- #1

Tony Stark

- 51

- 2

## Homework Statement

Flat space-time in polar coordinate is considered. The line element is

ds

^{2}= -dt

^{2}+dr

^{2}+r

^{2}(dθ

^{2}+sin

^{2}θdΦ

^{2})

The actual answers are given below, but I can't come up to them. Need urgent help.

## Homework Equations

dA = √g

_{11}g

_{22}dx

^{1}dx

^{2}

dV = √g

_{11}g

_{22}g

_{33}dx

^{1}dx

^{2}dx

^{3}

## The Attempt at a Solution

g

_{1}= 1

g

_{2}= r

^{2}

g

_{3}= r

^{2}sin

^{2}θ

⇒dA = √1.r

^{2}dr.dθ

dA= r dr dθ

(ACTUAL ANSWER= dA = r

^{2}sinθ dθ dΦ)

Cant calculate Volume

(ACTUAL ANSWER= dV= r

^{2}sinθ dθ dΦ dr)