Stability Analysis of the Dilatonic Black Hole in Two Dimensions

TL;DR

This paper demonstrates that two-dimensional dilaton gravity black holes are stable by showing the absence of local physical excitations and eliminating unstable modes through Hamiltonian and perturbation analysis.

Contribution

It provides a detailed Hamiltonian constraint analysis and perturbation study proving the stability and lack of local degrees of freedom in two-dimensional dilaton gravity.

Findings

Net degrees of freedom are zero in 2D dilaton gravity.

Exponential growth modes are eliminated outside the horizon.

The black hole solution is shown to be stable.

Abstract

We explicitly show that the net number of degrees of freedom in the two-dimensional dilaton gravity is zero through the Hamiltonian constraint analysis. This implies that the local space-time dependent physical excitations do not exist. From the linear perturbation around the black hole background, we explicitly prove that the exponentially growing mode with time is in fact eliminated outside the horizon. Therefore, the two-dimensional dilation gravity is essentially stable.