# Diamond-Shaped Regions as Microcosmoi

@article{Ribeiro2010DiamondShapedRA, title={Diamond-Shaped Regions as Microcosmoi}, author={P. Ribeiro}, journal={arXiv: General Relativity and Quantum Cosmology}, year={2010} }

We give a geometrically intrinsic construction of a global time function for relatively compact diamond-shaped regions in arbitrary spacetimes. In the case of Minkowski spacetime, the flow of diffeomorphisms associated to a suitably normalized gradient of this time function becomes the conformal isotropy subgroup of the diamond. In full generality, this time function is elegantly expressed in terms of the Lorentzian distance function, and it has an asymptotic behavior at large absolute times… Expand

#### References

SHOWING 1-10 OF 42 REFERENCES

Smoothness of Time Functions and the Metric Splitting of Globally Hyperbolic Spacetimes

- Physics, Mathematics
- 2005

The folk questions in Lorentzian Geometry which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic… Expand

Algebraic Holography in Asymptotically Simple, Asymptotically AdS Space-times

- Physics, Mathematics
- 2005

We describe a general geometric setup allowing a generalization of Rehren duality to asymptotically anti-de Sitter space-times whose classical matter distribution is sufficiently well-behaved to… Expand

THE COSMOLOGICAL TIME FUNCTION

- Physics, Mathematics
- 1998

Let be a time-oriented Lorentzian manifold and d the Lorentzian distance on M. The function is the cosmological time function of M, where as usual p< q means that p is in the causal past of q. This… Expand

Algebraic holography in asymptotically simple , asymptotically

- 2005

I’ll describe a general geometric setup allowing a generalization of Rehren duality to asymptotically anti-de Sitter spacetimes whose classical matter distribution is sufficiently well-behaved to… Expand

Diamond's temperature: Unruh effect for bounded trajectories and thermal time hypothesis

- Physics, Mathematics
- 2002

We study the Unruh effect for an observer with a finite lifetime, using the thermal time hypothesis. The thermal time hypothesis maintains that: (i) time is the physical quantity determined by the… Expand

The Wave Equation on a Curved Space–Time

- Physics
- 1976

F G Friedlander London: Cambridge University Press 1976 pp ix + 282 price £15 The continuing interest in general relativity has created the need for a book on the rigorous mathematical theory of wave… Expand

Modular dynamics in diamonds

- Physics, Mathematics
- 2010

We investigate the relation between the actions of Tomita-Takesaki modular operators for local von Neumann algebras in the vacuum for free massive and massless bosons in four dimensional Minkowskian… Expand

A new topology for curved space–time which incorporates the causal, differential, and conformal structures

- Physics
- 1976

A new topology is proposed for strongly causal space–times. Unlike the standard manifold topology (which merely characterizes continuity properties), the new topology determines the causal,… Expand

ASPECTS OF NONCOMMUTATIVE LORENTZIAN GEOMETRY FOR GLOBALLY HYPERBOLIC SPACETIMES

- Mathematics, Physics
- 2003

Connes' functional formula of the Riemannian distance is generalized to the Lorentzian case using the so-called Lorentzian distance, the d'Alembert operator and the causal functions of a… Expand

Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property

- Mathematics, Physics
- 2009

In a recent paper, we proved that a large class of spacetimes, not necessarily homogeneous or isotropous and relevant at a cosmological level, possesses a preferred codimension 1 submanifold, i.e.,… Expand