Related papers: Remarks on "singularities"
We solve the problem on flat extensions of a generic surface with boundary in Euclidean 3-space, relating it to the singularity theory of the envelope generated by the boundary. We give related results on Legendre surfaces with boundaries…
Alternatives to Einstein's theory of general relativity can be distinguished by measuring the parametrised post Newtonian parameters. Two such parameters $\beta$ and $\gamma$, equal to one in Einstein theory, can be obtained from static…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
This thesis deals with the problem of singularities in a family of extensions of General Relativity in the Metric-Affine formalism. I introduce the Metric-Affine formalism as a framework in which study extensions of GR. I review its…
What is the nature - continuous or discrete - of matter and of its fundamental interactions? The physical meaning, the properties and the consequences of a discrete scalar field are discussed; limits for the validity of a mathematical…
The curvature singularity in viable f(R) gravity models is examined when the background density is dense. This singularity could be eliminated by adding the $R^{2}$ term in the Lagrangian. Some of cosmological consequences, in particular…
The new approach to quantize the gravity based on the notion of differential algebra is suggested. It is shown that the differential geometry of this object can not be described in terms of points. The spatialization procedure giving rise…
In General Relativity a space-time $M$ is regarded singular if there is an obstacle that prevents an incomplete curve in $M$ to be continued. Usually, such a space-time is completed to form $\bar{M} = M \cup \partial M$ where $\partial M$…
A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the positions and orientations of the…
Our assumption that spacetime is a continuum leads to many challenges in mathematical physics. Singularities, divergent integrals and the like threaten many of our favorite theories, from Newtonian gravity to classical electrodynamics,…
We show that the phase transition previously observed in dynamical triangulation models of quantum gravity can be understood as being due to the creation of a singular link. The transition between singular and non-singular geometries as the…
Here we discuss direct links of the number of fundamental dimensions to the fundamental natural constants using simple arguments of dimensional analysis \corr{based on Maxwell's dimensions length (L), time (T) and mass (M) as well as the…
It has become obvious that certain singular phenomena cannot be explained by a mere investigation of the configuration space, defined as the solution set of the loop closure equations. For example, it was observed that a particular 6R…
The algebra and calculus of generalized differential forms are reviewed and employed to construct a class of generalized connections and to investigate their properties. The class includes generalized connections which are flat when…
Suppose a Lagrangian is constructed from its fields and their derivatives. When the field configuration is a distribution, it is unambiguously defined as the limit of a sequence of smooth fields. The Lagrangian may or may not be a…
Contemporary relativity theory is restricted in two points: (1) a use of the Riemannian space-time geometry and (2) a use of inadequate (nonrelativistic) concepts. Reasons of these restrictions are analysed in [1]. Eliminating these…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
Singularity theorems demonstrate the inevitable breakdown of the concept of continuous, classical spacetime under highly general conditions. Quantum gravity is expected to intervene to avoid singularities and models so far hint towards…
It is known that in f(R) theories of gravity with an independent connection which can be both non-metric and non symmetric, this connection can always be algebraically eliminated in favour of the metric and the matter fields, so long as it…
Singularities play an important role in General Relativity and have been shown to be an inherent feature of most physically reasonable space-times. Despite this, there are many aspects of singularities that are not qualitatively or…