Geodesic Form Research Articles

Geodesic round trips by parallel transport in quantum gravity.

We study the vacuum correlations of a gravitational field in any dimension $N>2$ using the perturbative expansion to order $G$. It is known that the usual Green's functions are meaningless in quantum gravity; moreover, we show that the traces of the holonomies of the Christoffel connection vanish, revealing a striking difference between gravity and Yang-Mills theories. In order to define meaningful holonomies we make two physical requirements: (1) the contours of the loop integrals must have "geodesic form and size;" (2) the full rotation matrices, not just their traces, must be averaged. Following these ideas we compute a "dumbbell correlation function" which turns out to behave like $\frac{G}{{D}^{N+2}}$, where $D$ is the geodesic distance. Finally, we write a gauge-invariant quantity which could replace the Wilson loop in reproducing the static potential energy between two sources.

Expansions of the affinity, metric and geodesic equations in Fermi normal coordinates about a geodesic

Fermi normal coordinates about a geodesic form a natural coordinate system for the nonrotating geodesic (freely falling) observer. Expansions of the affinity, metric, and geodesic equations in these coordinates in powers of proper distance normal to the geodesic are calculated here to third order, fourth order, and third order, respectively. An iteration scheme for calculation to higher orders is also given. For generality, we compute the affinity and the geodesic equations in an arbitrary affine manifold, and compute the metric in a Riemannian manifold with arbitrary signature.

Jacobi fields, totally geodesic foliations and geodesic differential forms

Jacobi fields, totally geodesic foliations and geodesic differential forms

Geodesic-dome houses using timber techniques

Although directed towards North American circumstances, the concept described here is concerned with low cost housing. It involves domes of geodesic form which utilise materials economically, incorporate a special wood-dowelled joint, and can be built by self-help labour. The author is a research scientist with the Department of the Environment, Western Forest Products Laboratory, Vancouver.

Geodesic Form of Schwarzschild's External Solution

THE line-elements usually appearing in relativistic cosmological studies are particular cases of the geodesic line-element1, obtainable from the most general form by subjecting the co-ordinate system to the restrictions2,