1. J.Gruszczak
Discrete Spectrum of the Deficit Angle and the Differential Structure of a Cosmic String
Int J Theor Phys, vol. 47, pp. 2911-2923 (2008).
[abstract] | Abstract:
Differential properties of Klein-Gordon and electromagnetic fields on the space-time of a straight cosmic string are studied with the help of methods of the differential space theory. It is shown that these fields are smooth in the interior of the cosmic string space-time and that they loose this property at the singular boundary except for the cosmic string space-times with the following deficit angles: \delta = 2π(1 −1/n), n = 1, 2, . . . . A connection between smoothness of fields at the conical singularity and the scalar and electromagnetic conical bremsstrahlung is discussed. It is also argued that the smoothness assumption of fields at the singularity is equivalent to the Aliev and Gal’tsov “quantization” condition leading to the above mentioned discrete spectrum of the deficit angle. | 2. J.Gruszczak, M.Heller
Differential Structure of Space-Time and its Prolongations to Singular Boundary
Int J Theor Phys, vol. 32, pp. 625-648 (1993).
| Abstract:
Abstract | 3. J. Gruszczak, M. Heller, Z. Pogoda
Cauchy Boundaries and b-Incompleteness of Space Times
Int J Theor Phys, vol. 30, pp. 555-565 (1991).
| Abstract:
Abstract | 4. J. Gruszczak
Cauchy Boundaries of Space- Times
Int J Theor Phys, vol. 29, pp. 37-43 (1990).
| Abstract:
Abstract | 5. J. Gruszczak, M. Heller and P. Muitarzynski
Physics With and Without the Equivalence Principle
Foundations of Physics, vol. 19, pp. 607-618 (1989).
[abstract] | Abstract:
A differential manifold (d-manifold, for short) can be defined as a pair (M, C), where M is any set and C is a family of real functions on M which is (i) closed with respect to localization and (ii) closed with respect to superposition with
smooth Euclidean functions; one also assumes that (iii) M is locally diffeomorphic to R n. These axioms have a traightforward physical interpretation. Axioms (i) and (ii) formalize certain "compatibility conditions" which usually are supposed to be assumed tacitly by' physicists. Axiom (iii) may be though of
as a (nonmetric) version of Einstein's equivalence principle. By dropping axiom (iii), one obtains a more general structure called a differential space (d-space). Every subset of R ~ turns out to be a d-space. Nevertheless it is mathematically a
workable structure. It might be expected that somewhere in the neighborhood of the Big Bang there is a domain in which space-time is not a d-manifold but still continues to be a d-space. In such a domain we would have a physics without the
(usual form of the) equivalence principle. Simple examples of d-spaces which are not d-manifolds elucidate the principal characteristics the resulting physics would
manifest. | 6. J. Gruszczak, M. Heller and P. Multtarzynski
A Generalization of Manifolds as Space-Time Model
Journal of Mathematical Physics, vol. 29, pp. 2576-2580 (1988).
| Abstract:
Abstract | |
