Non-relativistic metrics from back-reacting fermions

TL;DR

This paper explores how back-reacting fermions modify near-horizon geometries of extremal black holes, leading to non-relativistic Lifshitz and Schrödinger spacetimes as solutions in various dimensions.

Contribution

It demonstrates the existence of warped AdS_3 and Schrödinger solutions in theories with back-reacting fermions, generalizing the dynamical exponent in arbitrary dimensions.

Findings

Back-reacting fermions induce Lifshitz geometries from AdS_2.

Warped AdS_3 and Schrödinger solutions are found in theories with Chern-Simons terms.

The dynamical exponent is expressed in terms of fermion mass and dimensions.

Abstract

It has recently been pointed out that under certain circumstances the back-reaction of charged, massive Dirac fermions causes important modifications to AdS_2 spacetimes arising as the near horizon geometry of extremal black holes. In a WKB approximation, the modified geometry becomes a non-relativistic Lifshitz spacetime. In three dimensions, it is known that integrating out charged, massive fermions gives rise to gravitational and Maxwell Chern-Simons terms. We show that Schrodinger (warped AdS_3) spacetimes exist as solutions to a gravitational and Maxwell Chern-Simons theory with a cosmological constant. Motivated by this, we look for warped AdS_3 or Schrodinger metrics as exact solutions to a fully back-reacted theory containing Dirac fermions in three and four dimensions. We work out the dynamical exponent in terms of the fermion mass and generalize this result to arbitrary dimensions.