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These are questions asked by Rakshak

I am trying to calculate the Weyl Scalars for the Kerr metric and I get an error

"Error, (in simplify/recurse) numeric exception: division by zero"

g_[[5, 29, 1]];

When I try: 

It gives me the weyl scalars  but they dont look correct because some of the scalars are supposed to be zero for a type D spacetime.

When I look for petrov type II vacuum solutions in the Metric search, one of the metrics i get is Stephani [33,8,3].

But when I load the metric and calculate the Ricci or the Einstein tensor, they are not identically zero.
Am I using the metric search wrong or is there a glitch in the program?

Download Temp.mw

In the metric search command in the differential gometry package, you can use the petrov type of the Plebanski Tensor as a selection criteria.

But if you had a form of a metric tensor, how do you go about finding the petrov type of the Plebanski Tensor?

I know trig functions are hard to simplify in general but was wondering if there was any simplification command that comes in handy for trig functions of the following form.

sin(theta)^(A - 2)*cos(theta)^2 - sin(theta)^(A - 2) + sin(theta)^A

I am trying to make a very rough animation of a rotating pulsar magnetosphere that would very roughly resemble this gif.
I was able to make a sphere and the dipolar field lines. I was wondering if anyone could provide any possible suggestion regarding.

1. How do i animate the rotation such that the rotation axis is not z but slightly misaligned to z.

2. Is there a better way to make the field likes from the poles (jets).


[1.1, cos(theta), theta]

[1.1, cos(theta), theta]


sph := [.5, theta, phi]; c1 := [A*sin(phi)^2, 0, phi]; c2 := [A*sin(phi)^2, (1/6)*Pi, phi]; c3 := [A*sin(phi)^2, (1/3)*Pi, phi]; c4 := [A*sin(phi)^2, (1/2)*Pi, phi]; c5 := [A*sin(phi)^2, 2*Pi*(1/3), phi]; c6 := [A*sin(phi)^2, 5*Pi*(1/6), phi]

[A*sin(phi)^2, (5/6)*Pi, phi]





A := 2; plot3d([c1, c2, c3, c4, c5, c6, sph], phi = 0 .. 2*Pi, theta = 0 .. 2*Pi, coords = spherical, plotlist = true, scaling = constrained)





s1 := [sqrt(theta), 1, 1/10]; s2 := [sqrt(theta), 3, -1/10]; s3 := [sqrt(theta), 2, 1/10]; s4 := [sqrt(theta), 1.7, 1/7]

p := plot3d([sph, s1, s2, s3, s4, s5, s6, c1, c2, c3, c4, c5, c6], phi = 0 .. 2*Pi, theta = 0 .. Pi, coords = spherical, orientation = [-75, 58, 10], scaling = constrained, color = ["SkyBlue", "yellow", "yellow", "yellow", "yellow", "yellow", "yellow", "red", "red", "red", "red", "red", "red"])




plots[animate](plot3d, [[sph, s1, s2, s3, s4, s5, s6, c1, c2, c3, c4, c5, c6], theta = 0 .. Pi, phi = 0 .. 2*Pi, orientation = [B, 45, 52], coords = spherical], B = -180 .. 180)



Download Pulsar_temp.mw

3. Any other suggestions that could help with the aesthetics.

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