## Black-hole Analogues

**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 is actually emitting **thermal radiation** and that it would eventually evaporate. **Stephen Hawking **completed the thermodynamical treatment of black holes started by **Jacob Bekenstein **[Bekenstein, 1973] and, by studying the quantum fields around the **event horizon** of a black hole, concluded that they 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 it is still **one of the most intriguing (and studied) physical effects** and it is very important for the **unification** of quantum theory and gravity.

Any study of this topic should acknowledge its **problems**, both practical and conceptual. On the practical side, due to the **Chandrasekar limit** [Chandrasekar, 1931], stable astronomical black hole would emit radiation in a temperature far below the **cosmic microwave background**, such that an observation of Hawking radiation in astrophysics seems **unlikely**. This seemed to **doom** this effect to be only a theoretical prediction. Furthermore, 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 to be believed a **fundamental quantum limit**. We do not know how valid are our theories in that regime. This is known as the **trans-Planckian problem**.

**Laboratory analogues of black holes** could solve both of these problems. First, it is possible to determine experimental condition of several analogue systems that can, in principle, produce **measurable Hawking radiation**. All of these analogues are based 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, an event horizon is **created** as it was proposed by William Unruh [Unruh, 1981].

Analogue systems are inspired then by the following idea. Imagine a **river** flowing with increasing speed towards a waterfall and populated by **fish** with a certain maximum speed with respect to the water |v|. Then, fish far from the waterfall can swim as they please, as the water current is low there. Nevertheless, as they get closer and closer to the waterfall, the current is stronger and stronger, if |v| < c there is a point where the equality 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.

Nowadays there are **several experimental groups** trying to realize this analogy, including **water tanks**, **Bose-Einstein condensates**, **liquid Helium 3**, and **fiber optics**. We will be focusing in the last one, as it offers the most promising future.

Referencias

[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