Question: A curved spacetime has a spacetime interval ds = A(r)dt - B(r)dr - C(r)(rd0 + r sin 0dp) where r, 0, and are spherical

A curved spacetime has a spacetime interval ds = A(r)dt - B(r)dr

A curved spacetime has a spacetime interval ds = A(r)dt - B(r)dr - C(r)(rd0 + r sin 0dp) where r, 0, and are spherical coordinates, and where A(r), B(r), and C(r) are given functions of r. Show that (a) The circumference of the circle r = r is 2C(ri)r. (b) The area of the sphere r = r is 4trC(ri).

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a The circumference of the circle r r is calculated from the line element ds Ardt Brdr ... View full answer

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