Related papers: Einstein's first gravitational field equation 101 …
In Einstein's equation we suggest a geometrical object substituting the tensor of energy of impulse and tension. The obtained equation, together with the equation for external field, makes up the complete problem of mathematical equations…
It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle.…
The main purpose of the present paper is to show that a correction of one mistake was crucial for Einstein's pathway to the first version of the 1915 general theory of relativity, but also might have played a role in obtaining the final…
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…
General Relativity is today the best theory of gravity addressing a wide range of phenomena. Our understanding of physical laws, from cosmology to local scales, cannot be properly formulated without taking into account it. It is based on…
The rotational metric provides an exact solution to Einstein's clock-rate problem in curved spacetime, specifically, whether time flows more slowly at the equator of a compact object such as a neutron star than at its poles. It features a…
In this paper we consider a thought experiment involving the effect of gravitation on an ideal scale containing a photon. If the tidal forces inherent to a gravitational field are neglected, then one is led to scenario which seems to bring…
A general principle of non-equivalence for bodies and observers in different G potentials (GP) was derived from correspondence of the Einstein's equivalence principle either with optical physics or with gravitational experiments in which…
Following Einstein's definition of Lagrangian density and gravitational field energy density (Einstein, A., Ann. Phys. Lpz., 49, 806 (1916); Einstein, A., Phys. Z., 19, 115 (1918); Pauli, W., {\it Theory of Relativity}, B.I. Publications,…
Spacetimes generated by a lightlike particle source for topologically massive gravity and its limits - Einstein gravity and the pure gravitational Chern-Simons model - are obtained both by solving the field equations and by infinite boosts…
Does relativistic gravity provide arguments against the existence of a preferred frame? Our answer is negative. We define a viable theory of gravity with preferred frame. In this theory, the EEP holds exactly, and the Einstein equations of…
We first review the equivalence theorem of the f(R)-type gravity to Einstein gravity with a scalar field by deriving it in a self-contained and pedagogical way. Then we describe the problem of to what extent the equivalence holds. Main…
The starting point of quantum mechanics is the relationship between energy and momentum: energy is proportional to the squared momentum! As a result, energy and momentum have not been treated equally. The wave equation required by…
In the general relativity theory the basic ingredient to describe gravity is the geometry, which interacts with all forms of matter and energy, and as such, the metric could be interpreted as a true physical quantity. However the metric is…
Cosmological observations indicate that the Einstein equation may not be entirely correct to describe gravity. However, numerous modifications of these equations usually do not affect foundations of the theory. In this paper two important…
In Einstein theory of gravity the initial configuration of metric field and its time derivative are related to matter configuration by four equations called constraints. We use the method of conformal metrics (York Method) to solve…
It is well known that Einstein's General Relativity (GR) achieved a great success and overcame lots of experimental tests. On the other hand, GR also showed some shortcomings and flaws which today advise theorists to ask if it is the…
Communication by K. Schwarzschild to the Prussian Academy of Sciences, dealing with the gravitational field of a sphere of incompressible fluid.
Einstein regarded as one of the triumphs of his 1915 theory of gravity --- the general theory of relativity --- that it vindicated the action--reaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity…
Starting from first principles and general assumptions Newton's law of gravitation is shown to arise naturally and unavoidably in a theory in which space is emergent through a holographic scenario. Gravity is explained as an entropic force…