### Do neutron stars Hawking radiate?

Paper by Michael F. Wondrak, Walter D. van Suijlekom, and Heino Falcke can be found here.

Press release at the RU website can be found here: https://www.ru.nl/en/research/research-news/eventually-everything-will-evaporate-not-only-black-holes

In 1974 and 1975 Stephen Hawking published his ground-breaking papers “Black Hole Explosion?” and “Particle Creation by Black Holes”, proposing that black holes radiate. This was part of the early attempts to describe quantum fields in a curved spacetime, which is very difficult of course because quantum and gravity (still) do not go together very well. In summary, an impressive calculation shows that quantum effects cause a classically stationary back hole to emit thermal radiation, now called *Hawking radiation*. The black hole even evaporates eventually, leaving a perfect thermal state in the distant future, in which we observers find ourselves. For a clear overview we refer to the books by Wald (1994) and Parker & Toms (2009).

From these (or Hawking’s) expositions one realizes that it is essential that there is an event horizon in Hawking's calculation and in response to an original question whether neutron stars might also emit "Hawking radiation” the applicant has devoted a short calculation to it and this in turn led to a very interesting discussion. Most importantly, if you want to describe quantum fields for the neutron star + gravity system, you need to extend Hawking's calculation to a spacetime in which some region is separated – namely the interior of the neutron star – and know something about the quantum effects at the surface, but work without the presence of an event horizon.

More precisely, the sought-for radiation could arise from the more general principle of “particle creation from the curvature of spacetime”. In the early work of Leonard Parker (1968, 1969, 1971) this was explained carefully for expanding universes. The main and crucial assumption in both the black hole and cosmological case is that one can identify asymptotically flat spacetimes, where the ordinary principles of quantum fields make sense. An ingoing vacuum state is then mapped to an outgoing state by Bogoliubov transformations that can in principle be derived from the wave equation in the curved background. The resulting outgoing state is typically not the vacuum state any more; this is the sought-for particle creation, or, in other words, the radiation we are after.

The main challenge in the present project is thus to come up with a (simplified) model for the collapse of matter into a neutron star, where one can identify an asymptotically flat past (well outside the body and at early times) where geodesics begin that end at future null infinity – again assumed to be a flat region of spacetime. After suitable assumptions (spherically symmetric collapse, etc.) on the body, one expects the vacuum state at minus infinity to be transformed to a non-trivial thermal state at future null infinity. The properties of that state are then expected to be related to the physical properties of the (neutron) star.

About the importance of such a project: the outcome could say something about Hawking radiation for more general bodies, and would therefore go much further, especially in astronomy, than the still elusive black holes. In addition, there is a great deal of speculation and discussion in the popular media, but not so extensively in the scientific literature. For example, this article recently appeared in Forbes (with a slightly too bold title).

In addition to a somewhat exaggerated correction of an analogy used by Hawking in his popular science book to explain his 1974 work, it also suggests that Hawking radiation should indeed exist for every body, but of course without details. This project is intended to provide at least some of these details, which would be ground-breaking if the idea works.

References:

S.W. Hawking, Nature 248, 30 (1974)

S.W. Hawking, Commun. Math. Phys. 43, 199 (1975)

L. Parker and D.J. Toms, Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity (Cambridge University Press, 2009)

L. Parker, Phys. Rev. Lett. 21, 562 (1968).

L. Parker, Phys. Rev. 183, 1057 (1969).

L. Parker, Phys. Rev. D3, 346 (1971).

R. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics (Chicago University Press, 1994).