Related papers: Moving Manifolds and General Relativity
We study the approach to gravity in which our curved spacetime is considered as a surface in a flat ambient space of higher dimension (the embedding theory). The dynamical variable in this theory is not a metric but an embedding function.…
Spatial curvature is one of the fundamental cosmological parameters that is routinely constrained from observations. The forward modelling of observations, in particular of large-scale structure, often relies on large cosmological…
Motivated by possible observations of the black hole candidate in the center of our galaxy and the galaxy M87, ray-tracing methods are applied to both standard General Relativity (GR) and a recently proposed extension, the pseudo-complex…
General relativity can be presented in terms of other geometries besides Riemannian. In particular, teleparallel geometry (i.e., curvature vanishes) has some advantages, especially concerning energy-momentum localization and its…
The Hamiltonian approach to General Relativity is developed similarly to the Wheeler-DeWitt Hamiltonian cosmology, where the cosmological scale factor is treated as a time-like dynamic variable and its canonical momentum is considered as an…
The gravitational field equations in general relativity (GR) consist of a sophisticated system of nonlinear partial differential equations. Solving such equations in some generic off-diagonal forms is usually a hard analytic or numeric…
We develop a generic spacetime model in General Relativity which can be used to build any gravitational model within General Relativity. The generic model uses two types of assumptions: (a) Geometric assumptions additional to the inherent…
A covariant reformulation of General Relativity is briefly considered from three points of view: geometrodynamics, Lagrange-Euler field theory, and gauge field theory. From a geometrodynamics perspective, a definition of the reference frame…
The canonical formulation of general relativity is based on decomposition space--time manifold $M$ into $ R\times \Sigma$, this decomposition has to preserve the invariance of general relativity, invariance under general coordinates, and…
Understanding the observations of dynamical tracers and the trajectories of lensed photons at galactic scales within the context of General Relativity (GR), requires the introduction of a hypothetical dark matter dominant component. The…
Relying on a fundamental empirical identity of heavy and inertial mass it is proposed to bring a status of general theory of relativity (GTR) of Einstein up to a level of Unified Field Theory. To do this, a thoroughgoing revision of…
Low density plasmas in curved spacetimes, such as those found in accretion flows around black holes, are challenging to model from first principles, owing to the large scale separation between the characteristic scales of the microscopic…
The discovery of the accelerated expansion of the universe highlighted General Relativity's inability to naturally account for dark energy without invoking a finely tuned cosmological constant. In response, a wide range of alternative…
Singularities in Newton's gravitation, in general relativity (GR), in Coulomb's law, and elsewhere in classical physics, stem from two ill conceived assumptions: a) there are point-like entities with finite masses, charges, etc., packed in…
A new geometry, called General geometry, is constructed. It is proven that its the most simplest special case is geometry underlying Electromagnetism. Another special case is Riemannian geometry. Action for electromagnetic field and Maxwell…
General Relativity (GR) was proven via the direct detection of gravitational waves from the mergers of the binary black holes and binary neutron stars by the Advanced LIGO and Advanced Virgo detectors. These detections confirmed the…
This work is the extension of author`s research, where the modified theory of induced gravity (MTIG) is proposed. The theory describes two systems (stages): Einstein (ES) and "restructuring" (RS). We consider equations with quadratic…
This work presents the foundations of Singular Semi-Riemannian Geometry and Singular General Relativity, based on the author's research. An extension of differential geometry and of Einstein's equation to singularities is reported.…
The smooth gravitational singularities of the differential spacetime manifold based General Relativity (GR) are viewed from the perspective of the background manifold independent and, in extenso, Calculus-free Abstract Differential Geometry…
In this paper we study how to include the cosmological constant in geometric scalar theory of gravity (GSG). Firstly we show that the cosmological constant could not be modeled by a matter field, unlike in General Relativity. We also show…