# Analogue gravity

Nothing, not even light, can escape from a gravitational black hole. Still, quantum mechanics predicts that a black hole is not entirely black [Hawking, 1974] but that it emits thermal radiation and would eventually evaporate. Stephen Hawking completed the thermodynamical treatment of black holes started by Jacob Bekenstein [Bekenstein, 1973]. By studying the quantum fields around the event horizon of a black hole, Hawking concluded that black holes should emit a steady flux of thermal radiation with temperature proportional to the gravitational field strength at the event horizon. This effect is known today as Hawking radiation and is still one of the most intriguing (and studied) physical effects. The Hawking effect is significant for the unification of quantum theory and gravity.

Any study of this topic should acknowledge its practical and conceptual problems. On the practical side, due to the Chandrasekar limit [Chandrasekar, 1931], a stable astronomical black hole would emit radiation at a temperature far below the cosmic microwave background, so observing Hawking radiation in astrophysics seems unlikely. This fact seemed to doom this effect to be only a theoretical prediction. On the conceptual side, if one traces back the vacuum modes coming from the event horizon of the black hole, their frequency increases very quickly, such that they quickly exceed the Planck scale, widely believed to be a fundamental quantum limit. We need to find out how valid our theories are in that regime. This issue is known as the trans-Planckian problem.

These problems motivated the search for laboratory analogues of black holes that could solve both issues. First, it is possible to determine the experimental conditions in several analogue systems that can, in principle, produce measurable Hawking radiation. These analogues depend on a mathematical analogy between the space-time geometry of a black hole and a moving flow. When the flow velocity exceeds the speed of light in vacuum, it creates an event horizon, as William Unruh proposed [Unruh, 1981].

Analogue systems are inspired then by the following idea. Imagine a river flowing with increasing speed towards a waterfall "v" and populated by fish with a certain maximum speed with respect to the water "c". Then, fish far from the waterfall can swim as they please, as the water current is low. Nevertheless, as they get closer to the waterfall, the current gets stronger. If there is a point where the equality v = c is fulfilled, after this point, the current is so strong that fish cannot swim upstream anymore. This point is an analogue of the event horizon.

In 2008, Ulf Leonhardt proposed an analogue using light pulses traveling through optical fibers [Leonhardt, 2008]. This analogue opens the possibility of measuring the spontaneous creation of photons through the analogue of the Hawking effect. In 2018, I collaborated in an experiment led by Ulf Leonhardt to measure the optical analogue of Hawking radiation in the optical table. We could measure the two light signals predicted by the Hawking effect, one with positive and one with negative frequencies. We performed this experiment in the classical or stimulated regime [Drori, 2019].

Several experimental groups are trying to realize this analogy, including water tanks, Bose-Einstein condensates, liquid Helium 3, and fiber optics. We will focus on the last one, which offers the most promising future.

References

[Hawking, 1974] S.W. Hawking. Black hole explosions? Nature 248 (1974) 30-31

[Bekenstein, 1973] J.D. Bekenstein. Black Holes and Entropy, Phys. Rev. D 7 (1973) 2333

[Chandrasekar, 1931] S. Chandrasekhar. The Maximum Mass of Ideal White Dwarfs, Astrophys. J. 74 (1931) 81

[Unruh, 1981] W. G. Unruh. Experimental Black-Hole Evaporation? Phys. Rev. Lett. 46 (1981) 1351

[Leonhardt, 2008] T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, U. Leonhardt. Fiber-Optical Analog of the Event Horizon, Science 319

(2008) 1367-1370

[Drori, 2019] J. Drori, Y. Rosenberg, D. Bermudez, Y. Silberberg, U. Leonhardt. Observation of Stimulated Hawking Radiation in an Optical Analogue, Phys.

Rev. Lett 122 (2019) 010404