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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider perfect fluid bodies (stars) in general relativity, characterizedby particle number density and entropy per particle. A star is said to be indynamic equilibrium if it is a stationary, axisymmetric solution to theEinstein-fluid equations with circular flow. We prove that for a star indynamic equilibrium, the necessary and sufficient condition for thermodynamicequilibrium (extremum of total entropy S) is constancy of angular velocity(\Omega), redshifted temperature, and redshifted chemical potential. Friedmanpreviously identified positivity of canonical energy, E, as a criterion fordynamic stability and argued that all rotating stars are dynamically unstableto sufficiently nonaxisymmetric perturbations (the CFS instability), so ourmain focus is on axisymmetric stability. We show that for a star in dynamicequilibrium, mode stability holds with respect to all axisymmetricperturbations if E is positive on a certain subspace, V, of axisymmetricLagrangian perturbations that, in particular, have no Lagrangian change inangular momentum density. Conversely, if E fails to be positive on V, thenthere exist perturbations that can't become asymptotically stationary at latetimes. We further show that for a star in thermodynamic equilibrium, thecanonical energy in the rotating frame, E_r, is related to second order changesin ADM mass, M, and angular momentum, J, by E_r = \delta^2 M - \Omega \delta^2J. Thus, positivity of E_r for perturbations with \delta J = 0 is a necessarycondition for thermodynamic stability (local maximum of S). For axisymmetricperturbations we have E = E_r, so a necessary condition for thermodynamicstability with respect to axisymmetric perturbations is positivity of E on allperturbations with \delta J = 0, not merely on the perturbations in V. Many ofour results are in close parallel to results of Hollands and Wald for thetheory of black holes.

Dynamic and Thermodynamic Stability of Relativistic, Perfect Fluid Stars