Related papers: Einstein Against Singularities: Analysis versus Ge…
Einstein's theory of general relativity models the physical universe using spacetimes which satisfy Einstein's gravitational field equations. To date, Einstein's theory has been enormously successful in modeling observed gravitational…
The historical and conceptual foundations of General Relativity are revisited, putting the main focus on the physical meaning of the invariant ds, the Equivalence Principle, and the precise interpretation of spacetime geometry. It is argued…
Singular spacetimes are a natural prediction of Einstein's theory. Most memorable are the singular centers of black holes and the big bang. However, dilatonic extensions of Einstein's theory can support nonsingular spacetimes. The…
Now that an English translation of Schwarzschild's original work exists, that work has become accessible to more people. Here his original solution to the Einstein field equations is examined and it is noted that it does not contain the…
In Einstein's general relativity, with its nonlinear field equations, the discoveries and analyzes of various specific explicit solutions made a great impact on understanding many of the unforeseen features of the theory. Some solutions…
As is well-known, Newton's gravitational theory can be formulated as a four-dimensional space-time theory and follows as singular limit from Einstein's theory, if the velocity of light tends to the infinity. Here 'singular' stands for the…
The recognition that physical space (or space-time) is curved is a product of the general theory of relativity, such as dramatically shown by the 1919 solar eclipse measurements. However, the mathematical possibility of non-Euclidean…
The issue of the physical equivalence between the different coordinate system in Einstein theory is revised. Gauge fixing influences results of measurements and physics are different in two different coordinate system. Spacetime metric…
The established way of looking at special relativity is based on Einstein postulates: the principle of relativity and the constancy of the velocity of light. In the most general geometric approach to the theory of special relativity, the…
Einstein regarded as one of the triumphs of his 1915 theory of gravity --- the general theory of relativity --- that it vindicated the action--reaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity…
This article presents a brief review of some historical and philosophical aspects of Einstein's 1917 paper 'Cosmological Considerations in the General Theory of Relativity', a landmark work that denoted the starting point of modern…
Non-static, spherically symmetric clusters of counter-rotating particles, of the type first introduced by Einstein, are analysed here. The initial data space can be parameterized in terms of three arbitrary functions, namely; initial…
Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate…
We report on some advances made in the problem of singularities in general relativity. First is introduced the singular semi-Riemannian geometry for metrics which can change their signature (in particular be degenerate). The standard…
Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular…
We show that the Schwarzschild solution can be embedded in a class of nonstandard solutions of the vacuum Einstein's equations with arbitrary rotation curves. These nonstandard solutions have to be taken as physical if dark matter as needed…
Einstein's theory of General Relativity is the benchmark example for empirical success and mathematical elegance in theoretical physics. However, in spite of being the most successfully tested theory in physics, there are strong theoretical…
Einstein algebra, the concept due to Geroch, is essentially general relativity in an algebraic disguise. We introduce the concept of Einstein-Grassmann algebra as a superalgebra (defining a supermanifold) which is also an Einstein algebra.…
Einstein's special theory of relativity starts with assumptions about how observations conducted in relatively moving inertial frames must compare. From these assumptions, conclusions can be drawn regarding the laws of physics in any one…
Using the accepted methods to extract natural system behavior from the Einstein-Hilbert gravitational field tensor equation, a new coordinate transformation is analyzed. It is demonstrated that these extraction methods yield specific…