Thermodynamics of the Stephani Universes
The consistency of the thermodynamics of the most general class of a conformally flat solution with an irrotational perfect fluid source (the Stephani Universes) is examined herein. For the case when ...
The consistency of the thermodynamics of the most general class of a conformally flat solution with an irrotational perfect fluid source (the Stephani Universes) is examined herein. For the case when ...
Parametric manifolds. II. Intrinsic approach
A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) one-form field. Such a...
A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) one-form field. Such a...
Parametric manifolds. I. Extrinsic approach
J. Math. Phys. 36, 1378 (1995); doi:10.1063/1.531127
Issue Date: March 1995
You are not logged in to this journal. Log in
A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the one-parameter family of hypersurfaces orthogonal to the curves, each of which inherits a metric and connection from the original manifold via orthogonal projections; this is the well-known Gauss–Codazzi formalism. This formalism is generalized to the case where the foliation is not hypersurface orthogonal. Crucial to this generalization is the notion of deficiency, which measures the failure of the orthogonal tangent spaces to be surface forming, and which behaves very much like torsion. Some applications to initial value problems in general relativity will be briefly discussed. ©1995 American Institute of Physics.
| History: | Received 18 July 1994; accepted 24 August 1994 |
| Permalink: |
http://link.aip.org/link/?JMAPAQ/36/1378/1 |
| BUY THIS ARTICLE | (US$28) |
|
|
Connotea
CiteULike
del.icio.us
BibSonomy
KEYWORDS and PACS
MATHEMATICAL MANIFOLDS,
SURFACES,
DIFFERENTIAL GEOMETRY,
GENERAL RELATIVITY THEORY,
SPACE&minus,
TIME,
TORSION,
METRICS,
TENSOR FIELDS,
GRAVITATIONAL FIELDS,
RIEMANN SPACE,
VECTOR FIELDS
- 04.20.Cv
General relativity and gravitation Classical general relativity Fundamental problems and general formalism - 04.20.Ex
General relativity and gravitation Classical general relativity Initial value problem, existence and uniqueness of solutions - 02.40.Hw
Mathematical methods in physics Geometry, differential geometry, and topology Classical differential geometry - YEAR: 1995
PUBLICATION DATA
0022-2488 (print)
1089-7658 (online)
AIP
REFERENCES (17)
For access to fully linked references, you need to log in.
For access to fully linked references, you need to Log in.
- Z. Perjés, “The parametric manifold picture of space–time,”
Nucl. Phys. B 403, 809 (1993 ). - A. Zel'manov, Sov. Phys. Dokl. 1, 227–230 (1956).
- A. Einstein and P. Bergmann,
Ann. Math 39, 683–701 (1938 ); - this article was reprinted in Introduction to Modern Kaluza–Klein Theories, edited by T. Applequist, A. Chodos, and P. G. O. Freund (Addison–Welsey, Menlo Park, 1987).
- M. do Carmo, Riemannian Geometry, translated by F. Flaherty (Birkhäuser, Boston, 1992).
- R. Bishop and S. Goldberg, Tensor Analysis On Manifolds (Dover, New York, 1980).
- B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity (Academic, Orlando, 1983).
- S. Kobayashi and K. Nomizu, Foundations of Differential Geometry (Wiley, New York, 1963), Vol. I.
- R. Wald, General Relativity (University of Chicago, Chicago, 1984).
- M. Spivak, A Comprehensive Introduction to Differential Geometry (Publish or Perish, Houston, 1979), Vol. II.
- B. L. Reinhart, “The second fundamental from of a plane field,” J. Diff. Geom. 12, 619–627 (1977);
- Differential Geometry of Foliations (Springer-Verlag, New York, 1980).
- R. Jantzen and P. Carini, “Understanding space–time splittings and their relationships,” in Classical Mechanics and Relativity: Relationship and Consistency, edited by G. Ferrarese (Bibliopolis, Naples, 1991), pp. 185–241;
- R. Jantzen, P. Carini, and D. Bini, “The many faces of gravitoelectromagnetism,”
Ann. Phy. (NY) 215, 1–50 (1992 ). - S. Boersma and T. Dray, “Slicing, threading, and parametric manifolds,” Gen. Relativ. Gravit. (to appear).
- M. Lottermoser, “Über den Newtonschen Grenzwert der Allgemeinen Relativitätstheorie und die relativistische Erweit-erung Newtonscher Anfangsdaten,” Dissertation der Fakultät für Physik der Ludwig-Maximilians-Universität München, 1988.
- R. H. Gowdy, “Affine projection tensor geometry: Lie derivatives and isometries,” Preprint gr-qc/9408014;J. Math. Phys. 35, 1274–1301 (1994).
- S. Boersma and T. Dray, “Parametric manifolds. II. Intrinsic approach,” J. Math. Phys. 36, 1394–1403 (1995), following paper.
- S. G. Harris and R. J. Low, “Causal monotonicity and the Spahe of space" (in preparation);
- S. G. Harris and D. Garfinkle, “Ricci fall-off in static, globally hyperbolic, geodesically complete, Ricci-positive space-times” (to appear in Proceedings of the 7th Marcel Grossman Conference on General Relativity);
“The method of timelike two-surfaces,” in Differential Geometry and Mathemati cal Physics, Contemporary Mathematics, Vol. 170, edited by J. K. Beem and K. Duggal (American Mathematical Society, Providence, 1994).
