Related papers: Remarks on "singularities"
An introduction to extended theories of gravity formulated in metric-affine (or Palatini) spaces is presented. Focusing on spherically symmetric configurations with electric fields, we will see that in these theories the central singularity…
An attempt is made in order to clarify the so called regular black holes issue. It is revisited that if one works within General Relativity minimally coupled with non linear source, mainly of electromagnetic origin, and within a static…
How do the global properties of a Lorentzian manifold change when endowed with a vector field? This interesting question is tackled in this paper within the framework of Einstein-Aether (EA) theory which has the most general…
The introduction of General Relativity (GR) in 1915 revolutionized our understanding of gravity, but over time, its limitations in explaining phenomena like dark energy, dark matter, and quantum gravity have motivated alternative theories.…
In the current relativistic literature there are misleading considerations about some singular surfaces. An accurate geometric analysis allows to settle the question. No physical meaning is attributable to the spatial regions surrounded by…
We show that the term `superdifferential equation' has been employed in the literature to refer to different types of differential equations with even and odd variables. It is justified on physical and mathematical grounds that a subclass…
The Vector-Tensor (VT) theories of gravity are a class of alternative theories to General Relativity (GR) that are characterized by the presence of a dynamical vector field besides the metric. They are studied in attempts to understand…
General Relativity (GR) exists in different formulations, which are equivalent in pure gravity. Once matter is included, however, observable predictions generically depend on the version of GR. In order to quantify the resulting ambiguity,…
We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets…
Einstein's General Relativity (GR) is a dynamical theory of the spacetime metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearised level and show how a gauge theoretic Lagrangian for…
Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such…
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…
The issue of the transformations of units is treated, mainly, in a geometrical context. It is shown that Weyl-integrable geometry is a consistent framework for the formulation of the gravitational laws since the basic law on which this…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
We define the concept of self-similarity of an object by considering endomorphisms of the object as `similarity' maps. A variety of interesting examples of self-similar objects in geometry, algebra and arithmetic are introduced.…
The problem of formation of generic structures in the Universe is addressed, whereby first the kinematics of inertial continua for coherent initial data is considered. The generalization to self--gravitating continua is outlined focused on…
I have shown that the field defined by the Wheeler-DeWitt equation for \textit{pure gravity} is neither a standard gravitational field nor the field representing a particular universe. The theory offers a unified description of geometry and…
Many theories of gravity admit formulations in different, conformally related manifolds, known as the Jordan and Einstein conformal frames. Among them are various scalar-tensor theories of gravity and high-order theories with the Lagrangian…
We discuss new models of an `affine' theory of gravity in multidimensional space-times with symmetric connections. We use and develop ideas of Weyl, Eddington, and Einstein, in particular, Einstein's proposal to specify the space - time…
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…