相关论文: Reformulation of Einstein equations in the Fully C…
We prove existence and uniqueness of solutions of the semiclassical Einstein equation in flat cosmological spacetimes driven by a quantum massive scalar field with arbitrary coupling to the scalar curvature. In the semiclassical…
We consider solutions of the Einstein equations with cosmological constant $\Lambda\neq 0$ admitting conformal compactification with smooth scri $\mathscr{I^+}$. Metrics are written in the Bondi-Sachs coordinates and expanded into inverse…
We complete the visible, hidden, sectorial, and discrete symmetries of Ernst-like potential spaces in stationary, axisymmetric Einstein-Maxwell-Scalar Field (EMSF) and Einstein-ModMax-Scalar Field (EMMSF) theories. In the real potential…
By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a…
We present a theory of gravity based on Einstein's general relativity that is motivated by the paradoxes associated with time in relativistic rotating frames and certain exact solutions of Einstein's equations. We show that we can resolve…
In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these…
This article, written to appear as a chapter in "The Springer Handbook of Spacetime", is a review of the initial value problem for Einstein's gravitational field theory in general relativity. Designed to be accessible to graduate students…
The aim of this paper is to find higher order geometrical corrections to the Einstein-Hilbert action that can lead to only second order equations of motion. The metric formalism is used, and static spherically symmetric and…
We consider nonlocal modification of the Einstein theory of gravity in framework of the pseudo-Riemannian geometry. The nonlocal term has the form $\mathcal{H}(R) \mathcal{F}(\Box)\mathcal {G}(R)$, where $\mathcal{H}$ and $\mathcal{G}$ are…
It seems likely that the generalized Einstein equations are not complete and only partly account for the effect on the Universe dynamics of that part of the energy of the space environment the change of which is purely geometric. There are…
The flat/CFT dictionary between the bulk gravitational theory and boundary conformal field theory is systematically developed in this paper. Asymptotically flat spacetime is built up by asymptotically AdS hyperboloid slices in terms of…
We study the appearance of multiple solutions to certain decompositions of Einstein's constraint equations. Pfeiffer and York recently reported the existence of two branches of solutions for identical background data in the extended…
This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been…
This review examines the role of differential forms, Pfaffian systems, and hypersurfaces in general relativity. These mathematical constructions provide the essential tools for general relativity, in which the curvature of…
Using techniques from singular perturbation theory, we explicitly calculate the cosmological evolution in a class of modified gravity models. By considering the (m)CDTT model, which aims to explain the current acceleration of the universe…
We prove local existence of solutions to the Einstein--null dust system under polarized $\mathbb U(1)$ symmetry in an elliptic gauge. Using in particular the previous work of the first author on the constraint equations, we show that one…
The most general vacuum solution to Einstein's field equations with no incoming radiation can be constructed perturbatively from two infinite sets of canonical multipole moments, which are found to be mapped into each other under…
The Eddington Lagrangian in the purely affine formulation of general relativity generates the Einstein equations with the cosmological constant. The Ferraris-Kijowski purely affine Lagrangian for the electromagnetic field, which has the…
We continue recent work and formulate the gravitational vacuum Einstein equations over a locally finite spacetime by using the basic axiomatics, techniques, ideas and working philosophy of Abstract Differential Geometry. The whole…
This research is an extension of the author's article \cite{zar}, in which conformally invariant generalization of string theory was suggested to higher-dimensional objects. Special cases of the proposed theory are Einstein's theory of…