Asymmetry Horizon: Observations & Implications

• Asymmetry Horizon is a concept describing horizon-scale limits at which measurable asymmetries are bounded or generated across astrophysics, quantum information, and cosmology.
• In black-hole imaging, the asymmetry horizon marks the minimal detectable noncircularity caused by factors like scattering and plasma dynamics near the event horizon.
• In quantum and cosmological contexts, horizon effects dictate directional quantum steering and the sourcing or freezing of matter asymmetries through gravitational and thermodynamic processes.

Searching arXiv for the supplied papers and closely related uses of “asymmetry horizon” across black-hole imaging, quantum steering, and cosmological asymmetry. “Asymmetry horizon” appears in the literature considered here in several distinct but structurally related settings. In black-hole imaging, it denotes a practical floor on measurable shadow or ring asymmetry set by interstellar scattering, plasma dynamics, or radiative transfer near the horizon (Zhu et al., 2018, Medeiros et al., 2021, Faggert et al., 2024). In relativistic quantum information, it refers to the event horizon as the locus where Gaussian quantum steering becomes direction-dependent and bounded (Wang et al., 2015). In cosmology, it is used, or naturally interpreted, for horizon-defined thresholds at which asymmetries are sourced, frozen, or constrained through generalized horizon entropy, primordial black holes, reheating-era horizon crossing, or super-horizon mode modulation [(Luciano et al., 3 Nov 2025); (Hamada et al., 2016); (Xue, 28 Mar 2026); (Namjoo et al., 2014)]. This suggests a common usage: a horizon, horizon-scale observable, or horizon-crossing event sets a bound, transition, or ambiguity scale for an asymmetry.

Domain	Horizon notion	Asymmetry quantity
Horizon-scale black-hole imaging	Event horizon / photon ring / scattering screen	Shadow asymmetry $A$, brightness asymmetry, Fourier asymmetry, ring $m=1$ mode
Relativistic quantum information	Schwarzschild event horizon	Gaussian steering asymmetry $\Delta \mathcal{G}$
Early-universe cosmology	Apparent horizon / Hubble horizon / super-horizon modes	Baryon asymmetry $\eta_B$, particle-antiparticle contrast, hemispherical power asymmetry

1. Shadow asymmetry as a scattering-limited observable

In the Sgr A* shadow literature, the asymmetry horizon is defined most explicitly as a measurement floor imposed by refractive interstellar scattering. For a Kerr black hole in GR, the shadow or photon-ring boundary is sampled at points $(x_i,y_i)$, from which one defines centroid-subtracted radii $R_i$, the mean radius $\langle R\rangle$, and the degree of asymmetry

$$A \equiv 2\sqrt{\frac{1}{N}\sum_{i=1}^N (R_i-\langle R\rangle)^2}.$$

For a perfectly circular ring, $A=0$. For Sgr A*, intrinsic Kerr shadow asymmetry is expected to remain small, with $$A_{\rm Kerr}\lesssim 0.6\,\Theta_M \approx 3\,\mu{\rm as}$$, while the shadow diameter is $m=1$0 and the nominal 230 GHz EHT resolution is $m=1$1 (Zhu et al., 2018).

The central issue is that refractive scattering distorts the image on the same few-$m=1$2as scale as the GR signal. Zhu et al. develop a general analytic framework for image wander, distortion, and scattering-induced asymmetry. For a preferred Kolmogorov-like scattering description (“J18”), the mean refractive image wander, distortion, and asymmetry at 230 GHz are $m=1$3, $m=1$4, and $m=1$5. For a flatter-spectrum alternative (“GS06”), the corresponding values can rise to $m=1$6, $m=1$7, and $m=1$8. The latter is comparable to or larger than the intrinsic Kerr asymmetry scale, so a single-epoch measurement cannot cleanly separate spacetime-induced asymmetry from scattering-induced asymmetry (Zhu et al., 2018).

