Macroscopic Black Holes, Microscopic Black Holes and Noncommutative Membrane

TL;DR

This paper models the stretched membrane of a black hole as a perfect fluid with negative pressure and specific heat, proposing that its quanta may be noncommutative spacetime or microscopic black holes, with a unique dispersion relation.

Contribution

It introduces a novel fluid model for black hole membranes and suggests a new dispersion relation for fundamental quanta, linking noncommutative geometry and microscopic black holes.

Findings

Fluid on the membrane has negative pressure and specific heat.

Dispersion relation for quanta: E = m^2 / k.

Two interpretations: noncommutative spacetime or microscopic black holes.

Abstract

We study the stretched membrane of a black hole as consisting of a perfect fluid. We find that the pressure of this fluid is negative and the specific heat is negative too. A surprising result is that if we are to assume the fluid be composed of some quanta, then the dispersion relation of the fundamental quantum is $E=m^2/k$, with $m$ at the scale of the Planck mass. There are two possible interpretation of this dispersion relation, one is the noncommutative spacetime on the stretched membrane, another is that the fundamental quantum is microscopic black holes.