Related papers: Finding and using exact solutions of the Einstein …
Einstein's general relativity is the best available theory of gravity. In recent years, spectacular proofs of Einstein's theory have been conducted, which have aroused interest that goes far beyond the narrow circle of specialists. The aim…
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 solution generating methods discovered earlier for integrable reductions of Einstein's and Einstein - Maxwell field equations (such as soliton generating techniques, B$\ddot{a}$cklund or symmetry transformations and other…
We establish an algorithm that produces a new solution to the Einstein field equations, with an anisotropic matter distribution, from a given seed isotropic solution. The new solution is expressed in terms of integrals of known functions,…
We present a basics of the Einstein General Theory of Relativity. In the first part of this review we derive relations of Riemann geometry which are used in the General Relativity. In the second part we discuss Einstein Equations and some…
From modern observations of gravitational interactions, it can be inferred that there is much left to discover about the fundamental gravitational field. Since the advent of the General Theory of Relativity over a century ago, we have come…
We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.
In Einstein's equation we suggest a geometrical object substituting the tensor of energy of impulse and tension. The obtained equation, together with the equation for external field, makes up the complete problem of mathematical equations…
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…
The Einstein-Maxwell (or Einstein) system of field equations plays a substantial role in the modeling of compact stars. Although due to its non-linearity getting an exact solution for the system of field equations is a difficult task, the…
We present a simple method to obtain vacuum solutions of Einstein's equations in parabolic coordinates starting from ones with cylindrical symmetries. Furthermore, a generalization of the method to a more general situation is given together…
Relativistic field equations for a gas in special and general relativity are determined from the Boltzmann equation. The constitutive equations are obtained from the Chapman-Enskog methodology applied to a relativistic model equation…
We review recent mathematical results concerning the high-frequency solutions to the Einstein vacuum equations and the limits of these solutions. In particular, we focus on two conjectures of Burnett, which attempt to give an exact…
This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with…
Rigorous results on solutions of the Einstein-Vlasov system are surveyed. After an introduction to this system of equations and the reasons for studying it, a general discussion of various classes of solutions is given. The emphasis is on…
The nature of gravity is fundamental to understand the scaffolding of the Universe and its evolution. Einstein's general theory of relativity has been scrutinized for over ninety five years and shown to describe accurately all phenomena…
We show that the mass function method makes it much easier to obtain the exact solutions of Einstein equations. The known solutions for empty space and for the universe filled with dust-like matter are considered from the point of view of…
In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well known cone solution, which is locally…
The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split…
Modifications of Einstein's theory of gravitation have been extensively considered in the past years, in connection to both cosmology and quantum gravity. Higher-curvature and higher-derivative gravity theories constitute the main examples…