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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We investigate spherically symmetric spacetimes with an anisotropic fluid anddiscuss the existence and stability of a dividing shell separating expandingand collapsing regions. We resort to a 3+1 splitting and obtain gauge invariantconditions relating intrinsic spacetimes quantities to properties of the mattersource. We find that the dividing shell is defined by a generalization of theTolman-Oppenheimer-Volkoff equilibrium condition. The latter establishes abalance between the pressure gradients, both isotropic and anisotropic, and thestrength of the fields induced by the Misner-Sharp mass inside the separatingshell and by the pressure fluxes. This defines a local equilibrium condition,but conveys also a non-local character given the definition of the Misner-Sharpmass. By the same token, it is also a generalized thermodynamical equation ofstate as usually interpreted for the perfect fluid case, which now has thenovel feature of involving both the isotropic and the anisotropic stress. Wehave cast the governing equations in terms of local, gauge invariant quantitieswhich are revealing of the role played by the anisotropic pressures andinhomogeneous electric part of the Weyl tensor. We analyse a particularsolution with dust and radiation that provides an illustration of ourconditions. In addition, our gauge invariant formalism not only encompasses thecracking process from Herrera and coworkers but also reveals transparently theinterplay and importance of the shear and of the anisotropic stresses.

Local conditions separating expansion from collapse in spherically symmetric models with anisotropic pressures