See a Black Hole on a Shoestring

TL;DR

This paper explores analogies between vibrating strings and scalar fields in certain spacetimes, revealing new classifications and potential insights into horizons and quantum mechanics.

Contribution

It introduces a novel classification of spacetimes based on string analogies and explores their horizons, offering new perspectives on quantum horizon mechanics.

Findings

Strings follow hypercycloid curves related to spacetime geometries.

Horizon-like features appear at points where string tension vanishes.

Analogies suggest new methods to study quantum horizons.

Abstract

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 includes 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.