Dynamic and Thermodynamic Stability of Charged Perfect Fluid Stars

Abstract

We perform a thorough analysis of the dynamic and thermodynamic stability for the charged perfect fluid star by applying the Wald formalism to the Lagrangian formulation of Einstein-Maxwell-charged fluid system. As a result, we find that neither the presence of the additional electromagnetic field nor the Lorentz force experienced by the charged fluid makes any obstruction to the key steps towards the previous results obtained for the neutral perfect fluid star. Therefore, the criterion for the dynamic stability of our charged star in dynamic equilibrium within the symplectic complement of the trivial perturbaions with the ADM $3$-momentum unchanged is given by the non-negativity of the canonical energy associated with the timelike Killing field, where it is further shown for both non-axisymmetric and axisymmetric perturbations that the dynamic stability against these restricted perturbations also implies the dynamic stability against more generic perturbations. On the other hand, the necessary condition for the thermodynamic stability of our charged star in thermodynamic equilibrium is given by the positivity of the canonical energy of all the linear on-shell perturbations with the ADM angular momentum unchanged in the comoving frame, which is equivalent to the positivity of the canonical energy associated with the timelike Killing field when restricted onto the axisymmetric perturbations. As a by-product, we further establish the equivalence of the dynamic and thermodynamic stability with respect to the spherically symmetric perturbations of the static, spherically symmetric isentropic charged star.

arXiv comment20 pages, 1 figure, typos corrected, to appear in CQG

References in corpus (16)

• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Lectures on hydrodynamic fluctuations in relativistic theories
• The evolution of unstable black holes in anti-de Sitter space
• Stability of Black Holes and Black Branes
• Electron stars for holographic metallic criticality
• Effective field theory for dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current
• Global Anomalies, Discrete Symmetries, and Hydrodynamic Effective Actions
• Thermodynamical instabilities of perfect fluid spheres in General Relativity
• Dynamic and Thermodynamic Stability of Relativistic, Perfect Fluid Stars
• Electrically charged strange stars with an interacting quark matter equation of state
• Thermodynamical stability for perfect fluid
• Consistency between dynamical and thermodynamical stabilities for perfect fluid in $f(R)$ theories
• Thermodynamic equilibrium condition and the first law of thermodynamics for charged perfect fluids in electromagnetic and gravitational fields
• Consistency between dynamical and thermodynamical stabilities for charged self-gravitating perfect fluid

Cited by in corpus (1)

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