Well-posed evolution of field theories with anisotropic scaling: the Lifshitz scalar field in a black hole space-time
arXiv:2307.13041 · doi:10.1088/1475-7516/2023/11/001
Abstract
Partial differential equations exhibiting an anisotropic scaling between space and time -- such as those of Horava-Lifshitz gravity -- have a dispersive nature. They contain higher-order spatial derivatives, but remain second order in time. This is inconvenient for performing long-time numerical evolutions, as standard explicit schemes fail to maintain convergence unless the time step is chosen to be very small. In this work, we develop an implicit evolution scheme that does not suffer from this drawback, and which is stable and second-order accurate. As a proof of concept, we study the numerical evolution of a Lifshitz scalar field on top of a spherically symmetric black hole space-time. We explore the evolution of a static pulse and an (approximately) ingoing wave-packet for different strengths of the Lorentz-breaking terms, accounting also for the effect of the angular momentum eigenvalue and the resulting effective centrifugal barrier. Our results indicate that the dispersive terms produce a cascade of modes that accumulate in the region in between the Killing and universal horizons, indicating a possible instability of the latter.
28 pages, 11 figures, 1 table. Accepted for publication in JCAP
References in corpus (17)
- Quantum Gravity at a Lifshitz Point
- Topological Order and Conformal Quantum Critical Points
- Models of non-relativistic quantum gravity: the good, the bad and the healthy
- Horava-Lifshitz Cosmology: A Review
- Black holes in Einstein-aether and Horava-Lifshitz gravity
- Renormalization of Lorentz violating theories
- Slowly rotating black holes in Horava-Lifshitz gravity
- Bounding the speed of gravity with gravitational wave observations
- Phenomenology of theories of gravity without Lorentz invariance: the preferred frame case
- Cosmological constraints on deviations from Lorentz invariance in gravity and dark matter
- New binary pulsar constraints on Einstein-æther theory after GW170817
- Beta functions of (3+1)-dimensional projectable Horava gravity
- Cancellation of divergences in the nonprojectable Horava theory
- The relation between general relativity and a class of Hořava gravity theories
- Regular Black Holes and Horizonless Ultra-Compact Objects in Lorentz-Violating Gravity
- Black Holes in Ultraviolet-Complete Horava Gravity
- Lifshitz scaling, ringing black holes, and superradiance