Existence of space-like DHSs with negative null energy flux

Ascertain whether space-like dynamical horizon segments with negative null energy flux (𝔈<0) appear in physically interesting scenarios, by constructing explicit examples or proving constraints that exclude them.

Background

The review classifies dynamical horizon segments (DHSs) by signature and the sign of the null energy flux 𝔈, showing that space-like DHSs with positive 𝔈 occur broadly under the null/dominant energy condition and in gravitational collapse. Cases with negative 𝔈 require violations of energy conditions and stringent stress-energy properties.

While time-like DHSs with negative 𝔈 arise in settings such as semi-classical evaporation (negative energy inflow), the existence and physical relevance of space-like DHSs with 𝔈<0 is unclear and explicitly posed as an open question.