相关论文: Remarks on "singularities"
The ``geometry'', in the sense of the classical differential geometry of smooth manifolds (CDG), is put under scrutiny from the point of view of Abstract Differential Geometry (ADG), along with resulting, thereby, potential physical…
The paper concerns the fictitious entanglement of the so-called ``singularities'' in problems, pertaining to quantum gravity, due, in point of fact, to the way we try to employ, in that context, differential geometry, the latter being…
The nature of gravitational singularities has been questioned by some recent research, challenging the notion that classical determinism breaks down at these points. By allowing for dynamic changes in the orientation of spatial…
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…
We point out that spacetime singularities play a useful role in gravitational theories by eliminating unphysical solutions. In particular, we argue that any modification of general relativity which is completely nonsingular cannot have a…
Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's…
In the present paper, we outline and expound the fundamental and novel qualitative-cum-philosophical premises, principles, ideas, concepts, constructions and results that originate from our ongoing research project of applying the…
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.…
Although there is general agreement that a removal of classical gravitational singularities is not only a crucial conceptual test of any approach to quantum gravity but also a prerequisite for any fundamental theory, the precise criteria…
Seminar held at JINR, Dubna, May 15, 2012. In General Relativity, spacetime singularities raise a number of problems, both mathematical and physical. One can identify a class of singularities - with smooth but degenerate metric - which,…
A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at…
A `resolution' of the interior singularity of the spherically symmetric Schwarzschild solution of the Einstein equations for the gravitational field of a point-particle is carried out entirely and solely by finitistic and algebraic means.…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
In the present manuscript, I examine an intriguing relation at the classical level between general relativity and a theory where matter couples uniquely multiplicatively to geometry in the Lagrangian density. Interestingly, the…
We present a one-to-one correspondence between equivalence classes of embeddings of a manifold (into a larger manifold of the same dimension) and equivalence classes of certain distances on the manifold. This correspondence allows us to use…
We try to convince the reader that the categorical version of differential geometry, called Synthetic Differential Geometry (SDG), offers valuable tools which can be applied to work with some unsolved problems of general relativity. We do…
We briefly review some results concerning the problem of classical singularities in general relativity, obtained with the help of the theory of differential spaces. In this theory one studies a given space in terms of functional algebras…
We study here some consequences of the nonlinearities of the electromagnetic field acting as a source of Einstein's equations on the propagation of photons. We restrict to the particular case of a ``regular black hole'', and show that there…
String theory is a quantum theory that reproduces the results of General Relativity at long distances but is completely different at short distances. Mathematically, string theory is based on a very new -- and little understood -- framework…
A new scheme is proposed for dealing with the problem of singularities in General Relativity. The proposal is, however, much more general than this. It can be used to deal with manifolds of any dimension which are endowed with nothing more…