Dini prostoročas

• Thesis title in Czech: Dini prostoročas
• Thesis title in English: Dini spacetime
• Key words: netriviální prostoročasy;grafen;gravitace;kosmologie
• English key words: nontrivial spacetimes;graphene;gravity;cosmology
• Academic year of topic announcement: 2017/2018
• Thesis type: project
• Department: Institute of Particle and Nuclear Physics (32-UCJF)
• Supervisor: prof. Alfredo Iorio, Ph.D.
• Author: hidden - assigned by the advisor
• Date of registration: 10.05.2018
• Date of assignment: 10.05.2018

Guidelines

The candidate will perfom a study of the spacetime obtained as a product of flat time and a specific surface of constant negative Gaussian curvature, the Dini surface. She/he will do that by looking for the coordinate changes that can explicitly show the relation between this spacetime and known spacetimes. In particular, he will look for the coordinate changes that can present the metric in the explicitly conformally flat form, having in mind that the spacetime associated to Beltrami has been shown to be conformal to the Rindler spacetime.

References

- A. Iorio, Curved spacetimes and curved graphene: A status report of the Weyl symmetry approach, Int. J. Mod. Phys. D 24 (2015) 1530013.

- https://en.wikipedia.org/wiki/Rindler_coordinates

- Notes from the supervisor and small extracts from:
N.D. Birrell, P.C.W. Davies, Quantum Fields in Curved Space, Cambridge University Press, 1982;
R.M. Wald, General Relavity, The University of Chicago Press, 1984;
C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation, Freeman, 1973;
W.Rindler, Hyperbolic Motion in Curved Space Time, Phys. Rev. 119 (1960) 2082;
A.C. Ripken, Coordinate systems in De Sitter spacetime, Bachelor thesis Radboud University Nijmegen, 2013;
S. Carlip, Quantum Gravity in 2+1 Dimensions, Cambridge University Press, 2003;

Preliminary scope of work in English

In recent work, A. Iorio and coworkers have shown that surfaces of negative constant Gaussian curvature, when considered as the spatial part of a 2+1-dimensional spacetime metric with flat time part (constant time-time metric component), can be mapped into highly non-trivial spacetimes, all of which present some form of horizons.

The three examples treated in details are those of the three pseudospheres: (a) the Beltrami, (b) the elliptic and (c) the hyperbolic. The correspondence is established in the form of a conformal transformation that relates: the spacetime associated to (a) with the Rindler spacetime of an accelerated observer; the spacetime associated to (b) with the de Sitter spacetime, important in cosmology; the spacetime associated to (c) with the spacetime of the famous Banados-Teitelboim-Zanelli black hole.

On the other hand, the family of surfaces of negative constant Gaussian curvature is infinite. Results show that all of the associated (in the sense above clarified) spacetimes are conformally flat. The Dini surface is no longer a pseudosphere, but it is somehow the surface that comes next in the family. In fact, it can be described as a Beltrami surface that ‘spiralizes’, hence pushing the singular boundary further away with respect to the singular boundary of the Beltrami. For this and other reasons it is then interesting to study such spacetime.