This leads to the asymmetry horizon in its most literal observational sense: a stochastic floor $m=1$9 below which one cannot attribute noncircularity uniquely to the metric. Under J18, this floor is $\Delta \mathcal{G}$0 per 230 GHz observation and lies below the Kerr scale. Under GS06, it is $\Delta \mathcal{G}$1, above the Kerr scale. Because independent epochs sample different refractive realizations, the effective floor decreases approximately as $\Delta \mathcal{G}$2; for J18 at 230 GHz, averaging gives $\Delta \mathcal{G}$3 for $\Delta \mathcal{G}$4, $\Delta \mathcal{G}$5 for $\Delta \mathcal{G}$6, and $\Delta \mathcal{G}$7 for $\Delta \mathcal{G}$8 (Zhu et al., 2018).

A common misconception is to treat shadow asymmetry as purely a no-hair-theorem observable. The Sgr A* case is more restrictive: the asymmetry horizon is partly set by the line of sight through the turbulent ionized ISM, whereas M87* does not suffer the same strong-scattering limitation (Zhu et al., 2018).

2. Brightness asymmetry of horizon-scale rings

A different usage concerns the brightness asymmetry of horizon-scale images rather than the shape asymmetry of the shadow boundary. In GRMHD images, one side of the ring is brighter because Doppler beaming depends on the plasma angular velocity and the observer inclination. Palumbo et al. distinguish shape asymmetry from image brightness asymmetry and show that low brightness asymmetry is a sufficient but not necessary condition for low inclination: low-spin MAD flows can remain weakly asymmetric even when viewed edge-on because magnetic stresses reduce near-horizon azimuthal velocities well below the Keplerian value (Medeiros et al., 2021).

In that work, the relevant physical “horizon” is a near-horizon regime in parameter space where magnetic braking caps the achievable brightness asymmetry. SANE models remain closer to Keplerian rotation and become strongly crescent-like at high inclination, whereas the $\Delta \mathcal{G}$9 model retains low asymmetry even at $\eta_B$0. This implies that asymmetry alone is not a robust inclination diagnostic; it is degenerate with spin and accretion state (Medeiros et al., 2021).

For Sgr A*, Faggert et al. develop a Fourier-domain brightness-asymmetry statistic measured directly from EHT visibilities,

$\eta_B$1

where $\eta_B$2 is the baseline length of the first deep visibility minimum. Applying this to 2017 EHT data yields $\eta_B$3 and $\eta_B$4. Sgr A* is therefore inferred to have an unusually low degree of asymmetry, even lower than M87*. In a covariant semi-analytic model, this forces $\eta_B$5 if the plasma follows Keplerian profiles; alternatively, larger inclinations require significantly sub-Keplerian velocities and a black hole that is not spinning rapidly (Faggert et al., 2024).

The M87* literature uses yet another asymmetry measure, the $\eta_B$6 mode amplitude $\eta_B$7 in a circular Gaussian ring model,

$\eta_B$8

For the 2017, 2018, and 2021 EHT epochs, the inferred values are $\eta_B$9, $(x_i,y_i)$0, and $(x_i,y_i)$1. Comparing the observed distribution to KHARMA MAD simulations across spin, Palumbo et al. show that three epochs marginally disfavor $(x_i,y_i)$2, consistent with expectations from the Blandford–Znajek model for a nonzero-spin jet engine (Bernshteyn et al., 1 Jan 2026).

A further extension is polarization asymmetry. Two-temperature GRMHD simulations with radiative cooling show that cooling enhances the effective Faraday depth, increases the intrinsic asymmetry in both the ring structure and the polarization pattern, and raises the power in non-axisymmetric azimuthal polarization modes $(x_i,y_i)$3 relative to the dominant quadrupolar component $(x_i,y_i)$4. Cooling also produces stronger temporal variability in the polarization angle $(x_i,y_i)$5, including frequent sign reversals absent in non-cooling models (Long et al., 15 Jun 2026).

3. Event horizons and asymmetric quantum steering

In relativistic quantum information, the asymmetry horizon is the black-hole event horizon itself. In a Schwarzschild background, Wang et al. study Gaussian quantum steering for an inertial observer Alice, an accelerated observer Bob outside the horizon, and a hypothetical observer anti-Bob inside the horizon. The Hawking effect is described as a Gaussian channel that mixes Bob’s mode with an inaccessible partner mode behind the horizon, thereby degrading Alice–Bob steering and generating Bob–anti-Bob steering across the horizon (Wang et al., 2015).

