Lorentz violation signatures in the low-energy sector of Hořava gravity from black hole shadow observations

In this paper, we use the Hořava gravity model and EHT observations of supermassive black holes (BHs) to investigate signatures of Lorentz violation in real astrophysical environments. The Lorentz violation in the rotating Hořava BH spacetime are confined to the strong gravitational field region, being induced by the BH’s rotation. Due to the non-separability of the photon motion equations in this spacetime, we employed a numerical backward ray-tracing method to generate shadow images for various BH parameters. Subsequently, we extracted coordinate positions characterizing the shadow shape from high-pixel images to evaluate the parameter space of the BH. When evaluating M87*, Lorentz violation can occur with arbitrary strength. However, for Sgr A*, we can impose certain parameter constraints on Lorentz violation. These constraints depend on the BH’s spin. If future observations confirm Sgr A*’s spin parameter less than 0.81 at maximum inclination, current EHT results would challenge general relativity and support Lorentz violation in low-energy regimes.

💡 Research Summary

This paper investigates possible signatures of Lorentz violation (LV) in the low‑energy sector of Hořava gravity by exploiting the shadows of supermassive black holes (BHs) observed by the Event Horizon Telescope (EHT). The authors focus on the exact rotating Hořava BH solution derived by Devecioğlu and Park, which reduces to the Kerr metric when the LV parameter ℓ ≡ √(κξ) − 1 vanishes. For ℓ ≠ 0 the metric acquires extra contributions in g_tt and g_tφ that are proportional to the spin a, meaning that LV is confined to the strong‑field region around a rotating BH and disappears for a non‑rotating (Schwarzschild) case.

Because the LV term destroys the Carter constant, the photon null‑geodesic equations are non‑separable. The authors therefore adopt a numerical backward ray‑tracing scheme: photons are launched from an observer’s image plane, integrated backward in time using the full set of geodesic equations, and those that cross the event horizon are marked as shadow pixels. High‑resolution (16 K) images are generated for a grid of spin a/M and LV parameter ℓ values. To quantify the shadow shape they extract two observable quantities, the radius R_s of a reference circle and the distortion parameter δ_s = D/R_s, where D measures the horizontal shift of the leftmost edge relative to the reference circle.

The study reveals distinct LV‑induced deformations. For ℓ > 0 the shadow becomes progressively flattened in the horizontal direction, evolving from a circular to an “O‑shaped” contour, while the spin alone would produce a D‑shaped deformation. For ℓ < 0, especially at near‑extremal spins, the shadow first approaches a perfect circle, then flattens along the y‑axis and finally forms a horizontally oriented O‑shape. These opposite trends illustrate how LV can either enhance or counteract the frame‑dragging effect of rotation.

The authors then confront the theoretical shadows with EHT measurements of M87* and Sgr A*. For M87* (M ≈ 6.5 × 10⁹ M⊙, distance ≈ 16.8 Mpc, inclination ≈ 17°, angular diameter ≈ 42 ± 3 µas) they scan ℓ∈