Black holes are formed when extremely massive objects like stars collapse to a singularity – a point of infinite density. The gravitational field of a black hole is so great that nothing can escape its clutches, not even light. This creates a spherical region of space around the singularity entirely cut off from the rest of the universe and bounded by what is known as an event horizon.

An active area of research into the physics of black holes seeks to develop a consistent theory of quantum gravity. This is an important goal of theoretical physics that would reconcile quantum mechanics and Einstein’s general theory of relativity. In particular, by considering black holes in quantum superposition, physicists hope to gain insights into the quantum nature of space–time.

### Unruh–deWitt detector

In
the latest
work,
reported
in *Physical
Review
Letters*, Joshua
Foo and Magdalena
Zych of
the
University
of
Queensland
together
with Cemile
Arabaci and Robert
Mann at
the
University
of
Waterloo
outline
what
they
describe
as
a
new
operational
framework
for
studying
space–time
superpositions.
Rather
than
using
a
“top-down”
approach
to
quantize
general
relativity
they
instead
consider
the
effects
of
a
black
hole’s
quantum
state
on
the
behaviour
of
a
specific
physical
device
called
an
Unruh–deWitt
detector.

This is a hypothetical device that comprises a two-state system, such as a particle in a box, coupled to a quantum field. When in its low-energy state and exposed to electromagnetic radiation of just the right frequency, the system jumps to its higher state and registers a “click”.

This kind of detector can in theory be used to measure Unruh radiation, a heat bath of particles that is predicted to appear from the quantum vacuum to an observer that is accelerating through space. In the scenario laid out in the new research, it would instead capture Hawking radiation. This is radiation that is predicted to be created when virtual particle–antiparticle pairs within the quantum vacuum are ripped apart at a black hole’s event horizon – the antiparticle then disappearing into the void and the particle emitted into the surrounding space.

In their thought experiment, the quartet envisage an Unruh–deWitt detector located at a specific point outside a black hole’s event horizon, with the detector’s fixed position enabled by an acceleration away from the black hole that yields the Hawking radiation. The researchers consider the effect of a superposition of the black hole’s mass on the output of that detector.

### Superposition of distances

As they explain, the two masses yield different solutions to the field equations of general relativity and thereby distinct space–times. The resulting superposition of space–times in turn leaves the detector in a superposition of distances from the event horizon, creating what is in effect an interferometer whose arms are each associated with one of the black hole masses. The probability that the detector clicks depends on which masses are present in the superposition.

Doing
the
calculations
for
a
relatively
simple
black
hole
described in
two
spatial
dimensions
by
the
Banados–Teitelboim–Zanelli
formulation,
the
physicists
obtained
a
striking
result.
They
plotted
the
probability
of
detecting
a
particle
emitted
by
the
black
hole
as
a
function
of
the
square
root
of
the
superposition
mass
ratios
and
found
sharp
peaks
when
those
values
were
equal
to
1/*n*,
with *n* being
an
integer.

“This
result
provides
independent
support
for
Bekenstein’s
conjecture,”
the
researchers
write
in *Physical
Review
Letters*,
“demonstrating
how
the
detector’s
excitation
probability
can
reveal
a
genuinely
quantum-gravitational
property
of
a
quantum
black
hole”.

The four physicists stress that the result emerged from their calculations without assuming that the black-hole mass had to fall within the discrete bands predicted by Bekenstein’s conjecture. They add that their technique could be extended to more complex descriptions of black holes in three spatial dimensions, which they say, would provide additional insights regarding the effects of quantum gravity in our universe.