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

In this paper we study axial gravitational perturbations of an infinitestatic line source, represented by a form of the Levi-Civita metric. Theperturbations are restricted to axial symmetry but break the cylindricalsymmetry of the background metric. We analyze the gauge issues that arise insetting up the appropriate form of the perturbed metric and show that it ispossible to restrict to diagonal terms, but that this does not fix the gaugecompletely. We derive the perturbation equations and show that they can besolved by solving a third order ordinary differential equation for anappropriately chosen function of the perturbed metric coefficients. The set ofsolutions of this equation contains gauge trivial parts, and we show how toextract the gauge non trivial components. We introduce appropriate boundaryconditions on the solutions and show that these lead to a boundary valueproblem that determines the allowed functional forms of the perturbation modes.The associated eigenvalues determine a sort of "dispersion relation" for thefrequencies and corresponding "wave vector" components. The central result ofthis analysis is that the spectrum of allowed frequencies contains one unstable(imaginary frequency) mode for every possible choice of the background metric.The completeness of the mode expansion in relation to the initial value problemand to the gauge problem is discussed in detail, and we show that theperturbations contain an unstable component for generic initial data, and,therefore, that the Levi-Civita space times are gravitationally unstable. Wealso include, for completeness, a set of approximate eigenvalues, and examplesof the functional form of the solutions.

Axial gravitational perturbations of an infinite static line source