Is Hawking radiation a theory or a hypothesis? There are lots of articles, calling Hawking radiation a theory, but doesn't the definition of a scientific theory state that a theory is substantiated by a repeated testing and an overwhelming amount of evidence? Are those articles using non strict definition of a word theory, or do they make a mistake?
 A: In the case of Hawking radiation, the direct answer is "no, there is no direct test, nor can we imagine one with anything like current technology." But it is not some wild speculation made in vacuum. The extremely closely related Unruh effect can be derived from basic quantum field theory on a curved spacetime, and many QFT and GR texts have at least an outline of the derivation. (And some people even claim the Unruh effect is testable.) Maybe our derivation or interpretation or even some basic principle is wrong, sure, but there is still good evidentiary support for Hawking radiation.
Indirect evidence, when reasoned with correctly, is not so weak as it seems to many people. What follows below is my elaboration/rant on this last point.

The problem with the scientific method, as taught to school children and promulgated by science pundits, is that it is too narrow and linear. The story goes something like


*

*Form a testable hypothesis $H$.

*Gather evidence $E$.

*If $E$ supports $H$, $H$ is provisionally admitted as true, otherwise go back to step 1.


That's all well and good, but there is no room for logical deduction in this simple picture. And inferential reasoning isn't really there either. A more accurate outline would involve several processes operating in parallel on our collective "web of knowledge" $W$ (i.e. our set of scientific beliefs and their relationships to one another):


*

*Derive new beliefs to augment $W$:


*

*Start with beliefs $B_1, \ldots, B_n \in W$ and proposed belief $B'$,

*If $B'$ logically follows from $B_1, \ldots, B_n$, add $B'$ to $W$ along with the relation "logically derived from $B_1, \ldots, B_n$."


*Infer new beliefs to augment $W$:


*

*Gather experimental evidence $E_1, \ldots, E_n$.

*Come up with a new belief $B$ that explains $E_1, \ldots, E_n$.

*If $B$ does not logically conflict with the rest of $W$, add it to $W$.


*Test the consistency of $W$ with the real world. These are the same steps as given in the beginning.
This last process of experimental verification is certainly necessary on the whole. But it is entirely reasonable for there to be beliefs $B$ that are not directly experimentally verified. They could be inferred from large bodies of evidence as the only sensible thing we can come up with. Or the can be deduced from other parts of $W$. In fact, they can be deduced from very core principles of $W$ that would require monumental amounts of contrary evidence to overthrow.
For example, if $W$ contains Coulomb's law and the idea that physics is invariant under the Lorentz group with fixed speed of light $c$, then the Lorentz force law and all of Maxwell's equations can be derived logically. There is no need to test these to add them to $W$, because logically you should believe them as much as you believe in Coulomb's law and Lorentz transformations. And if you do find experimental evidence against, e.g., Maxwell's equations, then the doubt it casts may very well propagate back to Coulomb's law, since you can't throw out Maxwell yet leave its logical antecedents untouched.
A: It's a calculation in Quantum Field Theory in Curved (fixed) Space Time. The point is not whether the calculation is exact (on this, there is probably no doubt), but whether that semiclassical approximation is adequate to describe the black hole horizon. So yes, there are no experimental evidence (the effect is very small), and the radiation may very well be a mathematical result without physical implications.
