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Question: Using a Defined Tetrad

Question:Using a Defined Tetrad

Michael_Watson 125
define tensor physics
October 09 2015
1

 

I am trying to use the Define() funtion for the tetrad form of the Ricci Tensor. I use the Setup() function to define the tetradmetric and the tetrad labels. However, the function continues do some strange things with the d_ . It should be just a simple sum over the repeated indices, but I am getting imaginary terms.

 

  restart; with(Physics); with(Tetrads)

0, "%1 is not a command in the %2 package", Tetrads, Physics

 (1)

Physics:-Setup(coordinatesystems = {X}, spacetimeindices = greek, tetradindices = lowercaselatin, tetradmetric = Matrix([[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]], shape = symmetric), mathematicalnotation = true)

[coordinatesystems = {X}, mathematicalnotation = true, spacetimeindices = greek, tetradindices = lowercaselatin, tetradmetric = {(1, 2) = 1, (3, 4) = 1}]

 (2)

Physics:-Define(GammaT[a, b, c], RicciT[b, c] = -%d_[c](GammaT[`~a`, b, a])+%d_[a](GammaT[`~a`, b, c])-Physics:-`*`(GammaT[`~m`, b, a], GammaT[`~a`, m, c])+Physics:-`*`(GammaT[`~m`, b, c], GammaT[`~a`, m, a])-Physics:-`*`(GammaT[`~a`, b, m], GammaT[`~m`, c, a]-GammaT[`~m`, a, c]))

{Physics:-Dgamma[mu], GammaT[a, b, c], Physics:-Psigma[mu], RicciT[b, c], Physics:-d_[mu], Physics:-Tetrads:-eta_[a, b], Physics:-g_[mu, nu], Physics:-Tetrads:-l_[mu], Physics:-Tetrads:-m_[mu], Physics:-Tetrads:-mb_[mu], Physics:-Tetrads:-n_[mu], Physics:-KroneckerDelta[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}

 (3)

RicciT[1, 2]

-%d_[2](GammaT[`~1`, 1, 1]+GammaT[`~2`, 1, 2]+GammaT[`~3`, 1, 3]+GammaT[`~4`, 1, 4])-GammaT[`~1`, 1, 3]*GammaT[`~3`, 2, 1]-GammaT[`~3`, 1, 3]*GammaT[`~3`, 2, 3]-GammaT[`~4`, 1, 3]*GammaT[`~3`, 2, 4]+GammaT[`~4`, 1, 2]*GammaT[`~1`, 4, 1]+GammaT[`~4`, 1, 2]*GammaT[`~3`, 4, 3]+GammaT[`~4`, 1, 2]*GammaT[`~4`, 4, 4]+GammaT[`~1`, 1, 2]*GammaT[`~3`, 1, 3]+GammaT[`~1`, 1, 2]*GammaT[`~4`, 1, 4]+GammaT[`~2`, 1, 2]*GammaT[`~1`, 2, 1]+GammaT[`~2`, 1, 2]*GammaT[`~3`, 2, 3]+GammaT[`~2`, 1, 2]*GammaT[`~4`, 2, 4]+GammaT[`~3`, 1, 2]*GammaT[`~1`, 3, 1]+GammaT[`~3`, 1, 2]*GammaT[`~3`, 3, 3]+GammaT[`~3`, 1, 2]*GammaT[`~4`, 3, 4]-GammaT[`~1`, 1, 4]*GammaT[`~4`, 2, 1]-GammaT[`~3`, 1, 4]*GammaT[`~4`, 2, 3]-GammaT[`~4`, 1, 4]*GammaT[`~4`, 2, 4]-GammaT[`~1`, 1, 1]*GammaT[`~1`, 2, 1]-GammaT[`~3`, 1, 1]*GammaT[`~1`, 2, 3]-GammaT[`~4`, 1, 1]*GammaT[`~1`, 2, 4]-GammaT[`~1`, 1, 2]*GammaT[`~2`, 2, 1]-GammaT[`~3`, 1, 2]*GammaT[`~2`, 2, 3]-GammaT[`~4`, 1, 2]*GammaT[`~2`, 2, 4]-(1/2)*2^(1/2)*%d_[3](GammaT[`~2`, 1, 2])+(1/2)*2^(1/2)*%d_[3](GammaT[`~1`, 1, 2])+GammaT[`~2`, 3, 2]*GammaT[`~3`, 1, 2]+GammaT[`~2`, 4, 2]*GammaT[`~4`, 1, 2]+GammaT[`~1`, 1, 1]*GammaT[`~1`, 1, 2]+GammaT[`~1`, 1, 2]*GammaT[`~2`, 1, 2]-GammaT[`~1`, 2, 2]*GammaT[`~2`, 1, 1]-GammaT[`~2`, 1, 3]*GammaT[`~3`, 2, 2]-GammaT[`~2`, 1, 4]*GammaT[`~4`, 2, 2]+((1/2)*I)*2^(1/2)*%d_[1](GammaT[`~4`, 1, 2])-((1/2)*I)*2^(1/2)*%d_[4](GammaT[`~4`, 1, 2])+((1/2)*I)*2^(1/2)*%d_[1](GammaT[`~3`, 1, 2])+((1/2)*I)*2^(1/2)*%d_[4](GammaT[`~3`, 1, 2])+((1/2)*I)*2^(1/2)*%d_[2](GammaT[`~2`, 1, 2])+((1/2)*I)*2^(1/2)*%d_[2](GammaT[`~1`, 1, 2])

 (4)

 

``

 

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