Quantum-Facing and Speculative Constructions

Quantum-facing constructions address different questions that are too often compressed into one phrase—“quantum black hole.” Some are exact black-hole solutions of specified supergravity theories. Some are smooth horizonless solutions carrying the same conserved charges as restricted supersymmetric black holes. Others are proposals for generic microstates, evaporation endpoints, or horizonless compact objects. This directory orders them by what is controlled, not by how completely they promise to resolve a paradox.

Six constructions at different epistemic levels

Construction	Firmest object-level statement	Central unresolved step
Supersymmetric and string-theoretic black holes	Exact BPS solutions and protected entropy counts in specified compactifications and charge regimes	Extension to generic non-BPS, dynamical, astrophysical black holes
Fuzzball constructions	A string-theory programme supported by controlled families and microscopic arguments	Typical-state coverage, generic nonextremality, formation, and radiation
Microstate geometries	Explicit smooth, horizonless supergravity solutions with black-hole charges in restricted sectors	Whether classical geometries represent a sufficient or typical fraction of the quantum ensemble
Planck-star constructions	Loop-inspired bounce scenarios and partial transition models	A complete controlled collapse, matching, lifetime, and evaporation calculation
Black-hole remnants	A logically distinct endpoint class that can be made concrete in selected models	Entropy capacity, production, stability, and a ultraviolet-complete mechanism
Gravastars	General-relativistic thin-shell and anisotropic-matter equilibrium models	Formation, material origin, stability, rotation, and evidence for a surface

The first row is an exact-solution family, not a speculative alternative. The next two are related but not identical: “fuzzball” names a broad microscopic programme, whereas “microstate geometry” normally denotes a classical supergravity representative that can be checked for smoothness, charges, and causal pathologies. Planck stars and remnants concern evaporation or interior evolution. Gravastars are horizonless compact objects constructed with shells or anisotropic stresses and need not be quantum microstates at all.

The control ladder

The strongest starting point is a declared action or quantum theory, compactification, charges, moduli, and approximation regime. An exact solution of a low-energy supergravity action is not automatically exact in full string theory; large charge and weak curvature may suppress higher-derivative and loop corrections. Supersymmetry can protect selected quantities, but a protected index is not always the unweighted degeneracy.

For a horizonless geometry, exact field equations are only the first test. One must also verify smoothness, absence of closed timelike curves, flux quantization, asymptotic charges, stability, and the map to a quantum state. A large family of special coherent states does not establish typicality.

For an endpoint proposal, the minimum data are a causal spacetime history, quantum region, matching conditions, energy balance, lifetime, entropy flow, and semiclassical limit. A dimensional estimate for a core size or lifetime is useful as a hypothesis, not as a derived prediction. For a horizonless compact object, equilibrium must be supplemented by an equation of state, radial and nonradial stability, a formation channel, and a forward model for observations.

What the calculations and observations establish

Every page separates four levels: an exact or controlled calculation; an extrapolation to less symmetric or less protected states; a claim about collapse, evaporation, or radiation; and an empirical claim. The common frontier evidence cutoff is 20 August 2026. At that date, no observation uniquely identifies a fuzzball, microstate geometry, Planck star, remnant, or gravastar. Absence of unique evidence does not erase exact mathematical results, and exact mathematical results do not supply astrophysical realization.

Adverse checks are construction-specific. Supersymmetric counts must survive the weak/strong-coupling comparison in the protected sector. Microstate geometries must satisfy regularity and bubble or no-CTC conditions. Bounce models must survive semiclassical matching and lifetime checks. Remnants must address the large-species and pair-production objections without assuming their conclusion. Gravastars must pass junction, energy-condition, and stability analyses.

Study the underlying theory

BPS Black-Hole Solutions develops the detailed solutions and attractor mechanism. Comparative Requirements for Information-Recovery Frameworks explains how to compare information-recovery proposals. For dated assessments of evaporation endpoints and observations, read Evaporation Endpoints and Remnants and Evidence for Horizons versus Material Surfaces.