Probing observable features of Lorentz violation in low-energy Hořava gravity with accretion disk images of black hole

Abstract In this paper, we study the observable signatures of Lorentz violation (LV) in low-energy Hořava gravity by simulating the images and polarization features of rotating LV black holes using a backward ray-tracing method. Within a thin-disk accretion model and the ZAMO framework, we numerically solve the geodesics equation of photon and simulated the corresponding thin-disk images and polarization patterns. The results show that the LV parameter $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> strongly affects the inner shadow, brightness asymmetry, and polarization properties of the thin disk. The decrease of $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> leads to a more elliptical and untilted inner shadow, while increasing $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> produces a pronounced leftward “D”-shaped structure of critical curve. And, the variation of $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> alters the distribution of polarized intensity and polarization direction, especially near the critical curve. More importantly, it also shows that a positive $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> enhances the black hole’s angular velocity, while a negative one suppresses it, indicating that the sign of $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> determines the trend direction of the LV effect. These findings suggest that future high-resolution EHT observations combining the thin-disk images and polarization patterns could provide valuable tests of the LV effect.