Consider the 2-sphere with the metric dr² 1-p² (1) ds² = gabdxdxb =a² +r²d0² where a is a constant with length dimensions, 0 < r < 1 and 0 ≤ 0 < 2π. a. Make a drawing of each of the coordinate curves b. Show that with this coordinate system it is not possible to cover the entire surface of the 2-sphere.
Consider the 2-sphere with the metric dr² 1-p² (1) ds² = gabdxdxb =a² +r²d0² where a is a constant with length dimensions, 0 < r < 1 and 0 ≤ 0 < 2π. a. Make a drawing of each of the coordinate curves b. Show that with this coordinate system it is not possible to cover the entire surface of the 2-sphere.
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Transcribed Image Text:Consider the 2-sphere with the metric
ds²
=
a² (1-1²-7²7/²2 +1²40²)
dr²
p2
gabdxdxb
where a is a constant with length dimensions, 0 < r < 1 and 0 ≤ 0 < 2π.
a. Make a drawing of each of the coordinate curves b. Show that with this coordinate system it is not
possible to cover the entire surface of the 2-sphere.
=
(1)
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