See a black hole on a shoestring

The modes of vibration of hanging and partially supported strings provide useful analogies to scalar fields travelling through spacetimes that admit conformally flat spatial sections. This wide class of spacetimes include static, spherically symmetric spacetimes. The modes of a spacetime where the scale factor depends as a power law on one of the coordinates provide a useful starting point and yield a new classification of these spacetimes on the basis of the shape of the string analogue. The family of corresponding strings follow a family of curves related to the cycloid, denoted here as hypercycloids (for reasons that will become apparent). Like the spacetimes that they emulate, these strings exhibit horizons, typically at their bottommost points where the string tension vanishes; therefore, hanging strings may provide a new avenue for the exploration of the quantum mechanics of horizons.

Figure 1

The cross section of the confining surfaces, hypercycloids for $\beta =0.5$, 1 (the cycloid), 2, 3, and 4 from left to right. The curves are labeled with the value of $\beta$.