 
Summary: A oneparameter family of cylindrically
symmetric solution approaching Einstein's
universe
T. Amdeberhan
DIMACS, Rutgers Univ.
96 Frelinghuysen Rd.
Piscataway, NJ 088548010
tedy@dimacs.rutgers.edu
29 January 2003
Abstract
In this note we describe a stationary cylindrically symmetric solution of
Einstein's equation with matter consisting of a positive cosmological con
stant and an infinite cylinder of rotating dust. The solution approaches
Einstein static universe solution. This result is complementary to Iftime
[Class Quantum Grav 19 (2002)].
1 Introduction
The basic partial differential equations of general relativity are Einstein's field
equations. In general these equations are essentially hyperbolic and are coupled
to other partial differential equations describing the matter content of spacetime.
A special feature of the Einstein equations is that initial data cannot be given
