How then does a neutron star radiate into space even in the absence of anything to replenish the radiance? One of the solutions is a strange counterintuitive effect of contemporary physics that empty space is not empty. The quantum fields fill all space and even in places where there is no matter and light they nevertheless constitute a lowest energy state. Back in normal circumstances that ground state remains silent. But near a neutron star, the space in which we live is very strongly curved, and the zero-point energy of the quantum vacuum is not the same everywhere.
This is the conceptual connection between neutron stars and a phenomenon normally attributable to black holes. In curved spacetime, quantum fields may apparently behave in a way where there is other supposed concepts of emptiness in other places, and that discrepancy would be interpreted by a distant observer as actual radiation. Popular accounts usually refer to particle-antiparticle pairs appearing at an edge and being ripped apart by pops. That imagery is largely a bookkeeping trick, but the important thing is that curvature and acceleration do change what is considered to be the vacuum. In that way, the odd glow is not so much the burning of fuel, but a reconciliation of the books between quantum fields and gravity.
A theoretical paper of 2023 refined that concept by saying that curvature of spacetime contributes significantly to the generation of radiation even in the contexts other than the common black-hole example. In that publication, the wisdom of Hawking still remains but the emphasis is no longer on the event horizon but on the greater gravitational context: tidal gravity can part quantum excitations in a manner that is reminiscent of particle creation. It is provocative that the neutron stars create massive tidal gradients without developing a classical event horizon, and thus it is in them where the extent to which one can push these “Hawking-like” arguments is likely to be tested.
However, that extension is limited by a harsh limit which is naved in the quantum field theory on curved backgrounds: the stability of the vacuum is determined by spacetime symmetries.
A subsequent criticism summarised the main condition in the terms of general relativity: when the spacetime around an object contains an everywhere time-like preserving field, then the vacuum is not unstable and spontaneous particle creation does not take place, in its literal, radiative sense. Here, horizons are important, not as a special emitting surface, but as the location at which those symmetry conditions break down. The identical criticism saved a significant point: radiation linked to horizons need not have a point-source at the horizon, but rather the horizon determines whether the phenomenon can be physical at all.
In the case of neutron stars, the practical conclusion is that any “glow in empty space” must be detailed attentively. Neutron stars definitely cool thermally on their surfaces, lose energy in the emission of neutrinos, and may be burning in their magnetospheres. But any Hawking-type mechanism must have the special global structure which does not give quantum fields a unique, stable definition of vacuum everywhere. In the absence of that, curvature is a trigger incomplete.
Nevertheless, neutron stars continue to be a valuable laboratory to the further question, what does it mean by matter to “interact” with spacetime in the first place? In a popular formulation of general relativity, the Einstein field equations hold that matter and energy can define curvature, and curvature can give instructions to matter on how to move. In a more philosophically, but nonetheless technically inspired opinion, curvature may be treated as field-like, and the “vacuum” of quantum fields may be a response to that geometry. Neutron stars are on the margins of such descriptions: too small to be any better than geometrically extreme, but not always organized in such a manner as to make the vacuum misfit discharged in a steady stream outwards.
This strangeness, then, is not that neutron stars can radiate. It is that even the definition of what “empty space” is around them is one that is governed by geometry and the rules governing when that difference will be real radiation is whether spacetime contains a horizon or not.
