Related papers: Luis Santal\'o and classical field theory
Albert Einstein's journey to formulate the theory of general relativity involved significant shifts in his approach to gravitational field equations. Starting in 1912, he collaborated with Marcel Grossmann and initially explored broadly…
In the early phase of general relativity Elie Cartan and Hermann Weyl thought about the question of how the role of transformation groups could be transferred from classical geometry (Erlangen program) to differential geometry. They had…
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…
Was Einstein wrong? This paper provides a detailed technical review of Einstein's special and general relativity from an astrophysical perspective, including the historical development of the theories, experimental tests, modern…
The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed in recent work (collaboration with H.…
I provide a very brief sketch of some of Dirac's interests and work in gravity, particularly his Hamiltonian formulation of Einstein's theory and its relation to his earlier research.
We provide an introduction to selected recent advances in the mathematical understanding of Einstein's theory of gravitation.
One century after its formulation, Einstein's general relativity has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are…
In 1918, H. Weyl proposed a unified theory of gravity and electromagnetism based on a generalization of Riemannian geometry. In spite of its elegance and beauty, a serious objection was raised by Einstein, who argued that Weyl's theory was…
In previous works we have considered various aspects of the reception of the theories of Albert Einstein in our country. In particular, we discussed the impact of his visit to Argentina in 1925, and the precise content of the conferences…
The unification of electricity and magnetism achieved by special relativity has remained for decades a model of unification in theoretical physics. We discuss the relationship between electric and magnetic fields from a classical point of…
We sketch the foundations of classical electrodynamics, in particular the transition that took place when Einstein, in 1915, succeeded to formulate general relativity. In 1916 Einstein demonstrated that, with a choice of suitable variables…
Three thinkers of the 19th century revolutionized the science of logic, mathematics, and philosophy. Edmund Husserl (1859-1938), mathematician and a disciple of Karl Weierstrass, made an immense contribution to the theory of human thought.…
The main purpose of this paper is to analyse the earliest work of L\'eon Rosenfeld, one of the pioneers in the search of Quantum Gravity, the supposed theory unifying quantum theory and general relativity. We describe how and why Rosenfeld…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The…
In 1919 A. Einstein suspected first that gravitational fields could play an essential role in the structure of elementary particles. In 1937, P.A.M. Dirac found a miraculous link between the properties of the visible Universe and elementary…
We review the physics at the end of the nineteenth century and summarize the process of the establishment of Special Relativity by Albert Einstein in brief. Following in the giant's footsteps, we outline the scientific method which helps to…
In this survey we recognize Enrique Arrondo's contributions over the whole of its career, recalling his professional history and collecting the results of his mathematical production.
We summarize the main ideas of General Relativity and Lorentzian geometry, leading to a proof of the simplest of the celebrated Hawking-Penrose singularity theorems. The reader is assumed to be familiar with Riemannian geometry and point…
In 1945 Einstein concluded that [1]: 'The present theory of relativity is based on a division of physical reality into a metric field (gravitation) on the one hand, and into an electromagnetic field and matter on the other hand. In reality…