Black holes in Einstein-aether and Horava-Lifshitz gravity (1104.2889v2)

Abstract: We study spherical black-hole solutions in Einstein-aether theory, a Lorentz-violating gravitational theory consisting of General Relativity with a dynamical unit timelike vector (the "aether") that defines a preferred timelike direction. These are also solutions to the infrared limit of Horava-Lifshitz gravity. We explore parameter values of the two theories where all presently known experimental constraints are satisfied, and find that spherical black-hole solutions of the type expected to form by gravitational collapse exist for all those parameters. Outside the metric horizon, the deviations away from the Schwarzschild metric are typically no more than a few percent for most of the explored parameter regions, which makes them difficult to observe with electromagnetic probes, but in principle within reach of future gravitational-wave detectors. Remarkably, we find that the solutions possess a universal horizon, not far inside the metric horizon, that traps waves of any speed relative to the aether. A notion of black hole thus persists in these theories, even in the presence of arbitrarily high propagation speeds.

• The paper presents spherical black-hole solutions in Einstein-aether theory, revealing minimal metric deviations compared to the Schwarzschild solution.
• The study identifies a universal horizon that traps all wave speeds, underscoring key differences from classical black-hole models.
• Results offer insights into quantum gravity and motivate further observational tests with advanced gravitational-wave detectors.

Black Holes in Lorentz-Violating Theories: An Analysis of Einstein-aether and Hořava–Lifshitz Gravity

This paper explores black-hole solutions within the framework of Einstein-aether theory and its relation to Hořava–Lifshitz gravity. Both theories are modified gravity models that violate Lorentz invariance, a foundational symmetry of classical physics. Discrepancies in observations due to Lorentz violations could reveal new insights into the nature of spacetime and gravity.

Core Elements of the Study

The focus is on spherical black-hole solutions in Einstein-aether theory, which includes a unit timelike vector field known as the aether. This component breaks local Lorentz symmetry by defining a preferred direction in spacetime. The paper of these black holes extends to Hořava–Lifshitz gravity, a theory that aims to provide a quantum gravity framework and assumes Lorentz violation through anisotropic scaling between space and time at high energies. Notably, in the infrared (IR) limit, Hořava–Lifshitz gravity coincides with a restricted version of Einstein-aether theory, where the aether is hypersurface orthogonal.

Results and Observations

The paper identifies black-hole solutions that conform to known experimental constraints across the parameter space. Several noteworthy features of these black holes are:

• Metric Deviations: Deviations from the Schwarzschild solution outside the metric horizon are minimal, often within a few percent, making these differences challenging to detect with electromagnetic methods. However, future gravitational-wave detectors might detect such anomalies.
• Universal Horizon: Interestingly, solutions exhibit a universal horizon inside the metric horizon. This horizon traps waves of any speed relative to the aether, suggesting the persistence of the black-hole notion despite potentially infinite propagation speeds in Hořava–Lifshitz gravity.
• Interior Structure: Inside these black holes, the interplay between spacetime curvature and the aether field results in complex dynamical behavior. Close to the singularity, the aether field demonstrates oscillatory behavior while geometric quantities diverge.

Implications and Future Directions

These findings have several significant implications:

1. Astrophysical Observability: The weak deviations from standard black-hole metrics suggest current astrophysical studies might not easily distinguish these solutions without advances in observational techniques, such as improved gravitational-wave detection.
2. Theoretical Insight: The presence of universal horizons in these theories may offer new ways to think about information paradoxes and the nature of horizons in a quantum gravity context.
3. Parameter Space Exploration: While this paper has explored black holes in the context of Einstein-aether and Hořava–Lifshitz gravity, further studies could investigate more complex scenarios involving rotating black holes or incorporating matter fields.

This paper sets a foundation for understanding black holes within Lorentz-violating modified gravity theories, offering a bridge between observed phenomena and theoretical advances beyond general relativity. While current deviations in observables are minor, the continued development of observational technologies provides hope for empirical tests of these theoretical predictions, potentially leading to a broader understanding of fundamental physics.