English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Partial differential equations exhibiting an anisotropic scaling betweenspace and time -- such as those of Horava-Lifshitz gravity -- have a dispersivenature. They contain higher-order spatial derivatives, but remain second orderin time. This is inconvenient for performing long-time numerical evolutions, asstandard explicit schemes fail to maintain convergence unless the time step ischosen to be very small. In this work, we develop an implicit evolution schemethat does not suffer from this drawback, and which is stable and second-orderaccurate. As a proof of concept, we study the numerical evolution of a Lifshitzscalar field on top of a spherically symmetric black hole space-time. Weexplore the evolution of a static pulse and an (approximately) ingoingwave-packet for different strengths of the Lorentz-breaking terms, accountingalso for the effect of the angular momentum eigenvalue and the resultingeffective centrifugal barrier. Our results indicate that the dispersive termsproduce a cascade of modes that accumulate in the region in between the Killingand universal horizons, indicating a possible instability of the latter.

Well-posed evolution of field theories with anisotropic scaling: the Lifshitz scalar field in a black hole space-time