Related papers: Modified Einstein equations
The construction of conformally invariant gauge conditions for Maxwell and Einstein theories on a manifold M is found to involve two basic ingredients. First, covariant derivatives of a linear gauge (e.g. Lorenz or de Donder), completely…
Independent variation of the metric and connection in the Einstein-Hilbert action, called the Palatini variation, is generally taken to be equivalent to the usual formulation of general relativity in which only the metric is varied.…
Leading order gravitational corrections to the Einstein-Hilbert action can lead to a consistent picture of the universe by unifying the epochs of inflation and dark energy in a single framework. While the leading local correction induces an…
The bimetric variational principle is a subtle reinterpretation of general relativity that assumes the spacetime connection to be generated by an independent metric. Unlike the so called Palatini formalism that promotes the connection into…
We present an action principle formulation for the study of motion of an extended body in General Relativity in the limit of weak gravitational field. This gives the classical equations of motion for multipole moments of arbitrary order…
It is common knowledge that the Einstein-Hilbert action does not furnish a well-posed variational principle. The usual solution to this problem is to add an extra boundary term to the action, called a counter-term, so that the variational…
A Lagrange multiplier field restricts the quantum corrections to the Einstein-Hilbert action at one-loop order, yielding a model that is renormalizable and unitary while reproducing the Einstein field equations in the classical limit.
We study the generally covariant theory governing an isotropic spacetime region with uniform energy density. Gibbons, Hawking and York showed that fixing the induced boundary metric yields a well-posed variational problem. However, as we…
This paper has been withdrawn by the author after further work showed the proposed theoretical approach cannot fit planetary perihelion precession data. As presented, the theory doesn't fit gravitational light deflection by the sun either,…
The generalized uncertainty principle and a minimum measurable length arise in various theories of gravity and predict Planck-scale modifications of the canonical position-momentum commutation relation. Postulating a similar modified…
To explore the properties of space and initial singularities in the context of general relativity, where spacetime becomes poorly defined and no longer belongs to a regular manifold, we examine the evolution of the expansion of timelike…
Einstein's vierbein formulation of general relativity based on the notion of distant parallelism (teleparallelism) naturally introduces a covariant surface term in addition to the Einstein-Hilbert action. We investigate the action principle…
We study modifications of general relativity, GR, with nonlinear dispersion relations which can be geometrized on tangent Lorentz bundles. Such modified gravity theories, MGTs, can be modeled by gravitational Lagrange density functionals…
We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin,…
In the approach of the effective field theory of modified gravity, we derive the second-order action and the equation of motion for tensor perturbations on the flat isotropic cosmological background. This analysis accommodates a wide range…
It is known that a relative translational motion between the deflector and the observer affects gravitational lensing. In this paper, a lens equation is obtained to describe such effects on actual lensing observables. Results can be easily…
The problem of formulating synchronous variational principles in the context of General Relativity is discussed. Based on the analogy with classical relativistic particle dynamics, the existence of variational principles is pointed out in…
We study a non-commutative deformation of general relativity based on spectral invariants of a partial differential operator acting on sections of a vector bundle over a smooth manifold. We compute the first non-commutative corrections to…
The problem of eliminating divergences arising in quantum gravity is generally addressed by modifying the classical Einstein-Hilbert action. These modifications might involve the introduction of local supersymmetry, the addition of terms…
We argue that a conformally invariant extension of general relativity coupled to the Standard Model is the fundamental theory that needs to be quantized. We show that it can be treated by loop quantum gravity techniques. Through a gauge…