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What I know from GR, is that Einstein's fields equations have vacuum solutions. Nonetheless even that vacuum contains gravitational energy.

On the other hand one has the equivalence of energy and matter.

Then does it mean that, matter in some indirect way always exist?

One might elevate the discussion to quantum mechanics where there might be a Channel that connects gravity and matter where such transition can take place.

The least would be that for Black Hole solutions (yes it's not vacuum solution but I mention it for the sake of motivation!), at the semiclassical level (QFT in curved spacetime where curvature is less that the inverse of Compton Wavelength), Hawking radiation can create matter from gravitational energy stored in the gravitational field.

I was thinking, if it's possible fundamentally, to have classical curved vacuum spacetime solutions, where matter does not exist in any form but quantum fluctuations?

Or to put it differently, is it possible to start from a classical vacuum solution and create matter out of such solutions?

Qmechanic
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Bastam Tajik
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2 Answers2

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What I know from GR, is that Einstein's fields equations have vacuum solutions. Nonetheless even that vacuum contains gravitational energy.

Would you mind to write down the expression for gravitational energy that you mean?

On the other hand one has the equivalence of energy and matter.

What Einstein stated with his famous formula $E_{0}=m c^2$ is only that the mass $m$ of a body is equivalent to its rest energy $E_{0}$, see for reference $The~Einstein~ formula:~ E_{0}=mc^2$ by L. B. Okun, and not that energy is equivalent to mass.

Then does it mean that, matter in some indirect way always exist?

I would say, if spacetime exists then matter as well. They cannot exist without each other.

I was thinking, if it's possible fundamentally, to have classical curved vacuum spacetime solutions, where matter does not exist in any form but quantum fluctuations?

Quantum fluctuations I associate with wave functions that allow us to calculate probabilities of some physical values. The wave function is a mathematical and not a physical entity.

Or to put it differently, is it possible to start from a classical vacuum solution and create matter out of such solutions?

To my knowledge it is not possible.

JanG
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  • "This shows that matter can be generated quantum mechanically from gravitational vacuum energy!" Can you name any other reference (on arxiv?). I do not have that book. – JanG Oct 31 '22 at 09:44
  • The free version of the book: https://uwaterloo.ca/physics-of-information-lab/sites/ca.physics-of-information-lab/files/uploads/files/text.pdf page 89 onwards. Enjoy! @JanGogolin – Bastam Tajik Oct 31 '22 at 10:22
  • Let us continue this discussion in chat. – Bastam Tajik Oct 31 '22 at 12:41
  • The inquirer however was really annoyed by my answer. I find your answer correct (+1). The mass notion in GR is frame dependent and in contrary to mass defect superfluous. The parameter in Schwarzschild vacuum solution is not mass but a third of energy density at the event horizon (see for reference https://physics.stackexchange.com/a/679431/281096). – JanG Apr 16 '23 at 14:50
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In chapter 7 page 85 of Introduction to Quantum Effects in Gravity, it is shown that for a quantum scalar field in the de Sitter background (cosmological constant) matter is generated as a result of the [conformal]time dependence of the dispersion relation.

This shows that matter can be generated quantum mechanically from gravitational vacuum energy!

But now the question would be, is there any way to derive the vacuum energy (or cosmological constant) from the Ricci-flat vacuum solutions of GR? Since adding the cosmological constant by hand sounds quite ad hoc! It should also be borne in mind that this vacuum contains a scalar field whose vacuum energy contributes to the cosmological constant.

Bastam Tajik
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