Black hole voyeurism

Alexander Smith and Robert Mann

Alexander (right) is a PhD student in the department of Physics & Astronomy at the University of Waterloo. Robert (left), a past-president of the Canadian Association of Physicists, is a senior professor in the department of Physics & Astronomy and the department of Applied Mathematics at the University of Waterloo and an affiliate at the Perimeter Institute.

Could a quantum detector peek inside a black hole?

It has long been known that the thermal radiation emitted by a black hole can be detected by a particle detector, and even today the details of this process are an active area of research. But are such detectors sensitive to the interior structure of black holes? From a classical perspective, conventional wisdom would suggest not: the topological censorship theorem relegates all isolated topological structures (such as wormholes, topological knots, etc) to be hidden behind a horizon and thus inaccessible to observers by classical probes. But what would be the response of a quantum probe, as modelled (for example) by an Unruh–DeWitt particle detector?

To address this question we considered two black hole spacetimes whose exteriors were identical but whose interiors differed in their topology: the BTZ hole and its associated geon. The BTZ black hole is a (2+1) object that in some respects is similar to a Schwarzchild anti-de Sitter black hole. The associated geon is constructed by making a topological identification of the BTZ spacetime. Outside of the horizon the BTZ and geon spacetimes are identical, but the topological structure of their interiors differs.

We found that an Unruh–DeWitt detector held at a fixed distance outside the horizon will have a different response to the vacuum state of a scalar field (the Hartle–Hawking vacuum) for the BTZ space-time as compared to the geon. Unlike the BTZ case, the transition rate of a static particle detector in the geon spacetime changes with the proper time of the detector. This is a feature typically associated with a non-stationary spacetime; in some sense the geon acts as an intermediary between a conventional stationary spacetime and a dynamical one.

The take home message is that the topological structure of the BTZ and geon black holes, which is fully hidden behind the horizon, leaves a measurable imprint on the quantum field outside the horizon even though outside the horizon these spacetimes are classically indistinguishable.

In the future we hope to explore more realistic examples to see how and where this effect is best manifest. This should provide insight as to exactly what role horizons play in shielding topological information accessible by quantum means.

Read the full article in Classical and Quantum Gravity:
Looking inside a black hole
Alexander Smith and Robert Mann
Class. Quantum Grav. 31 082001

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