On wikipedia, there is the following :
A partition of unity can be used to define the integral (with respect
to a volume form) of a function defined over a manifold: One first
defines the integral of a function whose support is contained in a
single coordinate patch of the manifold; th...
1
In mathematics, a partition of unity of a topological space X is a set R of continuous functions from X to the unit interval [0,1] such that for every point,
x
∈
X
{\displaystyle x\in X}
,
there is a neighbourhood of x where all but a finite number of the functions of R are 0, and
the sum of all the function values at x is 1, i.e.,
∑
ρ
∈
R
ρ
(
x
)
=
1
{\displaystyle...
Suppose I'm hovering 1 meter away from the horizon of a Schwarzschild black hole and I'm holding a 2 meter long metal rod. Now I thrust the rod towards the horizon? What do I observe?
A satisfactory answer to this question needs to include a discussion of the following:
When the Schwarzschild...15
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