Demonstration 2 (israel): Reduction of Ricci to zero, calculation and simplification of the Kretschmann scalar in Israel coordinates.

> restart:

> grtw();

`GRTensorII Version 1.79 (R6)`

`2 February 2001`

`Developed by Peter Musgrave, Denis Pollney and Kay...

`Copyright 1994-2001 by the authors.`

`Latest version available from: http://grtensor.phy...

`e:/Grtii(6)/Metrics`

> qload(israel);

`Default spacetime` = israel

`For the israel spacetime:`

Coordinates

x(up)

`x `^a = vector([u, w, theta, phi])

`Line element`

` ds`^2 = 1/2*w^2*` d`*u^`2 `/(m*r(u,w))+2*` d`*u^`...

Constraints = [r(u,w) = 2*m+1/4*u*w/m]

`Israel coordinates (Phys. Rev. 143,1016)`

> grcalc(R(dn,dn),RiemSq);

Created definition for R(dn,dn,up,up)

`CPU Time ` = .180

> gralter(_,13);

Component simplification of a GRTensorII object:

Applying routine `Apply constraints repeatedly` to object R(dn,dn)

Applying routine `Apply constraints repeatedly` to object RiemSq

`CPU Time ` = .20e-1

> grdisplay(_);

`For the israel spacetime:`

`Covariant Ricci`

R(dn,dn)

`R `[a]*``[b] = `All components are zero`

`Full Contraction of Riemann`

`K ` = 196608*m^8/((8*m^2+u*w)^6)

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