THE POST-BIANCHI IDENTITIES IN THE GHP FORMALISM

1996 ◽  
Vol 05 (04) ◽  
pp. 407-418
Author(s):  
GARRY LUDWIG
Keyword(s):  
Petrov Type ◽  
Type I ◽  
Bianchi Identities ◽  
Canonical Frame ◽  
Integrability Conditions ◽  
Ghp Formalism ◽  
Vacuum Solutions

As is well-known, when searching for Petrov type I vacuum solutions the imposition of tetrad conditions leads to integrability conditions on the Bianchi identities. Such post-Bianchi equations are simplest in GHP. They are exhibited explicitly for both a “canonical” frame and an “aligned” frame. Choosing a particular gauge, however, complicates the situation considerably; many more conditions are obtained. When this is done for the “canonical” case the resulting equations, when translated to NP, are the Brans-Edgar equations. How all such equations can be checked is reviewed in some detail.

GEOMETRICAL CONSTRAINTS FOR D = 10, N = 1 SUPERGRAVITY

1989 ◽  
Vol 04 (15) ◽  
pp. 3819-3831 ◽  
Author(s):  
LING-LIE CHAU ◽  
CHONG-SA LIM
Keyword(s):  
Equations Of Motion ◽  
Bianchi Identities ◽  
Dynamical Consequence ◽  
Integrability Conditions ◽  
Geometrical Constraints ◽  
Additional Constraints

A set of geometrical constraints for D = 10, N = 1 supergravity is formulated. It has the meaning as integrability conditions on "hyperplanes" determined by light-like lines in the superspace. The dynamical consequence of these geometrical constraints is studied via Bianchi identities. Since no equations of motion have resulted, these geometrical constraints can form an off-shell set of constraints for the theory. We also discuss additional constraints that lead to Poincare supergravity equations of motion. The relation of the theory with D = 4 N = 4 supergravity is also illuminated.

scholarly journals Integrability conditions for the Bianchi identities as transformations in Schwarzschild space-time

1999 ◽  
Vol 41 (2) ◽  
pp. 260-270
Author(s):  
J. F. Q. Fernandes ◽  
A. W.-C. Lun
Keyword(s):  
Space Time ◽  
Gauge Invariant ◽  
Bianchi Identities ◽  
Schwarzschild Geometry ◽  
Integrability Conditions ◽  
The Relationship ◽  
Coordinate Gauge

AbstractWe investigate the relationship between the Bardeen-Press and the Regge-Wheeler equations for perturbations of the Schwarzschild geometry. We examine how tetrad and coordinate gauge invariant Regge-Wheeler field quantities arise naturally from the perturbed Bianchi identities in the modified Newman-Penrose (compacted spincoefficient) formalism. The integrability conditions for the Bianchi identities then provide the transformation identities relating these quantities to the Bardeen-Press quantities. The relationships between the Bardeen-Press quantities of opposite spin-weight also arise naturally in our approach.

scholarly journals Petrov type I spacetime and dual relativistic fluids

2014 ◽  
Vol 90 (4) ◽  
Author(s):  
Rong-Gen Cai ◽  
Qing Yang ◽  
Yun-Long Zhang
Keyword(s):  
Petrov Type ◽  
Type I ◽  
Relativistic Fluids

PETROV TYPE I, STATIONARY, AXISYMMETRIC, PERFECT FLUID SOLUTION OF EINSTEIN'S EQUATIONS

1999 ◽  
Vol 14 (01) ◽  
pp. 7-14
Author(s):  
E. KYRIAKOPOULOS
Keyword(s):  
Equation Of State ◽  
General Solution ◽  
Perfect Fluid ◽  
Petrov Type ◽  
Type I ◽  
Fluid Solution ◽  
Einstein’S Equations ◽  
Perfect Fluid Solution ◽  
Einstein's Equations ◽  
Static Limit

We present a four-parameter, algebraically general solution for the interior of a rigidly rotating, axisymmetric perfect fluid, with the equation of state μ = p + const . The solution is analytically simple and has a static limit.

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