Hawking Radiation and Neutron Stars

[amigocabal]

The theory of Hawking radiation (where black holes emit photons from just before the event horizon) is essentially an application of the equivalence principle to the Unruh effect, which predicts that accelerating observers will observe black body radiation where inertial observers would not observe them. All stationary observers near the event horizon of a black hole must accelerate to remain stationary, so they would observe radiation.

This would be also true of compact-enough neutron stars (those with radii between 1 and 1.5 Schwarzchild radii). An observer within the photon sphere of a neutron star must accerlate to avoid either leaving the photon sphere or striking the neuitron star's surface. Thus, the equivalence principle combined with the Unruh effect predicts that a stationary observer within the photon sphere must observe black body radiation.

Does this mean compact-enough neutron stars emit Hawking radiation?

[starslayer]

No, it does not. Neutron stars are larger than their Schwarzschild radii and so emit normal blackbody emission, although most of their emitted power is driven by their magnetic fields (their magnetic dipole radiation alone outweighs their BB emission by many orders of magnitude).

EDIT: Hawking radiation is not an application of the Unruh effect in any case; it is observed no matter where the observer happens to be, and its existence does not depend on how the observer is accelerating with respect to the black hole.

[Kuroneko]

EDIT: Hawking radiation is not an application of the Unruh effect in any case; it is observed no matter where the observer happens to be, and its existence does not depend on how the observer is accelerating with respect to the black hole.

There is no reason for it not to be. Locally, the Schwarzschild (or Kerr) horizon looks like the Rindler (acceleration) horizon in flat spacetime. Take the Schwarzschild spacetime near the horizon (r = 2m) equatorial plane (θ = π/2) and φ = 0, and apply the coordinate transformation
[1] x = 2m(θ-π/2), y = 2mφ, z = 4m sqrt(1-2m/r)
to the metric in Schwarzschild coordinates, giving:
[2] ds² = -(z/4m)²dt² + [1-(z/4m)²]-4dz² + [1-(z/4m)²]-2(dx² + cos²(x/2m) dy²)
Expand and drop the higher-order terms and you get the Rindler chart of Minkowski spacetime:
[3] ds² = -(z/4m)²dt² + (dx² + dy² + dz²),
which is the frame adapted to a uniformly accelerating observer with proper acceleration g = 1/4m to the z-direction. Then the temperature TUnruh = g/2π = 1/(8πM) = THawking.

For a stationary observer A near the the horizon, the Hawking radiation is very hot (observed level increased by diverging gravitational time dilation), but such an observer is also very strongly accelerating--it takes a lot of thrust to remain stationary near the horizon. Thus, a nearby freely falling observer B will simply say that the reason A is detecting the thermal mess is Unruh radiation.

There is of course a global difference, but intuitively all one really needs is to use the fact that for the Schwarzschild time, ∂t is a timelike Killing field that connects the stationary (strongly accelerating) frames near the horizon to the stationary (asymptotically non-accelerating!) frames at infinity. Hawking radiation can be thought of as taking a local Unruh effect at the event horizon boundary and extending it like that.

Neutron stars don't have a horizon, so the same boundary condition doesn't obtain.

[Surlethe]

Is there a coordinate-free interpretation of Hawking or Unruh radiation?