Exploring the landscape of black hole mimickers

We identify a general class of spacetime metrics that mimic the properties of black holes without possessing a true event horizon. These metrics are constrained by the requirements of being singularity-free and geodesically complete. Specifically, we study metrics that do not possess $Z_2$ symmetry and may deviate slightly or significantly from the symmetric case. Focusing on scalar perturbations propagating on such backgrounds, we analyze the resulting effective radial potentials and their dependence on different corners of the mimicker landscape. We further investigate the corresponding quasinormal modes and explore their characteristic features. Finally, we survey the landscape for potential observational signatures, including shadow properties and the possible presence or absence of echo effects.

💡 Research Summary

The paper investigates a broad class of static, spherically symmetric spacetimes that reproduce the external appearance of a black hole while lacking a true event horizon. The authors impose two fundamental physical requirements: the absence of curvature singularities and geodesic completeness for both null and timelike trajectories. Starting from the Schwarzschild metric expressed in a radial coordinate ρ, they allow small deformations in the exterior region (ρ > 0) and consider arbitrary, possibly large, modifications in the interior region (ρ < 0). The interior modifications break the usual Z₂ symmetry of the Schwarzschild extension, leading to a “landscape” of black‑hole mimickers.

A general metric ansatz is written as
ds² = −g(ρ) dt² + dρ² + r(ρ)²(dθ² + sin²θ dφ²).
The functions g(ρ) and r(ρ) must satisfy regularity at ρ = 0 (the would‑be horizon) and asymptotic flatness as ρ → +∞. In the deep interior the authors assume power‑law behaviours g ∼ g₀(−ρ)^{κ₁} and r ∼ r₀(−ρ)^{κ₂}. Geodesic completeness of radial null rays forces κ₁ ≥ −2; timelike and non‑radial null geodesics impose further classifications depending on the combination κ₁ − 2κ₂. Three regimes are identified: (A1) the effective potential V_null = g/r² vanishes at infinity, (A2) it approaches a constant, and (A3) it diverges. These regimes dictate whether particles can reach the interior asymptotic region.

Four concrete “test metrics” are introduced to explore distinct corners of the landscape:

1. Metric I – a mildly asymmetric wormhole where g(0) is small but non‑zero, preserving a smooth throat.
2. Metric II – an “infinite tube” wormhole with g growing without bound as ρ → −∞, representing a large positive κ₁.
3. Metric III – a wormhole with a semi‑permeable wall: g remains finite inside while r has a minimal value, modeling a partially reflecting surface.
4. Metric IV – a wormhole with an impenetrable wall: g rapidly tends to zero inside, acting as a perfect reflector.

For each metric the authors compute the effective radial potentials for null and timelike geodesics, identify the presence of photon spheres (unstable circular null orbits), and discuss stability. The existence of one or two photon spheres directly influences the size of the shadow. By solving the null‑geodesic equations they obtain the critical impact parameter and compare the resulting shadow radii with the Event Horizon Telescope measurements of M87* and Sgr A*. All four models can be made compatible with current shadow data, showing that shadow size alone cannot rule out horizonless alternatives.

The dynamical aspect is addressed through scalar perturbations. The wave equation on the background reduces to a Schrödinger‑like form with an effective potential V_eff(ρ) that inherits the structure of g(ρ) and r(ρ). Two numerical techniques are employed: (i) a hyperboloidal slicing method that compactifies the domain and naturally implements outgoing boundary conditions, and (ii) a matrix eigenvalue approach based on discretising the radial equation. Both methods are benchmarked against the symmetric Damour‑Sokolov (DS) wormhole, reproducing known quasinormal mode (QNM) spectra.

Results for the test metrics reveal distinct QNM signatures. Metric I’s spectrum closely matches the Schwarzschild QNMs, with negligible deviations and no late‑time echoes. Metrics II and III exhibit additional potential barriers or double‑peak structures, giving rise to long‑lived, low‑damping modes that appear as “echoes” following the primary ringdown. Metric IV, with its perfectly reflecting wall, produces a clear sequence of equally spaced echoes whose amplitude and delay encode the wall’s location and reflectivity. These echo patterns constitute observable discriminants between true black holes and horizonless mimickers in future gravitational‑wave detections.

The discussion connects these phenomenological models to possible underlying physics. While many wormhole constructions require exotic matter violating energy conditions, the authors note that similar effective metrics can arise in alternative gravity theories, higher‑dimensional setups, or via quantum effects such as Casimir energy or conformal‑anomaly backreaction. They also acknowledge that their analysis is limited to static, spherically symmetric spacetimes; extensions to rotating (Kerr‑like) backgrounds, dynamical formation scenarios, and nonlinear stability analyses (especially concerning the potential instability of multiple photon spheres) are identified as crucial future directions.

In summary, the paper provides a systematic classification of singularity‑free, geodesically complete spacetimes that mimic black holes, derives constraints from shadow observations, and highlights how scalar QNM spectra—particularly the presence or absence of late‑time echoes—offer a promising avenue to distinguish horizonless objects from true black holes with upcoming multimessenger observations.