Horizon: Multifaceted Perspectives

• Horizon is defined as a term with distinct disciplinary meanings, including causal boundaries in cosmology, visible limits in observation, temporal spans in forecasting, and proper names in software and experiments.
• The review distinguishes methodologies for measuring horizons, addressing challenges such as the correct interpretation of the Hubble radius, horizon transmission in 21-cm cosmology, and near-horizon geometries in black-hole physics.
• The discussion highlights practical implications across fields, demonstrating how accurate horizon modeling improves simulations in GRMHD, enhances forecasting in AI and finance, and refines observational data in astronomy.

to=arxiv_search 诺果json content='{"query":"HORIZON arXiv horizon review term multiple fields HORIZON", "max_results": 10, "sort_by": "submittedDate"}'

Searching arXiv for papers relevant to “HORIZON” across domains. to=arxiv_search code: {"query":"HORIZON", "max_results": 10, "sort_by": "submittedDate"} to=arxiv_search ՞նչ content='{"query":"title:HORIZON OR horizon", "max_results": 20}' Horizon is a technically overloaded term whose meaning depends on disciplinary context. In gravitation and cosmology it denotes causal, kinematic, or thermodynamic structures associated with null propagation and spacetime dynamics; in observational science it denotes the line-of-sight boundary set by terrain, atmosphere, or local topography; in machine learning, geophysical forecasting, and finance it denotes the temporal span over which actions, forecasts, or investor types are defined; and in several domains it appears as a proper name for software, numerical codes, and experiments (Schützhold, 2010, Bassett et al., 2021, Hu et al., 12 Feb 2026, Pistorius et al., 2020, Zink, 2011, Beisembaev et al., 2016).

1. Terminological scope

The literature represented here distinguishes several non-equivalent uses of the term. In some cases, a horizon is a genuine causal boundary. In others, it is a visible skyline, an attenuation boundary, or a planning horizon. In still others, “Horizon” is simply the name of an interface, detector, or code. One recurrent methodological point is that not every quantity labeled a horizon behaves as one; the proposed cosmological quantity $R_h$, for example, is explicitly argued to be a Hubble sphere rather than a true horizon (Lewis, 2013).

Domain	Sense of “horizon”	Representative source
Gravitation and cosmology	Event, particle, apparent, Hubble-related, or null-hypersurface structure	(Schützhold, 2010, Manzano et al., 1 Dec 2025)
Observational science	Local skyline or atmospheric/terrain visibility limit	(Bassett et al., 2021, Patat, 2011, Mirzoyan et al., 2019)
Temporal modeling and finance	Long-range decision, forecast, or investment span	(Hu et al., 12 Feb 2026, Liu et al., 28 May 2026, Vamossy, 29 Nov 2025)
Proper names	OpenStack dashboard, GRMHD code, EAS detector	(Pistorius et al., 2020, Zink, 2011, Beisembaev et al., 2016)

2. Causal and cosmological horizons

In analogue-gravity and cosmology-oriented treatments, a horizon is primarily a kinematic notion of lost causal contact. For low-energy quasiparticles in suitable media, the linearized dynamics can be written as a curved-spacetime wave equation, so event, particle, and apparent horizons acquire operational meaning without requiring Einstein dynamics for the background medium. In this framework, a horizon is defined by the effective light-cone structure, and horizon formation is associated with nonequilibrium behavior, amplification of quantum fluctuations, and, in black-hole analogues, Hawking-like emission (Schützhold, 2010).

Within flat FRW and especially de Sitter cosmology, horizon thermodynamics has been formulated in terms of the Hubble horizon radius $r_H=c/H$, Gibbons–Hawking temperature $T_H=\hbar H/(2\pi k_B)$, and Bekenstein–Hawking entropy $S_H=k_B c^3 A_H/(4\hbar G)$. A central result of this approach is the equality between the Helmholtz free energy on the horizon and the effective bulk energy inferred from the Friedmann equation, $F_H=E_{\mathrm{eff}}$, with $E_{\mathrm{eff}}=\rho c^2V=c^5/(2GH)$. This is interpreted as a holographic-like connection between thermostatistical quantities on the horizon and effective bulk cosmological dynamics (Komatsu, 2022).

