General Relativity Assignment #1
(1) Schaum's Outline: 3.23
(2) Schaum's Outline: 3.25
(3) Schaum's Outline: 3.28
(4) Schaum's Outline: 4.18
(5) Schaum's Outline: 4.26
(6) (a) Prove that the Kronecker Delta is a tensor.
(b) Prove also that has exactly the same constant components in all coordinate systems
(c) Evaluate in n-dimensional space.
(d) Evaluate in n-dimensional space.
(7) Consider the following expression
.
Use it to show that is not a tensor.
(8) Show that the following two expressions involving the affine connection are true.
(a)
(b)
To prove (b) use the partial derivative with respect to of the following expression
.
(9) By taking the covariant derivative of derive the expression for the covariant
derivative of .