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Dynamic Casimir effect tells us that a constantly-accelerated mirror should emit radiation due to interaction with vacuum. Following principle of equivalence, a similar mirror placed in static gravitational field should emit either.

So will planet which surface is covered with a mirror emit any radiation and if no, why not?

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The equivalence principle is local, true only in the limit. Locally the field of the planet is close to uniform, which is equivalent to a uniform acceleration. In the case of uniform acceleration the mirror does not emit (I think). –  MBN Jan 6 '12 at 11:46
    
@MBN "In the case of uniform acceleration the mirror does not emit" - where did you read it? Actually dynamic Casimir effect talks about any acceleration. –  Anixx Jan 6 '12 at 11:48
    
Unless I've misunderstood what you mean by the DCE, it just needs the mirror to be moving at relativistic speeds and acceleration is not required. –  John Rennie Jan 6 '12 at 18:25
    
@Anixx, I am not sure, that's why I said 'I think'. Why do you think there will be radiation in the case of uniform acceleration? The paper I was looking at is Fulling-Davies (1976) –  MBN Jan 6 '12 at 19:04
    
@John Rennie "it just needs the mirror to be moving at relativistic speeds and acceleration is not required." - in that case the linear momentum of the moving mirror would change and the mirror will change its speed due to interaction with vacuum (this contradicts the principle that all inertial frames are equal) –  Anixx Jan 6 '12 at 19:35
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1 Answer

The mirror has to be accelerating Otherwise you violate lorenzte invariance

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Please read what is Lorentz invariance.Link –  Curious Nov 11 '12 at 19:13
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