A distinct and explicitly critical line of argument concerns the so-called “Cosmic Horizon” $R_h=1/H$. In the flat FRW metric, the proper distance $d=ar$ of an incoming radial photon obeys $\dot d = Hd - 1$. Hence the surface $d=1/H$ is the point at which the photon has zero proper radial velocity relative to the observer, not a causal boundary. For a universe dominated by a fluid with equation of state $r_H=c/H$0, the same paper gives $r_H=c/H$1, so $r_H=c/H$2 can shrink, remain constant, or grow depending on the cosmic fluid; in models with phantom energy and evolving $r_H=c/H$3, a single null geodesic can cross $r_H=c/H$4 multiple times. The paper therefore rejects the claim that $r_H=c/H$5 is a new fundamental horizon or an infinite-redshift surface (Lewis, 2013).

3. Black-hole horizons and near-horizon structure

A modern geometric formalism treats a horizon as a null hypersurface equipped with a preferred null tangent field $r_H=c/H$6, with deformation tensor $r_H=c/H$7. On this basis, the notion of a $r_H=c/H$8-tuple encodes the zeroth-order horizon data, while the non-isolation tensor measures the degree to which the horizon fails to be isolated. The non-isolation tensor vanishes for homothetic, Killing, and isolated horizons. A generalized near-horizon equation then relates non-isolation, torsion, and curvature on arbitrary horizons, without assuming a particular topology or the absence of fixed points (Manzano et al., 1 Dec 2025).

For EVH black holes—extremal configurations whose vanishing horizon area is due to a shrinking one-cycle—the near-horizon geometry obeys strong structural theorems. Under broad assumptions, the near-horizon region contains a three-dimensional maximally symmetric subspace. If the strong energy condition holds and $r_H=c/H$9, this 3d sector is locally AdS$T_H=\hbar H/(2\pi k_B)$0 or, in a special case, locally flat. For near-EVH deformations, the AdS$T_H=\hbar H/(2\pi k_B)$1 factor is replaced by BTZ geometry (Sadeghian et al., 2015). In a different quasi-local construction, the spacetime near a non-extremal Kerr or Kerr–dS isolated horizon is reconstructed order by order in Bondi-like coordinates from intrinsic horizon data, specifically the horizon connection and the Newman–Penrose coefficient $T_H=\hbar H/(2\pi k_B)$2. In that reconstruction, the first radial coefficient of $T_H=\hbar H/(2\pi k_B)$3 encodes the surface gravity, while the $T_H=\hbar H/(2\pi k_B)$4 terms encode horizon rotation (Lewandowski et al., 2018).

Near-horizon degrees of freedom also appear in microscopic entropy proposals. For BTZ black holes, “horizon fluff” denotes a charge-constrained subset of near-horizon soft hairs that are invisible to observers away from the horizon yet reproduce the Bekenstein–Hawking entropy when counted with the Hardy–Ramanujan formula for partitions (Afshar et al., 2016). A different BTZ model replaces the true horizon by a Planckian stretched horizon treated as a Dirichlet boundary for a free scalar. In that setup, typical high-energy pure states built on the stretched-horizon vacuum yield boundary correlators that converge, in the small-$T_H=\hbar H/(2\pi k_B)$5 limit, to the Hartle–Hawking correlator of a smooth horizon, with finite-$T_H=\hbar H/(2\pi k_B)$6 corrections suppressed as $T_H=\hbar H/(2\pi k_B)$7 and becoming relevant only at late times (Burman et al., 2023).

Not all near-horizon analyses support smooth extendibility. In Einstein gravity extended by a Riemann-squared term, the extremal $T_H=\hbar H/(2\pi k_B)$8 equal-spin rotating black hole develops irrational powers in its near-horizon perturbative expansion. The paper argues that curvature invariants can remain finite while the spacetime nevertheless fails to admit a smooth interior extension across the horizon, so that the horizon becomes a natural boundary of spacetime rather than a harmless coordinate surface (Mao et al., 2023).

