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Fully covariant wave equations predict the existence of a class of inertial-gravitational effects that can be tested experimentally. In these equations inertia and gravity appear as external classical fields, but, by conforming to general…
We derive a general relation between the background effective actions, which directly proves that the two formulations of the Einstein-Hilbert theory with background fields are equivalent at the quantum level. This basic result has been…
We give a new expression for the supercurrent and its conservation in curved ${\cal N}=1$, $D=4$ superspace using the superconformal approach. The first component of the superfield, whose lowest component is the vector auxiliary field gives…
We give a linear response relation for perturbations in relativistic stars and classify them in terms of implicit and induced perturbations. The focus in this article is on the induced perturbations which may arise due to internal sources…
While loss-gain-induced Langevin noises have been intensively studied in quantum optics, the effect of a complex-valued nonlinear coupling coefficient on the noises of two coupled phase-conjugated optical fields has never been questioned…
The general idea to modify Einstein's field equations by promoting Newton's constant $G$ to a covariant differential operator $G_\Lambda(\Box_g)$ was apparently outlined for the first time in [12-15]. The modification itself originates from…
We derive the full set of field equations based on Hossenfelder's recent covariant formulation of the emergent gravity model, along with perturbative and exact solutions. The exact solution describes a static, spherically-symmetric…
We investigate the vacuum and charged spherically symmetric static solutions of the Einstein equations on cosmological background. The background metric is not flat, but curved, with constant - curvature spatial sections. Both vacuum and…
We consider a quantum scalar field on an arbitrary gravitational background. We obtain the effective {\it in-in} equations for the gravitational fields using a covariant and non-local approximation for the effective action proposed by…
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…
The semiclassical Einstein-Langevin equations which describe the dynamics of stochastic perturbations of the metric induced by quantum stress-energy fluctuations of matter fields in a given state are considered on the background of the…
A new solution of Einstein's vacuum field equations is discovered which appears as a generalization of the well-known Ozsvath-Schucking solution and explains its source of curvature which has otherwise remained hidden. Curiously, the new…
Exact time-dependent solutions of Einstein's gravitational field equation for a spherical mass moving with arbitrarily high constant velocity are derived and analyzed. The threshold conditions required for gravitational repulsion of…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
In the description of general covariance, the vierbein and the Lorentz connection can be treated as independent fundamental fields. With the usual gauge Lagrangian, the Lorentz connection is characterized by an asymptotically free running…
A formulation of Einstein's gravitational field equations in four space-time dimensions is presented using generalized differential forms and Cartan's equations for metric geometries. Cartan's structure equations are extended by using…
We construct the covariant nonlocal action for recently suggested long-distance modifications of gravity theory motivated by the cosmological constant and cosmological acceleration problems. This construction is based on the special…
We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…
We propose a revised formulation of General Relativity for cosmological settings, in which the Einstein constant varies with the energy density of the Universe. We demonstrate that this modification has only phenomenological impact of…
We investigate the background dynamics when dark energy is coupled to dark matter in the universe described by Einstein cosmology and Loop Quantum Cosmology. We introduce a new general form of dark sector coupling, which presents us a more…