There may be a serious conceptual error in the Hawking Gibbons paper of 1977

Unruh effect is

T(r) = hg(r)/ckB

for the black body photon temperature seen by the accelerating detector that is not seen by the unaccelerating detector.

It may well be that the Hawking radiation never makes it to the far field.

The only counter-evidence that it does is the Pioneer Anomaly.

The basic rule for static LNIFs is

covariant acceleration = (Newton's g-acceleration)(gravity time dilation)

For example in de Sitter (dS) space the CLASSICAL calculation is

g(r) ~ c^2/\r(1 - /\r^2)^-1/2

for the observer at r = 0

note that g(0) = 0 which contradicts Hawking & Gibbons that it should be c^2/\^1/2

this is for Unruh-Hawking radiation from the past dS horizon - of course we don't have on in our real universe.

The only way to get their result is to put in their term ad-hoc as a zero point type of correction not seen in the classical calculation.

Similarly for the simplest black hole

g(r) ~ (c^2rs/r^2)(1 - rs/r)^-1/2

with the observer at r ---> infinity

again   g(infinity) = 0

so we do not see the Unruh-Hawking radiation at infinity in the far field - unless we stick in the term ad-hoc again.


On Feb 1, 2011, at 10:45 AM, JACK SARFATTI wrote:

PS - the coordinates one uses don't matter in any physics theory obviously.
The physics of local gauge invariance in GR is that

1) the instantaneous relative velocity mapping between two un-accelerating inertial geodesic non-rotating coincident detectors measuring the same events is a redundant gauge transformation, i.e. Lorentz group SO1,3  LIF <--> LIF'

2) the instantaneous mapping between two accelerating non-inertial off-geodesic, possibly rotating coincident detectors measuring the same event is a redundant gauge transformation, i.e., T4(x) LNIF <--> LNIF'

so the above are 10 gauge transformations.

3) the instantaneous map between a LIF and a coincident LNIF , i.e. tetrad mapping  eI^u etc.

On Feb 1, 2011, at 10:35 AM, JACK SARFATTI wrote:


On Feb 1, 2011, at 2:26 AM, Paul Zielinski wrote:

Bottom line here is that even in the tetrad formalism frame invariance under LNIF' -> LNIF''  transformations means
covariance wrt general coordinate transformations. So frame invariance still presents itself as coordinate covariance
even in the tetrad formulation of the GTR. The (non-orthonormal) LNIF basis vectors change in lockstep with the
coordinates to which they are aligned.

What difference does it make to the physics?
What mathematical distinctions do you mean?
Show the equations.
If you can't show the equations then the above words have no importance.
A local frame is basically a material detector
The arbitrary coordinates one uses don't matter.
The acceleration g-force does matter.
the relative velocity between coincident detectors does matter.
The invariants constructed in each frame for the same measured events by different coincident detectors are the objective reality of the theory.

So this brings us back to my original question: Can the interaction between accelerating detectors and the physical
vacuum that supposedly produces Unruh radiation, or particle pair production in the Gibbons-Hawking model for cosmological event horizons, be given a generally covariant formulation in the GTR?  - Zielinski


 "the reality of the membrane can not be an invariant which all observers agree upon."

"An experiment of one kind will detect a quantum membrane, while
an experiment of another kind will not. However, no possibility exists for any observer to
know the results of both. Information involving the results of these two kinds of experiments
should be viewed as complementary in the sense of Bohr." - Susskind


June 1993
hep-th/9306069

The Stretched Horizon and Black Hole Complementarity
Leonard Susskind, L´arus Thorlacius,† and John Uglum‡

a “stretched horizon” or membrane description of the black hole, appropriate to a distant observer

the dissipative properties of the stretched horizon arise from a course graining of microphysical degrees of freedom that the horizon must possess.