4. Observational, terrestrial, and atmospheric horizons

In global 21-cm cosmology, the horizon enters directly into the forward model for the antenna temperature through a horizon transmission or attenuation map. Because the foregrounds are $T_H=\hbar H/(2\pi k_B)$9–$S_H=k_B c^3 A_H/(4\hbar G)$0 orders of magnitude brighter than the target 21-cm signal, even a small horizon mismatch can dominate the inferred cosmological signal. The paper shows that single-spectrum fits and independent multi-spectrum fits may absorb some horizon-induced bias, but they retain weak constraining power, with uncertainties at the K level. By contrast, multi-spectrum fits with shared parameters can reduce uncertainties to $S_H=k_B c^3 A_H/(4\hbar G)$1 mK, but only if the time dependence of the horizon effect is modeled accurately. To support such modeling, the paper introduces the Python package SHAPES for computing horizon profiles from elevation data, and demonstrates that including multiple horizon realizations in the training set can improve signal recovery dramatically; in one lunar example, $S_H=k_B c^3 A_H/(4\hbar G)$2 improved from 220 to 1.02 when the training set spanned the horizon uncertainty (Bassett et al., 2021).

For archaeoastronomy, the horizon is synthesized numerically from digital elevation models. The basic procedure samples terrain along a line of sight at fixed azimuth, computes the apparent altitude of each sampled point, and takes the maximum as the horizon altitude in that direction. The curvature-corrected working expression is

$S_H=k_B c^3 A_H/(4\hbar G)$3

with terrestrial refraction added as $S_H=k_B c^3 A_H/(4\hbar G)$4. Using SRTM90 data, the method is reported to be reliable when the horizon lies farther than about 10 km, with rms accuracy of about $S_H=k_B c^3 A_H/(4\hbar G)$5 in both azimuth and elevation under those conditions (Patat, 2011).

In very-high-energy gamma-ray astronomy, the horizon is approached as an observing regime rather than merely an obstruction. MAGIC very-large-zenith-angle observations extend almost to the horizon by calibrating atmospheric transmission through aperture photometry of nearby stars. Beyond about $S_H=k_B c^3 A_H/(4\hbar G)$6, atmospheric absorption becomes the dominant systematic, but the much larger shower footprint on the ground increases the collection area substantially. For zenith angles $S_H=k_B c^3 A_H/(4\hbar G)$7–$S_H=k_B c^3 A_H/(4\hbar G)$8, the paper reports a collection area of about $S_H=k_B c^3 A_H/(4\hbar G)$9 or more above 10 TeV, and presents a candidate event recorded at $F_H=E_{\mathrm{eff}}$0 with estimated energy 144.4 TeV (Mirzoyan et al., 2019).

5. “Horizon” as the name of systems, interfaces, and experiments

In cloud computing, Horizon is the default graphical user interface for OpenStack. It is described as powerful but oriented toward IT system administrators rather than researchers, because tasks such as creating an instance and connecting to it require familiarity with security groups, SSH key pairs, and networking. In the comparison presented by the Exosphere paper, Horizon required 10 clicks to create an instance, compared with 3 clicks for Exosphere, while basic provisioning times were of similar order (Pistorius et al., 2020).

In computational astrophysics, HORIZON is a standalone CUDA/C++ GPU code for solving general relativistic magnetohydrodynamics on a fixed spacetime background. It evolves the conservative 3+1 GRMHD system in the Cowling approximation, uses finite-volume shock capturing with TVD or PPM reconstruction, HLLE fluxes, third-order Runge–Kutta time stepping, and optional hyperbolic divergence cleaning, and was benchmarked against the CPU code Thor. For a $F_H=E_{\mathrm{eff}}$1 rotating-neutron-star test, the reported time for 100 evolution steps was 12.0 s in GPU single precision and 60.1 s in GPU double precision, compared with 785.2 s on 4 CPU cores; in a two-GPU weak-scaling test, the reported parallel efficiencies were 96.5% in single precision and 98.6% in double precision (Zink, 2011).

