Black holes and their horizons in semiclassical and modified theories of gravity

Robert B. Mann, Sebastian Murk, Daniel R. Terno

    Research output: Contribution to journalArticlepeer-review

    7 Citations (Scopus)


    For distant observers, black holes are trapped spacetime domains bounded by apparent horizons. We review properties of the near-horizon geometry emphasizing the consequences of two common implicit assumptions of semiclassical physics. The first is a consequence of the cosmic censorship conjecture, namely, that curvature scalars are finite at apparent horizons. The second is that horizons form in finite asymptotic time (i.e. according to distant observers), a property implicitly assumed in conventional descriptions of black hole formation and evaporation. Taking these as the only requirements within the semiclassical framework, we find that in spherical symmetry only two classes of dynamic solutions are admissible, both describing evaporating black holes and expanding white holes. We review their properties and present the implications. The null energy condition is violated in the vicinity of the outer horizon and satisfied in the vicinity of the inner apparent/anti-trapping horizon. Apparent and anti-trapping horizons are timelike surfaces of intermediately singular behavior, which manifests itself in negative energy density firewalls. These and other properties are also present in axially symmetric solutions. Different generalizations of surface gravity to dynamic spacetimes are discordant and do not match the semiclassical results. We conclude by discussing signatures of these models and implications for the identification of observed ultra-compact objects.

    Original languageEnglish
    Article number2230015
    Pages (from-to)2230015-1-2230015-95
    Number of pages95
    JournalInternational Journal of Modern Physics D
    Issue number9
    Early online date4 Jun 2022
    Publication statusPublished - 1 Jul 2022


    • Semiclassical gravity
    • modified gravity
    • black holes
    • apparent horizon
    • evaporation
    • white holes
    • energy conditions
    • thin shell collapse
    • surface gravity
    • information loss


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