Related papers: Degravitation and the relaxed Einstein equations
We discuss recently introduced scale-free Einstein equations, where the information from their trace part is lost. These equations are classically equivalent to General Relativity, yet the Newton constant becomes a constant of integration…
Starting with Newton's law of universal gravitation, we generalize it step-by-step to obtain Einstein's geometric theory of gravity. Newton's gravitational potential satisfies the Poisson equation. We relate the potential to a component of…
We propose a new generalisation of general relativity which incorporates a variation in both the speed of light in vacuum (c) and the gravitational constant (G) and which is both covariant and Lorentz invariant. We solve the generalised…
We employ the gravitational decoupling approach for static and spherically symmetric systems to develop a simple and powerful method in order to a) continuously isotropize any anisotropic solution of the Einstein field equations, and b)…
Like the Lovelock Lagrangian which is a specific homogeneous polynomial in Riemann curvature, for an alternative derivation of the gravitational equation of motion, it is possible to define a specific homogeneous polynomial analogue of the…
One of the leading issues in quantum field theory and cosmology is the mismatch between the observed and calculated values for the cosmological constant in Einstein's field equations of up to 120 orders of magnitude. In this paper, we…
We present a covariant multisymplectic formulation for the Einstein-Hilbert model of General Relativity. As it is described by a second-order singular Lagrangian, this is a gauge field theory with constraints. The use of the unified…
Based on investigations of the fundamental properties of the generalized Einstein Lagrangian density for a gravitational system, the theoretical foundations of the modified Einstein field equations and the Lorentz and Levi-Civita…
We use an important decoupling property of gravitational field equations in the general relativity theory and modifications, written with respect to nonholonomic frames with 2+2 spacetime decomposition. This allows us to integrate the…
We investigate infrared dynamics of four-dimensional Einstein gravity in de Sitter space. We set up a general framework to investigate dynamical scaling relations in quantum/classical gravitational theories. The conformal mode dependence of…
We construct a model for noncommutative gravity in four dimensions, which reduces to the Einstein-Hilbert action in the commutative limit. Our proposal is based on a gauge formulation of gravity with constraints. While the action is metric…
We explore possible cosmological consequences of a running Newton's constant $ G ( \Box ) $, as suggested by the non-trivial ultraviolet fixed point scenario in the quantum field-theoretic treatment of Einstein gravity with a cosmological…
A special class of conformal gravity theories is proposed to solve the long standing problem of the fine-tuned cosmological constant. In the proposed model time evolution of the inflaton field leaves behind a nearly vanishing, but finite…
From the Einstein field equations, in a weak-field approximation and for speeds small compared to the speed of light in vacuum, the following system is obtained \begin{align*} \nabla \times \overrightarrow{E_g} & = -\frac{1}{c}…
This thesis studies modified theories of gravity from a geometric viewpoint. We review the motivations for considering alternatives to General Relativity and cover the mathematical foundations of gravitational theories in Riemannian and…
The content of Einstein's theory of gravitation is encoded in the properties of the solutions to his field equations. There has been obtained a wealth of information about these solutions in the ninety years the theory has been around. It…
We investigate a simple variation of the Generalized Harmonic method for evolving the Einstein equations. A flat space wave equation for metric perturbations is separated from the Ricci tensor, with the rest of the Ricci tensor becoming a…
The new scale-covariant formulation of the Dirac's Large Number Hypothesis (LNH) is proposed. The basic equations of LNH are formulated in the scale-covariant and "G-invariant" (invariant on the transformation law for G) form. On the basis…
The Maxwell extension of the conformal algebra is presented. With the help of gauging the Maxwell-conformal group, a conformally invariant theory of gravity is constructed. In contrast to the conventional conformally invariant actions, our…
Certain features associated with the symmetry reduction of the vacuum Einstein equations by two commuting, space-like Killing vector fields are studied. In particular, the discussion encompasses the equations for the Gowdy $T^3$ cosmology…