# Near horizon symmetries, emergence of Goldstone modes and thermality

## TL;DR

This paper explores how near horizon symmetries and Goldstone modes contribute to black hole thermality, proposing a classical action framework and demonstrating inherent thermal behavior linked to horizon temperature.

## Contribution

It introduces a classical action for Goldstone modes near horizons and shows their instability leads to thermal properties, connecting symmetries to black hole thermality.

## Key findings

- Goldstone modes experience an inverted harmonic potential.
- Large number of Goldstone modes exhibit inherent thermal behavior.
- System temperature proportional to horizon temperature.

## Abstract

For a long time it is believed that black hole horizon are thermal and quantum mechanical in nature. The microscopic origin of this thermality is the main question behind our present investigation, which reveals possible importance of near horizon symmetry. It is this symmetry which is assumed to be spontaneously broken by the background spacetime, generates the associated Goldstone modes. In this paper we construct a suitable classical action for those Goldstone modes, and show that all the momentum modes experience nearly the same inverted harmonic potential, leading to an instability. Thanks to the recent conjectures on the chaos and thermal quantum system, particularly in the context of an inverted harmonic oscillator system. Going into the quantum regime, the system of large number of Goldstone modes with the aforementioned instability is shown to be inherently thermal. Interestingly the temperature of the system also turns out to be proportional to that of the well known horizon temperature. Therefore, we hope our present study can illuminate an intimate connection between the horizon symmetries and the associated Goldstone modes as a possible mechanism of the microscopic origin of the horizon thermality.