For a two-mode Gaussian state, steering asymmetry is

$(x_i,y_i)$6

The horizon induces qualitatively distinct directional effects: steering from Alice to Bob undergoes “sudden death” at finite Hawking temperature, while steering from anti-Bob to Bob exhibits “sudden birth.” Unlike entanglement degradation in curved spacetime, these transitions occur at finite values of the Hawking parameter $(x_i,y_i)$7 (Wang et al., 2015).

The asymmetry is nevertheless intrinsically bounded. For both Alice–Bob and Bob–anti-Bob bipartitions, the Gaussian steering asymmetry never exceeds $(x_i,y_i)$8. The paper also identifies a critical curve,

$(x_i,y_i)$9

which marks maximal steering asymmetry and simultaneously the transition between one-way and both-way steerability. In this setting, the asymmetry horizon is both spatial and parametric: the event horizon redistributes correlations between causally disconnected regions, and the $R_i$0 critical curve marks where their directional structure changes character (Wang et al., 2015).

4. Horizon thermodynamics, black-hole horizons, and matter asymmetry

In cosmology and black-hole baryogenesis, “asymmetry horizon” denotes a horizon-defined mechanism that sources or bounds baryon asymmetry. One realization uses a generalized mass-to-horizon entropy,

$R_i$1

derived by imposing the Clausius relation on the apparent horizon of a flat FLRW universe. The modified horizon entropy changes the Friedmann dynamics and yields a nonvanishing $R_i$2 even during radiation domination, so the standard gravitational-baryogenesis operator $R_i$3 can generate a nonzero baryon-to-entropy ratio. Matching the observed asymmetry gives the bound $R_i$4 at $R_i$5 (Luciano et al., 3 Nov 2025).

A distinct mechanism uses evaporating primordial black holes. Hook et al. introduce CP-violating curvature–current operators of the form $R_i$6, so the time dependence of an evaporating black hole generates an effective chemical potential at the horizon. Hawking radiation then becomes asymmetric between particles and antiparticles. In the simplest dimension-8 case, the horizon ratio $R_i$7 scales as $R_i$8, so the asymmetry becomes large late in the evaporation history. The horizon here is the local site at which CP-violating curvature couplings bias Hawking emission and seed a cosmological baryon or lepton asymmetry (Hamada et al., 2016).

A third realization appears in reheating-era particle-antiparticle perturbations. During reheating, gravitationally produced massive $R_i$9 pairs develop a relative-density perturbation $\langle R\rangle$0. When the relevant mode exits the Hubble horizon, the perturbation freezes and a nonzero asymmetry inside the horizon remains: $\langle R\rangle$1 The subsequent decays of $\langle R\rangle$2 and $\langle R\rangle$3 explain baryogenesis and leptogenesis, and the associated charged asymmetries source primordial magnetic fields with present-day bounds $\langle R\rangle$4 in the model example quoted by the paper (Xue, 28 Mar 2026).

These cases are not equivalent mechanisms, but they share a structural feature: a horizon quantity—apparent-horizon entropy, black-hole horizon chemical potential, or Hubble-horizon crossing—creates the condition under which a microscopically symmetric state evolves into a macroscopic asymmetry.

5. Super-horizon modes and hemispherical sky asymmetry

In CMB anomaly research, the asymmetry horizon is a super-horizon mode whose wavelength exceeds the observable universe but modulates the statistics of shorter modes. The standard phenomenological form is

$\langle R\rangle$5

with a dipole modulation amplitude $\langle R\rangle$6 that is large at low multipoles and small at high multipoles. The long-mode modulation literature shows that such an effect is controlled by the squeezed-limit bispectrum, not by equilateral non-Gaussianity: the same super-horizon mode that modulates the scalar power also induces consistency relations for tensor asymmetry and halo-bias asymmetry, while not producing dipole asymmetry in late-time $\langle R\rangle$7CDM acceleration because the super-horizon curvature perturbation is conserved in that background [(Namjoo et al., 2014); (Abolhasani et al., 2013)].

The “separate universe” treatment sharpens this picture. A fixed super-horizon mode shifts the local background field value, so the power spectrum and local $\langle R\rangle$8 in our patch are evaluated at a displaced background. This unifies the Erickcek–Kamionkowski–Carroll modulation picture with the Grishchuk–Zel’dovich quadrupole and shows that non-linear quadrupole contributions are unavoidable in parameter regimes that can produce the observed asymmetry (Kobayashi et al., 2015).

