Can Different Vacuum States in Curved Spacetime Appear Thermal to Each Other?

[grammophon]

Recently I attend a course on quantum field theory in curved space and find it's very difficult for me to understand vacuum state in curved spacetime properly.

For example, as I try to recover the Gibbons-Hawking temperature in dS space, I was told to solve Klein-Gordon equation in both planar and static coordinates (I use the textbook by Birrell and Davies (5.54) and (5.76)), then the spectrum of radiation detected by static observer can be deduced from Bogoliubov coefficient which are used to related the distinct vacuum states (Bunch-Davies vacuum and static vacuum) in two coordinates.

It is very confuse for me that, do the comoving observer in planar coordinates should define BD vacuum as a no-particle state ? If a comoving observer (w.r.t conformal time) in BD vacuum could see nothing, is this correct to say that he would detect a thermal spectrum when he turns to be static (comoving w.r.t cosmic time) since BD vacuum appears thermal then from the view of new static vacuum?

 

[Naty1]

As you are likely aware, in general different observers do see different vacuum states.
For example, Rindler coordinates and Schwarzschild coordinates reveal different vacuum states for inertial and accelerating observers.

This discussion may or may not answer the precise questions you ask, but will I think at least provide some useful insights... https://www.physicsforums.com/showthread.php?t=574548

 

[bapowell]

It is very confuse for me that, do the comoving observer in planar coordinates should define BD vacuum as a no-particle state ? If a comoving observer (w.r.t conformal time) in BD vacuum could see nothing, is this correct to say that he would detect a thermal spectrum when he turns to be static (comoving w.r.t cosmic time) since BD vacuum appears thermal then from the view of new static vacuum?

Yes, each of their respective vacua appear thermal to the other.

 

[grammophon]

Yes, each of their respective vacua appear thermal to the other.

Do you mean Bunch-Davies vacuum also appears thermal to a comoving observer w.r.t conformal time? Is this conflict with the fact that Bunch-Davies vacuum is defined for this comoving observer as a no-particle state?

I thought about such a process: at first, for a comoving observer w.r.t conformal time Bob, he can define a no-particle state as Bunch-Davies vacuum and detect no particle creation. Then, Bob turns to be static and a new no-particle state can be defined as static vacuum. Of course, no particle creation can be detected in new static vacuum. However, Bob would find the BD vacuum he got before appears thermal w.r.t to new vacuum, then a thermal spectrum can be detected.

Am I right on above picture? Hope for more help!