Black holes in Lorentz-violating gravity theories

TL;DR

This work analyzes black holes in Lorentz-violating gravity theories, focusing on Einstein-aether theory and Hořava gravity to understand horizon structure when Lorentz symmetry is broken. It shows that static, spherically symmetric black holes can resemble GR outside the horizon, but regularity conditions fix the aether charge and leave a GR-like one-parameter family; it also introduces the universal horizon as a causal boundary applicable to all modes in Hořava gravity, while æ-theory may lack such a horizon for slowly rotating black holes. The study finds small but potentially detectable deviations from GR in observables like ISCO and photon-sphere radii, with gravitational-wave tests—especially EMRIs—offering a promising avenue for constraints. The results highlight key differences between the theories in rotating cases and identify important open questions about stability and nonlinear dynamics of universal horizons.

Abstract

Lorentz-symmetry and the notion of light cones play a central role in the definition of horizons and the existence of black holes. Current observations provide strong indications that astrophysical black holes do exist in Nature. Here we explore what happens to the notion of a black hole in gravity theories where local Lorentz symmetry is violated, and discuss the relevant astrophysical implications. Einstein-aether theory and Horava gravity are used as the theoretical background for addressing this question. We review earlier results about static, spherically symmetric black holes, which demonstrate that in Lorentz-violating theories there can be a new type of horizon and, hence, a new notion of black hole. We also present both known and new results on slowly rotating black holes in these theories, which provide insights on how generic these new horizons are. Finally, we discuss the differences between black holes in Lorentz-violating theories and in General Relativity, and assess to what extent they can be probed with present and future observations.

Figures (4)

• Figure 1: The viable regions (in light blue) of the parameter space of æ-theory (left) and Hořava gravity (right). General Relativity corresponds to the origin in both cases. For æ-theory the viable region extends upwards in the vertical direction, and for Hořava gravity both upwards and downwards in the vertical direction.
• Figure 2: The fractional deviation away from General Relativity for the dimensionless product $\omega_{_{\rm ISCO}} r_g$, for æ-theory (left) and low-energy Hořava gravity (right), in the viable region of the parameter plane. Negative values mean that $\omega_{_{\rm ISCO}} r_g$ is smaller in Lorentz-violating gravity than in General Relativity. These figures are re-rendered versions of Figures 2 and 6 of Ref. Barausse:2011pu.
• Figure 3: The same as in Figure \ref{['isco']}, but for the dimensionless quantity $b_{\rm ph}/r_g$. Positive values mean that this quantity is larger in Lorentz-violating gravity than in General Relativity. These figures are re-rendered versions of Figures 4 and 8 of Ref. Barausse:2011pu.
• Figure 4: Left panel: the boost angle between the aether and the future-directed normal to the $r=$ constant hypersurfaces for æ-theory with $c_+=0.8$, $c_-=0.01$. $\theta_r$ vanishes for the first time soon after the metric horizon (located at $r=r_H$) is crossed, and the aether becomes normal to an $r=$constant hypersurface pointing inwards. Right panel: schematic space-time diagram of a black hole with a universal horizon. The green curves represent constant preferred-time hypersurfaces, and they get darker as one moves into the future. These curves span the exterior of the universal horizon (red line), but none of them crosses it. The curves that span the region inside the universal horizon do not extend into the exterior. This implies that any signal emitted in the interior will not be able to escape to the exterior, simply by the requirement that it travel into the future. More universal horizons may be present at smaller radii but we have truncated the region of the diagram between the second one and the singularity.