Gravothermal catastrophe and critical dimension in a $D$-dimensional asymptotically AdS spacetime

Abstract

We investigate the structure and stability of the thermal equilibrium states of a spherically symmetric self-gravitating system in a $D$-dimensional asymptotically Anti-de Sitter(AdS) spacetime. The system satisfies the Einstein-Vlasov equations with a negative cosmological constant. Due to the confined structure of the AdS potential, we can construct thermal equilibrium states without any artificial wall in the asymptotically AdS spacetime. Accordingly, the AdS radius can be regarded as the typical size of the system. Then the system can be characterized by the gravothermal energy and AdS radius normalized by the total particle number. We investigate the catastrophic instability of the system in a $D$-dimensional spacetime by using the turning point method. As a result, we find that the curve has a double spiral structure for $4\le D\le 10$ while it does not have any spiral structures for $D\ge 11$ as in the asymptotically flat case confined by an adiabatic wall. Irrespective of the existence of the spiral structure, there exist upper and lower bounds for the value of the gravothermal energy. This fact indicates that there is no thermal equilibrium solution outside the allowed region of the gravothermal energy. This property is also similar to the asymptotically flat case.

arXiv comment23 pages

References in corpus (30)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• On weakly turbulent instability of anti-de Sitter space
• Boson Stars in AdS
• Holographic Thermalization, stability of AdS, and the Fermi-Pasta-Ulam-Tsingou paradox
• Gravitational instability of finite isothermal spheres
• On the Nonlinear Stability of Asymptotically Anti-de Sitter Solutions
• Renormalization group, secular term resummation and AdS (in)stability
• Time-periodic solutions in Einstein AdS - massless scalar field system
• Renormalization, averaging, conservation laws and AdS (in)stability
• Rapid Thermalization in Field Theory from Gravitational Collapse
• Resonant dynamics and the instability of anti-de Sitter spacetime
• A comment on AdS collapse of a scalar field in higher dimensions
• Islands of stability and recurrence times in AdS
• Thermodynamical instabilities of perfect fluid spheres in General Relativity
• Relativistic stars with a linear equation of state: analogy with classical isothermal spheres and black holes
• Reply to "Comment on two-mode stability islands around AdS"
• Conditionally Extended Validity of Perturbation Theory: Persistence of AdS Stability Islands
• A proof of the instability of AdS for the Einstein--null dust system with an inner mirror
• Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes
• Relativistic Gravothermal Instabilities
• Gravitational turbulent instability of AdS${}_5$
• Corrigendum to "Thermodynamical instabilities of perfect fluid spheres in General Relativity"
• Caloric curves of classical self-gravitating systems in general relativity
• Charting the AdS Islands of Stability with Multi-oscillators?
• A numerical stability analysis for the Einstein-Vlasov system
• Gravitational instability caused by the weight of heat
• New islands of stability with double-trace deformations
• A critical dimension for the stability of perfect fluid spheres of radiation
• Thermal equilibrium states and instability of self-gravitating particles in an asymptotically AdS spacetime

Cited by in corpus (1)

• Einstein-Vlasov system with equal-angular momenta in ${\text{AdS}}_5$