Related papers: Einstein's aborted attempt at a dynamic steady-sta…
Based on some observations, the apparent energy, associated with gravity, of vacuums is defined, with that of normal vacuums to be zero and that of the vacuums losing some energy to be negative. An important application of the energy is its…
We consider steady state solutions of the massive, asymptotically flat, spherically symmetric Einstein-Vlasov system, i.e., relativistic models of galaxies or globular clusters, and steady state solutions of the Einstein-Euler system, i.e.,…
In 1939 Albert Einstein wrote a technical article that argued against the possibility that a star can be contracted to a single point: particles making up the star would end up rotating at velocities that were too high. In the same year,…
A new approach to the cosmological constant problem is proposed by modifying Einstein's theory of general relativity, using instead a scalar-tensor theory of gravitation. This theory of gravity crucially incorporates the concept of quantum…
In 1905, Einstein formulated his special relativity for point particles. For those particles, his Lorentz covariance and energy-momentum relation are by now firmly established. How about the hydrogen atom? It is possible to perform Lorentz…
We analyze the stability of the Einstein static universe by considering homogeneous scalar perturbations in the context of f(R) modified theories of gravity. By considering specific forms of f(R), the stability regions of the solutions are…
Had Einstein followed the Bianchi differential identity for the derivation of his equation of motion for gravitation, $\Lambda$ would have emerged as a true new constant of spacetime on the same footing as the velocity of light? It is then…
An elementary survey of mathematical cosmology is presented. We cover certain key ideas and developments in a qualitative way, from the time of the Einstein static universe in 1917 until today. We divide our presentation into four main…
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…
We are at a specific period of modern cosmology, during which the large increase of the amount of data leads to the idea that the determination of cosmological parameters has been achieved with a rather good precision. There is a large…
We consider the existence and stability of the Einstein static universe under the Generalized Uncertainty Principle (GUP) effects. We show that this solution in the presence of perfect fluid with a minimal length is cyclically stable around…
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…
Einstein's dream of describing elementary particles as solutions of a classical field theory is severely limited by our current understanding of Nature. Quantum theory is inconsistent with any local realistic theory such as evolving…
The stability of an Einstein static universe in the DGP braneworld scenario is studied in this paper. Two separate branches denoted by $\epsilon=\pm1$ of the DGP model are analyzed. Assuming the existence of a perfect fluid with a constant…
The quantum field theoretic prediction for the vacuum energy density leads to a value for the effective cosmological constant that is incorrect by between 60 to 120 orders of magnitude. We review an old proposal of replacing Einstein's…
This is an essay sketching the line of thinking which has led the present author to propose the constituent or atomic model of gravitation more than a decade ago. It turns out that viewing the problem of gravitation as a quantum many body…
Stability of the Einstein static universe versus the linear scalar, vector and tensor perturbations is investigated in the context of deformed Ho\v{r}ava-Lifshitz cosmology inspired by entropic force scenario. A general stability condition…
Reexamination of general relativistic experimental results shows the universe is governed by Einstein's static-spacetime general relativity instead of Friedmann-Lemaitre expanding-spacetime general relativity. The absence of expansion…
The 'hole argument'(the English translation of German 'Lochbetrachtung') was formulated by Albert Einstein in 1913 in his search for a relativistic theory of gravitation. The hole argument was deemed to be based on a trivial error of…
Within the framework of relativistic cosmology oscillating or cyclic models of the universe were introduced by A. Friedmann in his seminal paper of 1922. With the recognition of evolutionary cosmology in the 1930s this class of closed…