# Can Hawking Radiation ever be detected and does it exist? [duplicate]

I'm researching black hole Hawking radiation for a contest, and so far I get the overall gist of how the process works. But as far as I've searched, there hasn't been any confirmed observational evidence that it exists, other than laboratory simulations/recreations. Although the theoretical side of it makes sense, how do we know it exists?

## How do we know Hawking radiation exists?

Quantum Physics (Quantum Field Theory) and General Relativity are considered as the two main theories in physics, which can explain a broad range of phenomena at the scale of atoms and subatomic particles to the large scales of the universe, beyond the ability/validity of classical, nonrelativistic physics. They also offer a number of extraordinary predictions, many of which have been experimentally confirmed. So, we are sure about the validity of these theories (and we also know their limitations). If we accept the fundamental principles of these theories, the existence of Hawking radiation would be unquestionable, no matter how we interpret this phenomenon.

Hawking, traditionally, obtained it in 1974 by use of the study (quantization) of quantum fields near the event horizon of the Schwarzschild black hole background for different observers in different locations (this subject is called quantum field theory in curved background). Also, using the Heisenberg's uncertainty principle and applying the basic/elementary relations of quantum mechanics and general relativity, one can qualitatively obtain the Hawking temperature without requiring the knowledge of QFT and field quantization (see also Yakov Zeldovich, who first predicted radiation in rotating black holes). Hawking radiation is also predicted by a number of different approaches in physics, so at present there is no doubt about its existence, but the main problem is how to detect it. The are a number different methods for deriving the Hawking radiation such as evaluating thermal partition function of black holes (in zero-loop approximation of quantum gravity path integral formalism), unitary decay of near extremal D-brane states (in string theory) etc, which (I think) are beyond the scoop of this question. By the way, for these reasons, we expect that any quantum gravity theory which combines both quantum physics and general relativity (if exist any) must predict the Hawking radiation as well, undoubtedly.

## Is there any confirmed observational evidence for Hawking radiation?

Not yet. The existence of black holes is theoretically possible and now it has been experimentally verified, no doubt (see Reinhard Genzel's works). But, It seems we have serious difficulties for observing Hawking radiation. A straightforward calculation for the Hawking radiation of static (Schwarzschild) black holes results

$${T_{Hawking}} = \frac{{\hbar {c^3}}}{{8\pi G{M_ \odot }{k_B}}}\left( {\frac{{{M_ \odot }}}{M}} \right) = 6.17 \times {10^{ - 8}}\left( {\frac{{{M_ \odot }}}{M}} \right)\,{{\rm{K}}^\circ},$$

where $${M_ \odot }$$ is the mass of son and $$M$$ represents the black hole mass ($${k_B}$$= the Boltzmann constant, $$G$$ = Newton constant). The formation of black holes is possible if the initial mass of collapsing object be greater than the so-called Chandrasekhar limit, $$1.4$$ $${M_ \odot }$$ (i.e., $$2.765 \times 10^{30}$$ kg). This means that a solar-mass black hole ($$M \sim {M_ \odot }$$) has a temperature of about $$60$$ $${\rm{nK}}^\circ$$, and larger black holes ($$M > {M_ \odot }$$) have even lower temperatures. Now, compare this extremely tiny value with the cosmic microwave background radiation (CMB, which is faint cosmic background radiation filling all space), i.e. $${T_{CMB}} \approx 2.73\,{{\rm{K}}^\circ}$$. In conclusion, the temperature (Hawking radiation) of realistic black holes is significantly lower than the background temperature of the universe. Qualitatively, this argument is also valid for rotating black holes. This is the main reason why it is generally believed that the Hawking radiation cannot be observed, at least with the current technology of our detectors.

