equations for the spacetime metric become constraint equations. In the ultrastatic case, the Hadamard…
The present article deals with a formulation of the so called (vacuum) Palatini gravity as a general variational principle. In order to accomplish this goal, some geometrical tools related to the geometry of the bundle of connections of the…
Modified gravity theories such as Einstein scalar Gauss Bonnet (EsGB) contain higher derivative terms in the spacetime curvature in their action, which results in modifications to the Hamiltonian and momentum constraints of the theory. In…
The characteristic initial (boundary) value problem has numerous applications in general relativity (GR) involving numerical studies, and is often formulated using Bondi-like coordinates. Recently it was shown that several prototype…
We make a rigorous study of classical field equations on a 2-dimensional signature changing spacetime using the techniques of operator theory. Boundary conditions at the surface of signature change are determined by forming self-adjoint…
The framework of a theory of gravity from the quantum to the classical regime is presented. The paradigm shift from full spacetime covariance to spatial diffeomorphism invariance, together with clean decomposition of the canonical…