Several early-universe mechanisms instantiate the same structure. In loop quantum cosmology, a pre-inflationary bounce excites long-wavelength modes, producing a strongly scale-dependent squeezed bispectrum. Correlations between observable modes and super-horizon modes then generate a dipole-dominated CMB power asymmetry with large-angle amplitude $\langle R\rangle$9, while higher multipoles and small-scale asymmetry remain suppressed (Agullo, 2015).

In tachyonic-field models, a complex field $$A \equiv 2\sqrt{\frac{1}{N}\sum_{i=1}^N (R_i-\langle R\rangle)^2}.$$0 evolving along a tachyonic potential produces a red isocurvature spectrum with

$$A \equiv 2\sqrt{\frac{1}{N}\sum_{i=1}^N (R_i-\langle R\rangle)^2}.$$1

and can generate $$A \equiv 2\sqrt{\frac{1}{N}\sum_{i=1}^N (R_i-\langle R\rangle)^2}.$$2 across the horizon if the observed universe exits the horizon within $$A \equiv 2\sqrt{\frac{1}{N}\sum_{i=1}^N (R_i-\langle R\rangle)^2}.$$3 e-foldings of the beginning of tachyonic evolution for $$A \equiv 2\sqrt{\frac{1}{N}\sum_{i=1}^N (R_i-\langle R\rangle)^2}.$$4 in the range $$A \equiv 2\sqrt{\frac{1}{N}\sum_{i=1}^N (R_i-\langle R\rangle)^2}.$$5 (McDonald, 2013).

A topological-defect variant attributes the asymmetry to a pre-inflationary $$A \equiv 2\sqrt{\frac{1}{N}\sum_{i=1}^N (R_i-\langle R\rangle)^2}.$$6 defect that imprints a phase gradient across the region that becomes our observable universe. The phase variation is protected while the defect is inside the horizon and then frozen by causality after horizon exit; later, the associated pseudo-Goldstone field oscillates and decays, modulating the radiation density. The parameter region highlighted in that work is $$A \equiv 2\sqrt{\frac{1}{N}\sum_{i=1}^N (R_i-\langle R\rangle)^2}.$$7 and $$A \equiv 2\sqrt{\frac{1}{N}\sum_{i=1}^N (R_i-\langle R\rangle)^2}.$$8 (Yang et al., 2016).

6. Comparative meaning and limitations of the term

Across these domains, “asymmetry horizon” does not denote a single invariant observable or one formal theory. The phrase instead marks a family of situations in which a horizon, horizon-scale image feature, or horizon-crossing event defines the scale at which asymmetry becomes bounded, masked, generated, or frozen. This suggests four recurring meanings.

First, it can be an observational floor: in Sgr A* shadow measurements, scattering sets the smallest asymmetry that can be reliably interpreted geometrically (Zhu et al., 2018). Second, it can be a dynamical cap: in black-hole image brightness, near-horizon plasma conditions can limit the asymmetry attainable at fixed inclination (Medeiros et al., 2021). Third, it can be a directional redistribution boundary: the Schwarzschild horizon changes who can steer whom, but only up to the $$A \equiv 2\sqrt{\frac{1}{N}\sum_{i=1}^N (R_i-\langle R\rangle)^2}.$$9 bound (Wang et al., 2015). Fourth, it can be a freeze-out or sourcing scale: horizon crossing or horizon thermodynamics turns long-wavelength perturbations or curvature couplings into persistent matter or sky asymmetries [(Luciano et al., 3 Nov 2025); (Namjoo et al., 2014)].

A further implication is that “asymmetry” itself is context-dependent. In the cited works it may mean shadow noncircularity, azimuthal brightness contrast, polarization-mode power outside $A=0$0, directional Gaussian steering, baryon-to-entropy ratio, particle-antiparticle number contrast, or hemispherical modulation of the CMB. Treating these as interchangeable would be misleading. The utility of the phrase lies instead in the repeated appearance of horizons as the structures that set asymmetry thresholds and transition scales across black-hole imaging, quantum information in curved spacetime, and early-universe cosmology.