A curved spacetime has a spacetime interval ds = A(r)dt - B(r)dr - C(r)(rd0 + r...

 

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A curved spacetime has a spacetime interval ds² = A(r)dt² - B(r)dr² - C(r)(r²d0² + r² sin² 0dp²) 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 = r₁ is 2√C(ri)r₁. (b) The area of the sphere r = r₁ is 4tr²C(ri). A curved spacetime has a spacetime interval ds² = A(r)dt² - B(r)dr² - C(r)(r²d0² + r² sin² 0dp²) 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 = r₁ is 2√C(ri)r₁. (b) The area of the sphere r = r₁ is 4tr²C(ri).

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