But this is not the end of the story. Until writing this answer, since any direct observational evidence is potentially ruled out, we have to seek indirect experimental evidence, e.g., by means of simulations or analog systems. The subject of analog gravity and its different models have been invented for this purpose. Analogue gravity is a research programme which investigates analogues of phenomena in general relativity (such as black holes) within other physical systems, typically (but not exclusively) condensed matter systems, with the aim of gaining new insights into their corresponding problems. Naively, the mathematics governing both the black hole and analog systems are similar. So, there exist a number of analog gravity models which share the same essential properties with black holes such as event horizon and Hawking radiation. For example:

• In this paper (published in Nature Physics), the author created a narrow, low density, very low temperature atomic Bose-Einstein condensate, containing an analog black hole horizon and an inner horizon, as in a charged black hole, and in this analog black hole model, he's observed the Hawking radiation emitted by the black hole.

• In this paper (published in Phys. Rev. Lett.), the authors utilized the analogy between the propagation of fields around black holes and surface waves on moving water and they experimentally (omitting details) confirmed the Hawking process.

• In this paper (published in Phys. Rev. Lett.), an (famous) analog of a black hole, known as sonic black hole, in a Bose-Einstein condensate has been created in which sound waves, rather than light waves, cannot escape the event horizon.

• This is a nice link in Physics Stack Exchange about analog gravity which is a water flow analogy with a black hole. It is a discussion about a good (home) experiment with a black hole analog! Also, this one maybe useful for you.

If you search in web about these analog black holes, you quickly find many interesting papers for confirmation of Hawking radiation, especially in Nature Astronomy Journal.

## Is there any astrophysical candidate for detecting Hawking radiation?

Well, yes, but we are not sure about the existence of them. As proposed by Hawking, primordial black holes are well-motivated candidates for detecting black hole (Hawking) radiation. These are hypothetical types of black holes that formed soon after the Big Bang (as a result of fluctuations in the early Universe). Studies speculate that, depending on the model, primordial black holes could have initial masses ranging from $$10^{-8}$$ kg to more than thousands of solar masses. This is an interesting, remarkable result and I explain why.

In fact, a black hole that initially has mass $$M$$ will eventually evaporate to nothing. According to the Hawking radiation formula of a Schwarzschild black hole, i.e.,

$${T_{Hawking}} = \frac{{\hbar {c^3}}}{{8\pi G{M_ \odot }{k_B}}}\left( {\frac{{{M_ \odot }}}{M}} \right),$$

Hawking radiation further decreases the black hole mass and black holes with very small mass would experience runaway evaporation, creating a burst of radiation at the final phase (The evaporation would actually be pretty catastrophic, as it would release about as much energy as a large thermonuclear bomb during this time). But, the problem is that if we can observe these explosions during our time. Straightforward calculations by implementing the Stefan-Boltzmann law show that the life time of a black hole is as

$${\tau _{{\rm{life}}}} = \frac{{256{\pi ^3}k_B^4}}{{3G\sigma {\hbar ^4}}}{(GM)^3} = (2.095 \times {10^{67}}\,{\rm{year}})\,{\left( {\frac{M}{{{M_ \odot }}}} \right)^3},$$

where $$\sigma$$ is the well-known Stefan-Boltzmann constant. For the solar-mass black holes this is much greater than the age of the universe (i.e., $$13.8$$ billion years), so they are not good candidates. On the other hand, by use of the above formula one can show that primordial black hole with mass lower than $$10^{11}$$ kg would not have survived to the present due to Hawking radiation. But, interestingly, for primordial black hole (if they exist) with mass lower than the solar mass ($$2 \times 10^{30}$$ kg) and also greater than $$10^{11}$$ kg, it is possible to detect/observe the final stage of their life, which is a big explosion equivalent to a hydrogen bomb yielding millions of megatons of explosive force! Along these lines, there exist a number investigations, e.g., see these [1], [2], [3] and [4].

Of course, as usual, there exist some technical/fundamental difficulties to experimentally detect Hawking radiation in primordial black holes. This is the beginning of another story (For a good discussion see this link).

• thanks for the detailed answer! – AdiBak Apr 13 at 20:46
• What exactly is the T Hawking? A kind "of black body temperature"? In other words how does it relates to the freq of the emission? – Alchimista Apr 17 at 11:14
• – Ad Astra May 27 at 12:48