1,608 research outputs found
Finding and using exact solutions of the Einstein equations
The evolution of the methods used to find solutions of Einstein's field
equations during the last 100 years is described. Early papers used assumptions
on the coordinate forms of the metrics. Since the 1950s more invariant methods
have been deployed in most new papers. The uses to which the solutions found
have been put are discussed, and it is shown that they have played an important
role in the development of many aspects, both mathematical and physical, of
general relativity.Comment: 15 pages, LaTeX2e, aipproc.cls, invited lecture to appear in the
Proceedings of ERE05 (the Spanish Relativity Meeting), Oviedo, September
2005, to be published by the American Institute of Physics. v2: Remarks on
black hole entropy corrected. Other minor change
Local freedom in the gravitational field revisited
Maartens {\it et al.}\@ gave a covariant characterization, in a 1+3 formalism
based on a perfect fluid's velocity, of the parts of the first derivatives of
the curvature tensor in general relativity which are ``locally free'', i.e. not
pointwise determined by the fluid energy momentum and its derivative. The full
decomposition of independent curvature derivative components given in earlier
work on the spinor approach to the equivalence problem enables analogous
general results to be stated for any order: the independent matter terms can
also be characterized. Explicit relations between the two sets of results are
obtained. The 24 Maartens {\it et al.} locally free data are shown to
correspond to the quantities in the spinor approach, and the
fluid terms are similarly related to the remaining 16 independent quantities in
the first derivatives of the curvature.Comment: LaTeX. 13 pp. To be submitted to Class. Quant. Gra
An exterior for the G\"{o}del spacetime
We match the vacuum, stationary, cylindrically symmetric solution of
Einstein's field equations with , in a form recently given by Santos,
as an exterior to an infinite cylinder of dust cut out of a G\"{o}del universe.
There are three cases, depending on the radius of the cylinder. Closed timelike
curves are present in the exteriors of some of the solutions. There is a
considerable similarity between the spacetimes investigated here and those of
van Stockum referring to an infinite cylinder of rotating dust matched to
vacuum, with .Comment: 11 pages, LaTeX 2.09, no figures. Submitted to Classical and Quantum
Gravit
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