Fermionic halos at finite temperature in AdS/CFT

Carlos R Argüelles,Nicolás E Grandi

doi:10.1007/jhep05(2018)118

Abstract

We explore the gravitational backreaction of a system consisting in a very large number of elementary fermions at finite temperature, in asymptotically AdS space. We work in the hydrodynamic approximation, and solve the Tolman-Oppenheimer-Volkoff equations with a perfect fluid whose equation of state takes into account both the relativistic effects of the fermionic constituents, as well as its finite temperature effects. We find a novel dense core-diluted halo structure for the density profiles in the AdS bulk, similarly as recently reported in flat space, for the case of astrophysical dark matter halos in galaxies. We further study the critical equilibrium configurations above which the core undergoes gravitational collapse towards a massive black hole, and calculate the corresponding critical central temperatures, for two qualitatively different central regimes of the fermions: the diluted-Fermi case, and the degenerate case. As a probe for the dual CFT, we construct the holographic two-point correlator of a scalar operator with large conformal dimension in the worldline limit, and briefly discuss on the boundary CFT effects at the critical points.

Highlights

The issue of Tolman-Oppenheimer-Volkoff equations for neutral fermions in thermodynamic equilibrium at finite temperature, was first investigated in [10] in asymptotically flat backgrounds
As can be seen in the plots, the expected core-halo structure appears at large values of γ and becomes more marked when the central degeneracy Θ0 and the central temperature T0 are large
We investigated the solution to Einstein equations sourced by to a weakly-coupled selfgravitating fermionic fluid at finite temperature in global AdS spacetime

Summary

Introduction

The issue of Tolman-Oppenheimer-Volkoff equations for neutral fermions in thermodynamic equilibrium at finite temperature, was first investigated in [10] in asymptotically flat backgrounds. While the dense core structure is maintained against self-gravity by the degeneracy pressure, the halo holds it own weight by thermal pressure Such structures allow for a good description of the dark matter halos when contrasted with baryonic data of galaxies, providing at the same time an alternative to the standard picture of a supermassive black hole sitting at the galactic nucleus [14]–[16]. Further extensions of such a theoretical model but including fermion self-interactions was introduced in [15].

Results

Discussion

Conclusion