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criticisms of the einstein field equation - Alpha Institute for Advanced ...

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CHAPTER 4. VIOLATION OF THE DUAL BIANCHI IDENTITY . . .<br />

0 i0<br />

Scalar Charge Density (-R i )<br />

ρ = 0<br />

i µj<br />

Current Density Class 1 (-R µ )<br />

J1 = 0<br />

J2 = 0<br />

J3 = 0<br />

i µj<br />

Current Density Class 2 (-R µ )<br />

J1 = 0<br />

J2 = 0<br />

J3 = 0<br />

i µj<br />

Current Density Class 3 (-R µ )<br />

J1 = 0<br />

J2 = 0<br />

J3 = 0<br />

4.4.3 General Cro<strong>the</strong>rs metric<br />

This is a general spherical symmetric metric with a general function C(r). It<br />

does not describe a vacuum in general since Ricci and Einstein tensors are<br />

different from zero.<br />

Coordinates<br />

x =<br />

⎛<br />

⎜<br />

⎝<br />

t<br />

r<br />

ϑ<br />

ϕ<br />

⎞<br />

⎟<br />

⎠<br />

149

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