Related papers: How Einstein Got His Field Equations
We review here the main contributions of Einstein to the quantum theory. To put them in perspective we first give an account of Physics as it was before him. It is followed by a brief account of the problem of black body radiation which…
We continue recent work and formulate the gravitational vacuum Einstein equations over a locally finite spacetime by using the basic axiomatics, techniques, ideas and working philosophy of Abstract Differential Geometry. The whole…
Exact time-dependent solutions of Einstein's gravitational field equation for a spherical mass moving with arbitrarily high constant velocity are derived and analyzed. The threshold conditions required for gravitational repulsion of…
We present a historical review of Einstein's 1917 paper 'Cosmological Considerations in the General Theory of Relativity' to mark the centenary of a key work that set the foundations of modern cosmology. We find that the paper followed as a…
As is well known, in order for the Einstein--Hilbert action to have a well defined variation, and therefore to be used for deriving field equation through the stationary action principle, it has to be amended by the addition of a suitable…
This note is based on a relatively unknown paper of Albert Einstein published in 1941 in the Revista de la Universidad Nacional de Tucuman. That work can be regarded as the prequel of the one written in 1943 in collaboration with Wolfgang…
In this work we propose a new procedure for to extract global information of a space-time. We considered a space-time immersed in a higher dimensional space and we formulate the equations of Einstein through of the Frobenius conditions to…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
The field equations of pre-geometric theories of gravity are derived and analysed, both without and with matter. After the spontaneous symmetry breaking that reduces the gauge symmetry of these theories \`a la Yang-Mills, a metric structure…
We derive the Einstein tensor from the Fisher information metric that is defined by the probability distribution of a statistical mechanical system. We find that the tensor naturally contains essential information of the energy-momentum…
A generalization of General Relativity is studied. The standard Einstein-Hilbert action is considered in the Palatini formalism, where the connection and the metric are independent variables, and the connection is not symmetric. As a result…
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 Ernst formulation of the Einstein equations is generalised to accommodate $f(R)$ theories of gravity. It is shown that, as in general relativity, the axisymmetric $f(R)$ field equations for a vacuum spacetime that is either stationary…
In 1917 F. Klein proposed his work on projective geometry to A. Einstein for further developments of general relativity. Klein had a peculiar way to consider the relationship between mathematics and physics, based on his Erlanger Programm…
General relativity is a set of physical and geometric principles, which lead to a set of (Einstein) field equations that determine the gravitational field, and to the geodesic equations that describe light propagation and the motion of…
The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field appears as gauge field. The problems on quantization and…
In this essay we marshal evidence suggesting that Einstein gravity may be an emergent phenomenon, one that is not ``fundamental'' but rather is an almost automatic low-energy long-distance consequence of a wide class of theories.…
In 1919 Einstein tried to solve the problem of the structure of matter by assuming that the elementary particles are held together solely by gravitational forces. In addition, Einstein also assumed the presence inside matter of…
Using the Einstein gravitation theory we show how to obtain the basic equations which predict the gravitational waves. This paper was written to graduate and post-graduate students of Physics. We deduce the equations didactically following…
The Einstein-Hilbert action (and thus the dynamics of gravity) can be obtained by combining the principle of equivalence, special relativity and quantum theory in the Rindler frame and postulating that the horizon area must be proportional…