Radial temperature gradient of a black hole


by kmarinas86
Tags: black, gradient, hole, radial, temperature
kmarinas86
kmarinas86 is offline
#1
Oct4-11, 03:04 PM
P: 1,011
Assuming that the accretion disk has been totally consumed by the black hole, does the temperature of the black hole due to Hawking radiation vary with respect with proximity with the black hole? For example, if I were next to the black hole, would this radiation would have a higher temperature than I was far away?

Should the temperature gradient, in effect, be corrected for gravitational redshift, such that the temperature declines as distance from the blackhole's center decreases? Or should the temperature gradient not get corrected for the gravitational redshift, such that the temperature of the blackhole at some location is determined by the local observer at its local coordinate frame, rather than from a global coordinate frame of reference?

If light cannot escape beyond the black hole's event horizon. Doesn't that make it a heat sink? If it is a heat sink, musn't that mean that, as far as thermodynamics are concerned, that it must be treated as a colder body, and not a hotter one, so a black hole does not have infinite temperature and entropy? Also, wouldn't an evaporating black hole be evaporating due to the universe heating it up?
Phys.Org News Partner Physics news on Phys.org
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Mapping the road to quantum gravity
Chameleon crystals could enable active camouflage (w/ video)
DaleSpam
DaleSpam is offline
#2
Oct4-11, 03:18 PM
Mentor
P: 16,485
Quote Quote by kmarinas86 View Post
Should the temperature gradient, in effect, be corrected for gravitational redshift, such that the temperature declines as distance from the blackhole's center decreases? Or should the temperature gradient not get corrected for the gravitational redshift, such that the temperature of the blackhole at some location is determined by the local observer at its local coordinate frame, rather than from a global coordinate frame of reference?
That is an interesting question. Is a redshifted black body spectrum even a black body spectrum?
Bill_K
Bill_K is online now
#3
Oct4-11, 04:09 PM
Sci Advisor
Thanks
Bill_K's Avatar
P: 3,861
Is a redshifted black body spectrum even a black body spectrum?
Yes indeed.

DaleSpam
DaleSpam is offline
#4
Oct4-11, 05:53 PM
Mentor
P: 16,485

Radial temperature gradient of a black hole


Then it would definitely seem that the temperature of a black hole, as determined by the black body spectrum of Hawking radiation, would depend on the distance from the black hole. I don't know if the equation for Hawking radiation is at the event horizon or at infinity.
Pengwuino
Pengwuino is offline
#5
Oct4-11, 06:09 PM
PF Gold
Pengwuino's Avatar
P: 7,125
Quote Quote by DaleSpam View Post
Then it would definitely seem that the temperature of a black hole, as determined by the black body spectrum of Hawking radiation, would depend on the distance from the black hole. I don't know if the equation for Hawking radiation is at the event horizon or at infinity.
If I understand Hawking's derivation, it's the temperature seen at infinity.
phinds
phinds is online now
#6
Oct4-11, 08:31 PM
PF Gold
phinds's Avatar
P: 5,718
Quote Quote by kmarinas86 View Post
... Also, wouldn't an evaporating black hole be evaporating due to the universe heating it up?
Hawking radiation is not dependent on the surrounding temperature, so no I don't think so.
Bill_K
Bill_K is online now
#7
Oct5-11, 02:53 PM
Sci Advisor
Thanks
Bill_K's Avatar
P: 3,861
Should the temperature gradient, in effect, be corrected for gravitational redshift, such that the temperature declines as distance from the black hole's center decreases?
I think this is the answer. It increases! This is taken from Birrell & Davies, p.282.

"For the Unruh vacuum, FU(E)/unit proper time = 1/E(eE/kT - 1) where kT = [64π2M2(1 - 2M/R)]-. As the detector approaches the horizon (R → 2M) the temperature of the flux determined by the detector diverges. This is due to the fact that the detector must be noninertial to maintain a fixed distance from the black hole The magnitude of the acceleration relative to the local freely-falling frame is M/[R2(1 - 2M/R)]. Such acceleration gives rise to the detection of additional particles. As the horizon is approached, the acceleration diverges, as does the temperature."


Register to reply

Related Discussions
temperature within the epicenter of a Black hole. Special & General Relativity 8
Temperature during black hole collapse Special & General Relativity 12
Does a black hole have a temperature profile? Cosmology 2
Black Hole Temperature and Entropy Astrophysics 5
temperature of black hole Special & General Relativity 1