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


   .d'inverno 5.9


Use it to show that  is not a tensor.

(8)        Show that the following two expressions involving the affine connection are true.





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 .