Falling into a black hole

TL;DR

Using the duality between string theory and field theory, the paper investigates how the concept of an object's position becomes ill-defined inside a black hole horizon, highlighting the limitations of classical notions in quantum gravity.

Contribution

The paper applies the field theory dual to a black hole to analyze the notion of position for infalling particles, revealing the ambiguity of position inside the horizon.

Findings

Position is well-defined outside the horizon

Inside the horizon, position becomes ill-defined

Different definitions of position for infalling and outgoing particles

Abstract

String theory tells us that quantum gravity has a dual description as a field theory (without gravity). We use the field theory dual to ask what happens to an object as it falls into the simplest black hole: the 2-charge extremal hole. In the field theory description the wavefunction of a particle is spread over a large number of `loops', and the particle has a well-defined position in space only if it has the same `position' on each loop. For the infalling particle we find one definition of `same position' on each loop, but there is a different definition for outgoing particles and no canonical definition in general in the horizon region. Thus the meaning of `position' becomes ill-defined inside the horizon.