On “Hard Stars” in General Relativity - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Annales Henri Poincare Année : 2019

On “Hard Stars” in General Relativity

Résumé

We study spherically symmetric solutions to the Einstein–Euler equations which model an idealised relativistic neutron star surrounded by vacuum. These are barotropic fluids with a free boundary, governed by an equation of state which sets the speed of sound equal to the speed of light. We demonstrate the existence of a 1-parameter family of static solutions, or “hard stars” and describe their stability properties: First, we show that small stars are a local minimum of the mass energy functional under variations which preserve the total number of particles. In particular, we prove that the second variation of the mass energy functional controls the “mass aspect function”. Second, we derive the linearisation of the Euler–Einstein system around small stars in “comoving coordinates” and prove a uniform boundedness statement for an energy, which is exactly at the level of the variational argument. Finally, we exhibit the existence of time-periodic solutions to the linearised system, which shows that energy boundedness is optimal for this problem.

Dates et versions

hal-02165513 , version 1 (26-06-2019)

Identifiants

Citer

Grigorios Fournodavlos, Volker Schlue. On “Hard Stars” in General Relativity. Annales Henri Poincare, 2019, 20 (7), pp.2135-2172. ⟨10.1007/s00023-019-00793-4⟩. ⟨hal-02165513⟩
48 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More