## calculating a tensorial term ...

Hi guys ,

i computed a tensorial term with respect to a metric and i think i made mistake !! what do you think ?

problem.mw

Best Regards

## Metric and Kronecker delta...

This might be considered nit-picking, but nonetheless I think there is an issue: The metric tensor and its inverse are types (0,2) and (2,0) tensors, respectively. When once contracted with each other, the result is the Kronecker delta, which is then (necessarily) a tensor of type (1,1). I am therefore surprised to find that in Maple, this Kronecker delta is implemented as a type (0,2) tensor, via the command KroneckerDelta:

`KroneckerDelta[mu,nu];`

I don't think this makes any proper sense. I think that such an object of type (0,2) is, in fact, the metric itself. On a similar note, the (mixed tensor type) objects g_[mu,~nu] and g_[~mu,nu] are actually both Kronecker deltas, because they correspond to the metric having one index raised by contraction with the inverse metric itself. But, nonetheless, the following is the case:

```g_[ mu,~nu],
g_[~mu, nu];```

Relatedly, consider the following single contraction of the metric with its own inverse:

`SumOverRepeatedIndices(g_[mu,nu]*g_[~nu,~sigma]);`

Although this sum is formally quite correct, I think it should be given as just a Kronecker delta (of the correct mixed tensor type, that is).

## Distance metric to cartesian coordinates...

Can someone help me with this:

reverse_eng.mw

happy new year!

## How to define a metric tensor in 3-d (r, theta, p...

Helle everybohy,

I need to setup a metric tensor in 3-d but with the varalble r, and .  So I try this:

>with(Physics); Setup(mathematicalnotation = true, dimension = 3)

>Setup(coordinates = spherical[r, theta, varphi], metric = M)

where M is the metric that I need to use.  But the last command does not work.  Il I don't write [r, theta, varphi], it work but it's r, theta and t.

Mario Lemelin

mario.lemelin@cgocable.ca

## Metric Perturbation...

Hi All,

I'm using the Physics package, which enables GR calculations, ie defining metrics and tensor algebra.

Was just curious if it were possible to add a perturbation to the metric when calculating Ricci and Christoffels.

I would like something like

g_[] = g1_[mu,nu] + h[mu,nu]

And then do a calculation like,

Ricci[].

I know this would be possible if I define everything and re-write the calculations for calculating Ricci, i.e

Define(g1[mu,nu], h[mu,nu]);

and the proceed with GR calculations to find Ricci, however was hoping there was an easier way to do this.

Any help is appreciated.

Thanks guys.

## Equations of motions for Euclidean and Minkowski...

by: Maple 13

This procedure calculate the equations of motions for Euclidean space and Minkowski space  with help of the Jacobian matrix.

Procedures
Calculation the equation of motions for Euclidean space and Minkowski space

 Calling Sequence

Parameters

 parameterSequence - eq out equation of motion g out metric xup out velocitiy vector xa in position vector xu in vector of the independet coortinates eta in signature matrix for Minkowski space var in independet variable

 >

Procedur Code

 >
 >

Input

 >

 >

Output EOM

 >
 (5.1)

Output Line-Element

 >
 (6.1)

Output Metric

 >
 (7.1)
 >
 >

Procedures
Calculation the equation of motions for Euclidean space and Minkowski space

 Calling Sequence

Parameters

 parameterSequence - eq out equation of motion g out metric xup out velocitiy vector xa in position vector xu in vector of the independet coortinates eta in signature matrix for Minkowski space var in independet variable

 >

Procedur Code

 >
 >

Input

 >

 >

Output EOM

 >
 (5.1)

Output Line-Element

 >
 (6.1)

Output Metric

 >
 (7.1)
 >
 >

## Problem with PDEs ...

I'm trying to build a Maple procedure that will generate vector fields on a metric with certain properties. Working with metric g over the coordinates {u,v,w}, call the field X = (a(u,v,w), b(u,v,w), c(u,v,w)). The field should satisfy <X, X> = 0 and have the directional covariant derivative of X in the direction of each coordinate vector field = 0 (with resepct to the Levi-Civita conenction).

Basically, these conditions yield a system of 3 PDEs and an algebraic expressionin terms of a,b,c. I've been trying to solve them using pdsolve, but I'm getting the error message:

>Error, (in pdsolve/sys) the input system cannot contain equations in the arbitrary parameters alone; found equation depending only on _F1(u,v,w): _F1(u,v,w)

I've attached my worksheet. Can anyone help me out?

Thanks! ppwaves.mw

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