A simplified derivation of the Geroch group in two-dimensional reduced gravity

Journal Article · Sun May 01 04:00:00 EDT 1983 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.525795· OSTI ID:6043601

Wu, Y; Ge, M

By generalizing our previous treatment of hidden symmetry in two-dimensional chiral models, a simple and explicit approach is proposed to the Geroch group for the vacuum Einstein equations with the metric tensor depending only on two variables (''two-dimensional reduced gravity''). An infinite number of infinitesimal transformations for the metric tensor preserving the equations of motion are summarized by an explicit parametric transformation and the commutators among them are calculated in a simple and straightforward way. These transformations and their group structure are further identified to be those of the well-known Geroch group.

• Research Organization: Institute for Advanced Study, Princeton, New Jersey 08540
• DOE Contract Number: AC06-81ER40048
• OSTI ID: 6043601
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 24:5; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
DIFFERENTIAL EQUATIONS
EINSTEIN FIELD EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FIELD EQUATIONS
GRAVITATION
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
SYMMETRY GROUPS
TENSORS
TRANSFORMATIONS
TWO-DIMENSIONAL CALCULATIONS