What does a zero area element in the metric mean?
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In mathematics, a volume element provides a means for integrating a function ..... Here we will find the volume element on the surface that defines area in the usual sense.
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let us take the metric as........
ds2=λ(r)dt2−λ−1(r)dr2−R(r)2dΩ2ds2=λ(r)dt2−λ−1(r)dr2−R(r)2dΩ2
where
λ(r)=r+ωr+hλ(r)=r+ωr+h
and
R(r)2=r(r+h)R(r)2=r(r+h)
At r=−hr=−h, the area element disappears, does this have any physical interpretation?
There is a problem because the temporal part diverges and the radial part goes to zero, but if ω=hω=h, the metric is finite.
ds2=λ(r)dt2−λ−1(r)dr2−R(r)2dΩ2ds2=λ(r)dt2−λ−1(r)dr2−R(r)2dΩ2
where
λ(r)=r+ωr+hλ(r)=r+ωr+h
and
R(r)2=r(r+h)R(r)2=r(r+h)
At r=−hr=−h, the area element disappears, does this have any physical interpretation?
There is a problem because the temporal part diverges and the radial part goes to zero, but if ω=hω=h, the metric is finite.
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