## AIAS result: Kruskal Riccis not vanishing ???

### Gerhard W. Bruhn, Darmstadt University of Technology

11th Oct 2008

Evans on his blog: ...but the transform to Kruskal coordinates leads to a non-zero Ricci tensor, Einstein tensor and non-fulfillment of dual Bianchi identity. This is disastrous for the physics described ...

Evans on p.10 of paper#120: The worst error in black hole theory is the use of Kruskal metric {1-12,20}. The code found that this is mathematically erroneous because it produces a non-zero Ricci tensor and Einstein tensor, and also violates the Cartan/Evans dual identity.

Though the Kruskal metric is the result of a coordinate transform of the Finkelstein metric the AIAS ''computer experts'' communicate the vanishing of the Finkelstein Riccis (Sect 1.1.7-8), in contrast to the non-vanishing of the Kruskal Riccis (Sect 1.1.7-8).

This conclusion of the AIAS team is premature and false: The ''experts'' should use their mind where the computer could not help. E.g. for the Kruskal Riccis R01 and R10:

The problem is that r=r(u,v) is defined merely implicitly. Nevertheless it is possible to get the required informations about the derivatives ru and rv etc as occurring in the computer results: The application of ∂uv to Carroll's equation

u² − v² = (r/2GM − 1) exp (r/2GM)                                                 (7.80)

yields the relation

F' ruv + F'' rurv = 0,

where ' denotes differentiation with respect to r of F = (r/2GM − 1) exp (r/2GM), hence

F' = r/4G²M² exp (r/2GM),                 F'' = 1/4G²M² (1 + r/2GM) exp(r/2GM),

and thus

### R01= R10 ~ r ruv + (1 + r/2GM) rurv = 0 .

The vanishing of the other Kruskal Riccis can be shown quite similar on the basis of Carroll's eq.(7.80). Left to the ''experts'' as an exercise.

### However the ''experts'' should notice after all that the dualized 1st Bianchi does not hold in general. Any further effort is useless.

Recently Evans attempts to falsly attribute his wrong ''dual identity'' to É.Cartan by naming it ''the original Cartan identity''. This is an impudent attempt to deceive unsuspecting readers. Cartan has nothing to do with Evans' unqualified assumptions.