scholarly journals Small scale structure of spacetime: The van Vleck determinant and equigeodesic surfaces

2015 ◽  
Vol 92 (2) ◽  
Author(s):  
D. Jaffino Stargen ◽  
Dawood Kothawala
Keyword(s):  
Scale Structure ◽  
Small Scale ◽  
Small Scale Structure ◽  
Van Vleck

Small-scale structure of spacetime and its implications

2019 ◽  
Vol 28 (06) ◽  
pp. 1950079
Author(s):  
Dawood Kothawala
Keyword(s):  
Lower Bound ◽  
Perturbative Expansion ◽  
Scale Structure ◽  
Small Scale ◽  
Metric Tensor ◽  
Small Scale Structure ◽  
Van Vleck ◽  
Tensor Formula ◽  
Effective Description ◽  
World Function

If there exists a lower bound [Formula: see text] to spacetime intervals which is Lorentz-invariant, then the effective description of spacetime that incorporates such a lower bound must necessarily be nonlocal. Such a nonlocal description can be derived using standard tools of differential geometry, but using as basic variables certain bi-tensors instead of the conventional metric tensor [Formula: see text]. This allows one to construct a qmetric [Formula: see text], using the Synge’s world function [Formula: see text] and the van Vleck determinant [Formula: see text], that incorporates the lower bound on spacetime intervals. The same nonanalytic structure of the reconstructed spacetime which renders a perturbative expansion in [Formula: see text] meaningless, will then also generically leave a non-trivial “relic” in the limit [Formula: see text]. We present specific results derived from [Formula: see text] where such a relic term manifests, and discuss several implications of the same. Specifically, we will discuss how these results: (i) suggest a description of gravitational dynamics different from the conventional one based on the Einstein–Hilbert Lagrangian, (ii) imply a dimensional reduction to [Formula: see text] at small scales and (iii) can be significant for the idea that the cosmological constant itself might be related to some nonlocal vestige of the small-scale structure of spacetime. We will conclude by discussing the ramifications of these ideas in the context of quantum gravity.

scholarly journals A Search for Very Compact Structure in 17 OH Masers

1988 ◽  
Vol 129 ◽  
pp. 255-256
Author(s):  
A. J. Kemball ◽  
P. J. Diamond ◽  
F. Mantovani
Keyword(s):  
Galactic Disk ◽  
Hii Regions ◽  
Scale Structure ◽  
Small Scale ◽  
Compact Structure ◽  
Small Scale Structure ◽  
Interstellar Scattering

The apparent spot sizes of OH masers appear to be significantly broadened when seen through the inner galaxy or large extents of the galactic disk (Burke 1968). Bowers et al (1980) found evidence of small-scale structure (≲ 50 mas) in OH sources at distances of less than 5 kpc but this was characteristically absent in very distant sources (≳ 8kpc) at galactic longitudes 1 ≲ 40°. This result is typically explained in terms of interstellar scattering (ISS) by intervening diffuse HII regions.

Analysis of the small-scale structure of turbulence on smooth and rough walls

2003 ◽  
Vol 15 (1) ◽  
pp. 35-46 ◽  
Author(s):  
D. Poggi ◽  
A. Porporato ◽  
L. Ridolfi
Keyword(s):  
Scale Structure ◽  
Small Scale ◽  
Small Scale Structure ◽  
Rough Walls

Small-scale structure of the Taylor–Green vortex

1983 ◽  
Vol 130 (-1) ◽  
pp. 411 ◽  
Author(s):  
Marc E. Brachet ◽  
Daniel I. Meiron ◽  
Steven A. Orszag ◽  
B. G. Nickel ◽  
Rudolf H. Morf ◽  
...  
Keyword(s):  
Scale Structure ◽  
Small Scale ◽  
Small Scale Structure
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