e article is a tribute to Hermann Minkowski leading from his geometry of numbers to an attempt at using Finsler geometry for a break of Lorentz invariance.

Ya.B. Zeldovich was a pre-eminent Soviet physicist whose seminal contributions spanned many fields ranging from physical chemistry to nuclear and particle physics, and finally astrophysics and cosmology. March 8, 2014 marks Zeldovich’s birth centenary, and this article attempts to convey the zest with which Zeldovich did science, and the important role he played in fostering and mentoring a whole generation of talented Scientists.

The objective of this paper is not simply to present an historical overview of Einstein’s cosmological considerations, but to discuss the central role they played in shaping the paradigm of relativistic cosmology. This, we’ll show, was a result of both his actions and, perhaps more importantly, his inactions. Accordingly, discussion won’t simply be restricted to Einstein’s considerations, as we’ll analyse relevant contributions to the relativistic expansion paradigm during the approximately twenty years following Slipher’s first redshift measurements in 1912.

We review and strengthen the arguments given by Einstein to derive his first gravitational field equation for static fields and show that, although it was ultimately rejected, it follows from General Relativity (GR) for negligible pressure. Using this equation and considerations folowing directly from the equivalence principle (EP), we show how Schwarzschild metric and other vacum metrics can be obtained immediately. With this results and some basic principles, we obtain the metric in the general spherically symmetric case and the corresponding hydrostatic equilibrium equation. For this metrics we obtain the motion equations in a simple and exact manner that clearly shows the three sources of difference (implied by various aspects of the EP) with respect to the Newtonian case and use them to study the classical tests of GR.

The QBist view of science, first put forth to dispel the fog from quantum foundations, also clears up a longstanding puzzle in classical physics.

This article has a dual purpose: i) to provide a flavor of the scientific highlights of the landmark conference, GR3, held in July 1962 at Jablonna, near Warsaw; and, ii) to present a bird’s eye view of the tremendous advances that have occurred over the half century that separates GR3 and GR20, which was again held in Warsaw in July 2013.

Julian Schwinger (1918–1994), founder of renormalized quantum electrodynamics, was arguably the leading theoretical physicist of the second half of the 20th century. Thus it is not surprising that he made contributions to gravity theory as well. His students made major impacts on the still uncompleted program of constructing a quantum theory of gravity. General Relativity and Quantum Cosmology (gr-qc) himself had no doubt of the validity of general relativity, although he preferred a particle-physics viewpoint based on gravitons and the associated fields, and not the geometrical picture of curved spacetime. This note provides a brief summary of his contributions and attitudes toward the subject of gravity.

Starting from a short review of the «classical» space problem in the sense of the 19th century (Helmholtz — Lie — Klein) it is discussed how the challenges posed by special and general relativity to the classical analysis were taken up by Hermann Weyl and Elie Cartan. Both mathematicians reconsidered the space problem from the point of view of transformations operating in the infinitesimal neighbourhoods of a manifold (spacetime). In a short outlook we survey further developments in mathematics and physics of the second half of the 20th century, in which core ideas of Weyl’s and/or Cartan’s analysis of the space problem were further investigated (mathematics) or incorporated into basic theories (physics).

Shannon’s notion of relative information between two physical systems can function as foundation for statistical mechanics and quantum mechanics, without referring to subjectivism or idealism. It can also represent a key missing element in the foundation of the naturalistic picture of the world, providing the conceptual tool for dealing with its apparent limitations. I comment on the relation between these ideas and Democritus.

This is one chapter of the collection of problems in cosmology, in which we assemble the problems that concern one of the most distinctive features of general relativity and cosmology—the horizons. The first part gives an elementary introduction into the concept in the cosmological context, then we move to more formal exposition of the subject and consider first simple, and then composite models, such as Λ CDM. The fourth section elevates the rigor one more step and explores the causal structure of different simple cosmological models in terms of conformal diagrams. The section on black holes relates the general scheme of constructing conformal diagrams for stationary black hole spacetimes. The consequent parts focus on more specific topics, such as the various problems regarding the Hubble sphere, inflation and holography.
This version contains only formulations of 97 problems. The full collection, with solutions included, is available in the form of a wiki-based resource at this http URL The cosmological community is welcome to contribute to its development.