Related papers: Validity of the Einstein Hole Argument
The two defining features of the Einsteinian gravity are that it is self interactive as well as it links universally to all particles including zero mass particles. In the process of obtaining the Schwarzshild solution for gravitational…
Einstein, when he began working on the general theory of relativity, believed that energy of any kind is the source of the gravitational field. Therefore, the energy of gravity, like any energy, must be the source of the field. It was…
We study two large classes of alternative theories, modifying the action through algebraic, quadratic curvature invariants coupled to scalar fields. We find one class that admits solutions that solve the vacuum Einstein equations and…
The Einstein postulates assert an invariance of the propagation speed of light in vacuum for any observer, and which amounts to a presumed absence of any preferred frame. The postulates appear to be directly linked to relativistic effects…
According to the Einstein, Weinberg, and M{\o}ller energy-momentum complexes, we evaluate the energy distribution of the singularity-free solution of the Einstein field equations coupled to a suitable nonlinear electrodynamics suggested by…
We review the underpinnings of the standard Newton-Einstein theory of gravity, and identify where it could possibly go wrong. In particular, we discuss the logical independence from each other of the general covariance principle, the…
This expository paper relates the Hole Argument in general relativity (GR) to the well-known theorem of Choquet-Bruhat and Geroch (1969) on the existence and uniqueness of globally hyperbolic solutions to the Einstein field equations. Like…
We review the experimental evidence for Einstein's special and general relativity. A variety of high precision null experiments verify the weak equivalence principle and local Lorentz invariance, while gravitational redshift and other clock…
The usual derivation of Einstein's field equations from the Einstein--Hilbert action is performed by silently assuming the metric tensor's symmetric character. If this symmetry is not assumed, the result is a new theory, such as Einstein's…
We show that the mass function method makes it much easier to obtain the exact solutions of Einstein equations. The known solutions for empty space and for the universe filled with dust-like matter are considered from the point of view of…
In his Autobiographical Notes, Einstein mentioned that on his road to the final theory of general relativity it was a major difficulty to accustom himself to the idea that coordinates need not possess an immediate physical meaning in terms…
We consider exact solutions of Einstein equations defining static black holes parametrized by off-diagonal metrics which by anholonomic mappings can be equivalently transformed into some diagonal metrics with coefficients being very similar…
Vigneron [Foundations of Physics, 54, 15, (2024)] recently proposed a modification of general relativity in which a non-dynamical term related to the spatial topology is introduced in the Einstein equation. The original motivation for this…
Every general relativity textbook emphasizes that coordinates have no physical meaning. Nevertheless, a coordinate choice must be made in order to carry out real calculations, and that choice can make the difference between a calculation…
By consideration of a Einstein-dilaton non-linear charged gravitating system, it has been shown that this theory is confronted with the problem of indeterminacy. It means that the number of independent differential equations is one less…
Extensions of Einstein gravity with higher-order derivative terms arise in string theory and other effective theories, as well as being of interest in their own right. In this paper we study static black-hole solutions in the example of…
According to the no-hair theorem, static black holes are described by a Schwarzschild spacetime provided there are no other sources of the gravitational field. This requirement, however, is in astrophysical realistic scenarios often…
A central idea in general relativity is that physics should not depend on the space-time coordinates in use \cite{einstein}. But the qualitative description of various phenomena can appear superficially quite different. Here we consider…
A new paradigm for black holes is introduced. It is known as the External Energy Paradigm. The paradigm asserts that all energies of a black hole are external quantities; they are absent inside the horizon. These energies include…
In this paper, we consider the problem of existence and uniqueness of solutions to the Einstein field equations for a spatially flat FLRW universe in the context of stochastic eternal inflation where the stochastic mechanism is modelled by…