#### Document Type

Working Paper

#### Date

2-27-1995

#### Embargo Period

9-28-2010

#### Keywords

Regge calculus, General relativity

#### Language

English

#### Disciplines

Mathematics | Physics

#### Description/Abstract

The convergence properties of numerical Regge calculus as an approximation to continuum vacuum General Relativity is studied, both analytically and numerically. The Regge equations are evaluated on continuum spacetimes by assigning squared geodesic distances in the continuum manifold to the squared edge lengths in the simplicial manifold. It is found analytically that, individually, the Regge equations converge to zero as the second power of the lattice spacing, but that an average over local Regge equations converges to zero as (at the very least) the third power of the lattice spacing. Numerical studies using analytic solutions to the Einstein equations show that these averages actually converge to zero as the fourth power of the lattice spacing.

#### Repository Citation

Miller, Mark A., "Regge Calculus as a Fourth Order Method in Numerical Relativity" (1995). *Physics.* Paper 16.

http://surface.syr.edu/phy/16

#### Source

Metadata from ArXiv.org

## Additional Information

14 pages, LaTeX, 8 figures mailed in separate file or email author directly. his work was partially supported by a Fellowship from Syracuse University and NSF ASC 93 18152 / PHY 93 18152 (ARPA supplemented).