In cosmic-ray physics, Horizon-T is an extensive-air-shower detector at the Tien Shan high-altitude Science Station, near Almaty, Kazakhstan. It was designed to study individual showers above $F_H=E_{\mathrm{eff}}$2 across zenith angles $F_H=E_{\mathrm{eff}}$3–$F_H=E_{\mathrm{eff}}$4, using eight charged-particle detection points separated by up to about 1 km and an optical subsystem for Vavilov–Cherenkov light. A defining feature is few-nanosecond timing, motivated by the 20–30 ns crossing time of a near-vertical $F_H=E_{\mathrm{eff}}$5 shower disk at 100 m from the axis (Beisembaev et al., 2016). After the March 2018 upgrade, the instrument was renamed Horizon-10T, with 10 charged-particle detection points separated by up to about 1.3 km, additional glass and scintillator detectors, and cable-delay and attenuation calibration based on reflected pulses. The upgraded system is reported to have a geometric factor of about $F_H=E_{\mathrm{eff}}$6 at $F_H=E_{\mathrm{eff}}$7 (Beznosko et al., 2018).

6. Temporal horizons in learning, forecasting, and finance

In embodied AI, a horizon is the temporal span over which sequential credit assignment must be performed. LongNav-R1 argues that long-horizon navigation should not be treated as a sequence of independent next-action predictions. Instead, it formulates navigation as a multi-turn RL process,

$F_H=E_{\mathrm{eff}}$8

and introduces Horizon-Adaptive Policy Optimization, a critic-free estimator that uses a Gaussian temporal kernel so that baseline estimation is local in time. With 4,000 rollout trajectories, the paper reports that LongNav-R1 improves Qwen3-VL-2B success rate from 64.3% to 73.0%; for episodes beyond 200 steps, the finite-window variant with $F_H=E_{\mathrm{eff}}$9 achieved 15.4% success rate, whereas the uniform-baseline variant achieved zero (Hu et al., 12 Feb 2026).

In long-range geophysical emulation, “horizon-aware” forecasting means training a single model to predict multiple future lead times rather than only the next step. A multi-horizon graph neural network for Pine Island Glacier represents the ISSM mesh as a graph, predicts residual state increments for several horizons at once, and performs coarse-to-fine rollout to reduce drift. Over a 180-month forecast window, the reported errors for the horizon set $E_{\mathrm{eff}}=\rho c^2V=c^5/(2GH)$0 were $E_{\mathrm{eff}}=\rho c^2V=c^5/(2GH)$1, $E_{\mathrm{eff}}=\rho c^2V=c^5/(2GH)$2, and $E_{\mathrm{eff}}=\rho c^2V=c^5/(2GH)$3, compared with 108.77, 207.05, and 30.91 for a standard one-step autoregressive rollout (Liu et al., 28 May 2026).

In empirical finance, investment horizon is a characteristic of the retail investor base. Using StockTwits posts from 2010–2021, stocks are classified as predominantly Long-Term when the pre-announcement share of long-term users in the $E_{\mathrm{eff}}=\rho c^2V=c^5/(2GH)$4 window exceeds 50%. The paper reports that long-horizon stocks exhibit larger immediate earnings reactions and larger post-announcement drift: the fully controlled estimates are about $E_{\mathrm{eff}}=\rho c^2V=c^5/(2GH)$5 percentage points over days 0–1, $E_{\mathrm{eff}}=\rho c^2V=c^5/(2GH)$6 percentage points over days 2–75, and $E_{\mathrm{eff}}=\rho c^2V=c^5/(2GH)$7 percentage points over days 0–75. A long-minus-short strategy is summarized as generating 0.43% monthly alpha (Vamossy, 29 Nov 2025).