Fetching the paper…

Reading the bibliography…

2012

The Discrete Geometry of a Small Causal Diamond

Roy, Mriganko, Sinha, Debdeep, Surya, Sumati

Original
PDF
Post on X

Understand

We study the discrete causal set geometry of a small causal diamond in a curved spacetime using the average abundance of k-element chains or total orders in the underlying causal set C.

We begin by obtaining the first order curvature corrections to the flat spacetime expression for the abundance using Riemann normal coordinates.
For fixed spacetime dimension this allows us to find a new expression for the discrete scalar curvature of C as well as the time-time component of its Ricci tensor in terms of the abundances of k-chains.
We also find a new dimension estimator for C which replaces the flat spacetime Myrheim-Meyer estimator in generic curved spacetimes.

The Discrete Geometry of a Small Causal Diamond · Around

Built on

S. Hawking, A. King & P. McCarthy, J. Math. Phys. 17
1976
Earlier work this paper cites.
D. Malament, J. Math. Phys. 18
1977
Earlier work this paper cites.
J. Myrheim, CERN preprint TH-2538 (1978)
1978
Earlier work this paper cites.
L. Bombelli, J. Lee, D. Meyer, R.D. Sorkin, Phys. Rev. Lett. 59
1987
Earlier work this paper cites.
D.A. Meyer, The Dimension of Causal Sets, PhD thesis, (M.I.T., 1988)
1988
Earlier work this paper cites.

Similar

L. Bombelli, D. A. Meyer, Phys. Lett. A 141
1989
Cited alongside, same era.
G. Brightwell, R. Gregory, Phys. Rev. Lett. 66
1991
Cited alongside, same era.
L. Bombelli and J. Noldus, Class. Quant. Grav
2004
Cited alongside, same era.
S. Major, D.P. Rideout, S. Surya, J.Math.Phys.48:032501, (2007)
2007
Cited alongside, same era.
G. W. Gibbons and S. N. Solodukhin, Phys. Lett. B 649
2007
Cited alongside, same era.
L. Glaser and S. Surya, in preparation
Cited in the paper.
S. Khetrapal and S. Surya, in preparation
Cited in the paper.
M. Roy, D. Sinha, S. Surya, in progress
Cited in the paper.

Then

L. Bombelli, J. Henson and R. D. Sorkin, Mod.Phys.Lett.A 24
2009
Later among the works it cites.
D. Rideout and P. Wallden, Class. Quant. Grav. 26
2009
Later among the works it cites.
S. Major, D. Rideout and S. Surya, Class. Quant. Grav. 26
2009
Later among the works it cites.
D. M. T. Benincasa and F. Dowker, Phys. Rev. Lett. 104
2010
Later among the works it cites.
S. Surya, Class. Quant. Grav. 29
2012
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…