Related papers: Realization of Einsteins Machian Program
In this note we prove that the version of Newton algorithm with line search we used in [2] converges quadratically.
The "Newtonian" or non-relativistic decomposition of Einstein's gravitational field is useful in the post-Newtonian approximation. We obtain the full non-quadratic Einstein-Hilbert action in terms of these fields as well as the harmonic…
Here we describe a stationary cylindrically symmetric solution of Einstein's equation with matter consisting of a positive cosmological and rotating dust term. The solution approaches Einstein static universe solution.
There are many ways of embedding a 4D spacetime in a given higher-dimensional manifold while, satisfying the field equations. In this work we extend and generalize a recent paper by Mashhoon and Wesson ({\it Gen. Rel. Gravit.} {\bf 39},…
Computer programs may go wrong due to exceptional behaviors, out-of-bound array accesses, or simply coding errors. Thus, they cannot be blindly trusted. Scientific computing programs make no exception in that respect, and even bring…
We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared…
In this paper Einstein develops some crucial ideas about superconductivity
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 produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products…
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…
In this paper the circulant Hadamard conjecture is proved.
We prove several extensions of the Erdos-Fuchs theorem.
The invariant subspace problem is solved correcting my earlier attempts [6]-[12].
We establish a regularity theorem for the Harmonic - Einstein Equation. As a byproduct of the local regularity, we also have a compactness theorem on Harmonic - Einstein equation. The method is mainly the Moser iteration technique which has…
We prove that any compact complex surface with positive first Chern class admits an Einstein metric which is conformally related to a Kaehler metric. The key new ingredient is the existence of such a metric on the blow-up of the complex…
We formalize the multi-graded Proj construction in Lean4, illustrating mechanized mathematics and formalization.
Remarks on mathematical proof and the practice of mathematics.
We construct new examples of Einstein metrics by perturbing the conformal infinity of geometrically finite hyperbolic metrics and by applying the inverse function theorem in suitable weighted H\"older spaces.
In this paper we consider the coupled system given by the first variation of the conformal Dirac-Einstein functional. We will show existence of solutions by means of perturbation methods.
Motivated by integrability of the sine-Gordon equation, we investigate a technique for constructing desired solutions to Einstein's equations by combining a dressing technique with a control-theory approach. After reviewing classical…