Newman-Penrose Formalism

-Tetrad formalism

-Special cases

-NP formalism

-GHP method

-Application Summary Tetrad formalism

-Introduction At every point in space set up four linearly independent vectors

where Tetrad formalism

-Intrinsic Derivative & Ricci Rotation Coefficients

Define Ricci rotation coefficients

Intrinsic derivative Tetrad formalism

- Commutation relations Tetrad formalism - Ricci & Bianchi Identities

-Generalization

-Coordinate and Tetrad transformation Special Tetrad system

-Four vectors at each point are in the direction of the coordinate axes; that is, parallel to the four coordinate differentials :

-base vectors of a Cartesian coordinate system in the local Minkowski system of the point concerned :

-null vectors as tetrad vectors

using this system, complex tetrad components can arise • Special cases

NP tetrad Null tetrad approach to NP Formalism

-Introduction

- Spin Coefficient in terms of Ricci Rotation Coefficients Weyl, Ricci and Riemann Tensors in NP formalism NP set of equations:

• commutation relations, • Ricci Identities, • eliminant relations • Bianchi Identities Ricci Identities Bianchi Identities:

Spinor calculus • Spinors in minkowskian space, Isomorphism between Unimodular T. and L.T.s Spinors in minkowskian space

define

is invariant Spinors in minkowskian space General connection between Tensors and Spinors and Spinor Affine Connection 2-Spinor approach to NP Formalism

Dyad Formalism Spin Coefficients in terms of Spinor Affine Connection GHP δ’= New and appropriate operations Application summary

-In finding & analyzing new solutions of Einstein field equations

-In studying asymptotic properties of radiation fields

-In particular GHP method turn out to be very effective in 2-surfaces calculations

-Developing approaches to quantization through the study of complexified space times!