Near Horizon Extremal Geometry Perturbations: Dynamical Field Perturbations vs. Parametric Variations

TL;DR

This paper demonstrates that linearized field perturbations around Near Horizon Extremal Geometries satisfy the Entropy Perturbation Law and are limited to parametric variations, clarifying the nature of dynamics in these geometries.

Contribution

It establishes that linearized perturbations obey the Entropy Perturbation Law and are restricted to variations within the NHEG solution space, clarifying their dynamical properties.

Findings

Perturbations satisfy the Entropy Perturbation Law.

Perturbations are limited to parametric variations of NHEG solutions.

Analysis clarifies the 'no-dynamics' statements in previous works.

Abstract

In arXiv:1310.3727 we formulated and derived the three universal laws governing Near Horizon Extremal Geometries (NHEG). In this work we focus on the Entropy Perturbation Law (EPL) which, similarly to the first law of black hole thermodynamics, relates perturbations of the charges labeling perturbations around a given NHEG to the corresponding entropy perturbation. We show that field perturbations governed by the linearized equations of motion and symmetry conditions which we carefully specify, satisfy the EPL. We also show that these perturbations are limited to those coming from difference of two NHEG solutions (i.e. variations on the NHEG solution parameter space). Our analysis and discussions shed light on the "no-dynamics" statements of arXiv:0906.2380 and arXiv:0906.2376.