Quantum fields in curved spacetime and back-reaction

5 problems

• Does the achronal averaged null energy condition hold in curved spacetime?

  Open

  Quantum fields can have negative energy locally, which could in principle hold open wormholes or build time machines. A weaker condition, energy averaged along light rays that never come back to their own past, would exclude these, but it is unproved in curved spacetime.

• Does quantum back-reaction forbid the formation of time machines?

  Partially resolved

  General relativity allows spacetimes with closed loops in time, along which one could return to one's own past. Hawking conjectured that quantum effects always destroy such loops as they start to form, but this is shown only in limited cases.

• Is de Sitter space stable against infrared quantum back-reaction?

  Contested

  In an expanding universe with a cosmological constant, quantum fluctuations of light fields and gravitons can accumulate over time. Some argue that this slowly screens or destabilizes the expansion; others argue the effect is an artifact of the calculation.

• Prove the restricted quantum focusing conjecture for semiclassical gravity

  Partially resolved

  The classical singularity theorems assume energy is never negative, which quantum fields violate. A quantum replacement based on the entropy of the fields plus the area of a surface would restore the theorems, but its original strong form fails in simple models and a weaker form is still a conjecture.

• When is the semiclassical Einstein equation a controlled approximation?

  Open

  A common shortcut treats spacetime classically and matter quantum mechanically, with spacetime curved by the average energy of the quantum fields. The shortcut fails when quantum fluctuations of that energy are large, and its precise range of validity is unknown.