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I'm curious about the P,T,C-parity of graviton?

1)Are these graviton's parities even or odd?

2)Is the C,P,T-parity alternatively conserved in Einstein gravity? And does the CPT theorem still hold in Einstein gravity?

3)And do these conservations rely on the background space-time?

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  • Aren't these two different questions? Re the second question, GR doesn't admit global symmetries, e.g., it doesn't make sense in general to talk about time-reversing a solution to the Einstein field equations (although it may make sense in some cases). –  Sep 01 '14 at 03:33

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About CPT-conservation.

If you talk about graviton then you talk about linearized GR.

There is theory which tells us that all irreducible representations $\left(\frac{n}{2}, \frac{m}{2} \right) \oplus \left( \frac{m}{2}, \frac{n}{2}\right)$ of the Lorentz group is invariant under $C, P, T$ transformations. The theory of graviton (it may be defined without using GR) is the theory $\left(2, 0 \right) \oplus \left( 0, 2\right)$ (graviton is massless particle with helicities $2, -2$), so indeed this theory is invariant under $C, P, T$ transformations.

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