[Paper Review] Physical black holes in semiclassical gravity

Sebastian Murk, Daniel R. Terno|arXiv (Cornell University)|Oct 25, 2021

Astrophysical Phenomena and Observations4 citations

TL;DR

This paper investigates the formation of physical black holes in semiclassical gravity under the condition that the apparent horizon forms in finite time for a distant observer. It shows that such horizons require violation of the null energy condition, lead to non-accretion after formation, and render standard surface gravity definitions incompatible with Hawking-like radiation, suggesting observed astrophysical black holes may not possess true horizons due to insufficient time for formation or quantum gravity effects.

ABSTRACT

We derive and critically examine the consequences that follow from the formation of a regular black or white hole horizon in finite time of a distant observer. In spherical symmetry, only two distinct classes of solutions to the semiclassical Einstein equations are self-consistent. Both are required to describe the formation of physical black holes and violate the null energy condition in the vicinity of the outer apparent horizon. The near-horizon geometry differs considerably from that of classical solutions. If semiclassical physics is valid, accretion into a black hole is no longer possible after the horizon has formed. In addition, the two principal generalizations of surface gravity to dynamical spacetimes are irreconcilable, and neither can describe the emission of nearly-thermal radiation. Comparison of the required energy and timescales with established semiclassical results suggests that if the observed astrophysical black holes indeed have horizons, their formation is associated with new physics.

Motivation & Objective

• To determine the physical and geometric consequences of a regular black hole horizon forming in finite time for a distant observer in spherical symmetry.
• To assess whether semiclassical gravity allows for consistent black hole formation without singularities or new physics.
• To evaluate the viability of standard surface gravity definitions and Hawking radiation in dynamical spacetimes with finite-time horizon formation.
• To investigate whether observed astrophysical black holes could actually be horizonless ultra-compact objects due to insufficient time for horizon formation.

Proposed method

• Derives and classifies spherically symmetric solutions to the semiclassical Einstein equations under the assumption of finite-time horizon formation.
• Applies the apparent horizon as the defining feature of a physical black hole, replacing the global event horizon with a local, observable concept.
• Analyzes the near-horizon geometry using the Kodama vector and surface gravity definitions, comparing the peeling and Kodama versions.
• Evaluates energy conditions, particularly the null energy condition (NEC), in the vicinity of the outer apparent horizon.
• Compares the resulting dynamics with known semiclassical results, including Hawking radiation and Page's evaporation law.
• Assesses timescales for horizon formation and compares them with Hawking decay times to evaluate physical feasibility.

Experimental results

Research questions

• RQ1 What are the geometric and dynamical consequences of forming a regular apparent horizon in finite time for a distant observer in spherical symmetry?
• RQ2 How does the violation of the null energy condition near the horizon affect accretion and radiation emission in semiclassical gravity?
• RQ3 Why are the two standard definitions of surface gravity incompatible in dynamical spacetimes with finite-time horizon formation?
• RQ4 Can the standard prediction of nearly-thermal Hawking radiation be realized in such dynamical solutions?
• RQ5 Do observed astrophysical black holes actually possess horizons, or could they be horizonless due to insufficient time for formation?

Key findings

• Only two distinct classes of spherically symmetric solutions to the semiclassical Einstein equations are self-consistent when a regular horizon forms in finite time for a distant observer.
• The formation of a physical black hole horizon requires violation of the null energy condition in the vicinity of the outer apparent horizon, implying exotic matter or quantum effects.
• After horizon formation, accretion into the black hole is no longer possible under semiclassical physics, implying either evaporation or white hole-like expansion.
• The Kodama surface gravity is zero at the instant of horizon formation, contradicting the standard value of 1/(4M) expected from semiclassical results.
• The two principal definitions of surface gravity — peeling and Kodama — are irreconcilable in dynamical spacetimes, undermining the derivation of Hawking radiation.
• The timescale for horizon formation is comparable to the Hawking decay time for macroscopic black holes, suggesting that observed astrophysical black holes may not yet have formed horizons.