- #1

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1 - I have some notes where the Kretschmann Invariant is defined as R

_{k}= R

_{abuv}R

^{abuv}and is given in Schwarzschild coordinates as R

_{k}= 48u

^{2}/r

^{6}. My notes say this is an invariant field so that its value at any point as evaluated in one frame is the same when evaluated in any other frame. But its value depends on r so when switching from one frame to another the value of r will change which means R

_{k}will change. What is wrong with my thinking ?

2 - I came across the following in a "derivation" of the Einstein field equations : g

^{v}

_{v}= 4. I don't understand how or why this is true. As far as I know the components of g are normally not constants. On a similar issue what is η

^{v}

_{v}where η is the Minkowski metric. For a general tensor A does A

^{v}

_{v}= A ? and what is A ? Is it a scalar ? an invariant ?

Thanks in anticipation for any help