Integration in the GHP formalism I: A coordinate approach with applications to twisting type N spaces

1996 ◽  
Vol 28 (6) ◽  
pp. 707-733 ◽  
Author(s):  
Garry Ludwig ◽  
S. Brian Edgar
Keyword(s):  
Ghp Formalism

scholarly journals Symmetry analysis of radiative spacetimes with a null isotropy using GHP formalism

2014 ◽  
Vol 46 (10) ◽  
Author(s):  
S. Brian Edgar ◽  
Michael Bradley ◽  
M. Piedade Machado Ramos
Keyword(s):  
Symmetry Analysis ◽  
Ghp Formalism

scholarly journals A new look at the Bondi-Sachs energy-momentum

2021 ◽  
Author(s):  
Jörg Frauendiener ◽  
Chris Stevens
Keyword(s):  
Unit Sphere ◽  
Gauss Curvature ◽  
Null Infinity ◽  
Conformally Invariant ◽  
Lorentzian Metric ◽  
Correct Definition ◽  
Ghp Formalism ◽  
Bondi Mass ◽  
Definition Of ◽  
Bondi Energy

Abstract How does one compute the Bondi mass on an arbitrary cut of null infinity I when it is not presented in a Bondi system? What then is the correct definition of the mass aspect? How does one normalise an asymptotic translation computed on a cut which is not equipped with the unit-sphere metric? These are questions which need to be answered if one wants to calculate the Bondi-Sachs energy-momentum for a space-time which has been determined numerically. Under such conditions there is not much control over the presentation of I so that most of the available formulations of the Bondi energy-momentum simply do not apply. The purpose of this article is to provide the necessary background for a manifestly conformally invariant and gauge independent formulation of the Bondi energy-momentum. To this end we introduce a conformally invariant version of the GHP formalism to rephrase all the well-known formulae. This leads us to natural definitions for the space of asymptotic translations with its Lorentzian metric, for the Bondi news and the mass-aspect. A major role in these developments is played by the “co-curvature”, a naturally appearing quantity closely related to the Gauß curvature on a cut of I.

scholarly journals The geometry of the (modified) GHP-formalism

1974 ◽  
Vol 37 (4) ◽  
pp. 327-329 ◽  
Author(s):  
Jürgen Ehlers
Keyword(s):  
Ghp Formalism

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.

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