Oscar Cunningham

Can someone help me fix the Wikipedia page on the black hole information paradox (https://en.wikipedia.org/wiki/Black_hole_information_paradox)? It says

> the black hole radiates mass at a rate given by dM/dt = -aT⁴ where a is constant related to fundamental constants, including the Stefan–Boltzmann constant and certain properties of the black hole spacetime called its greybody factors.

The next paragraph says that M is inversely proportional to T and that the black hole evaporates in time proportional to M³. But this isn't consistent because solving dM/dt = -a/M⁴ gives an evaporation time proportional to M⁵.

I think it's the first formula that's wrong and it should be dM/dt = -aT². But I don't know quite enough to feel confident making an edit. Is there someone out there who knows what the fix should be?

#Physics #BlackHole #BlackHoles

Black hole information paradox - Wikipedia

Mar 24 at 6:06amWeb
Show threadMatthew Conroy1d ago
@OscarCunningham You could write about this on the article's talk page to alert other editors to the issue.
Show threadgjm1d ago
@OscarCunningham I am even more not-an-expert than you are, but FWIW the Wikipedia page on Hawking radiation says that the luminosity of Hawking radiation for a black hole of mass 𝑀 is 𝑎𝑀⁻² and says explicitly what 𝑎 is, as well as giving the explicit reciprocal relation between 𝑀 and 𝑇. One could transfer the formulae from that page to the BHIP page with a reasonably clear conscience, I think.
Show threadArthur Smith1d ago
@OscarCunningham thermal radiation is proportional to the product of area and the fourth power of temperature, so yes the "a" in that formula cannot be constant. Black hole area is proportional to radius squared, and radius is proportional to mass, so your M^-2 has to be right.
Show threadOscar Cunningham1d ago
@apsmith @gjm Thanks both, that all makes sense so I made the change. The wording seemed alright already so I just changed the 4 to a 2.
Show threadStephen Brooks 🦆13h ago
@OscarCunningham @apsmith @gjm Right but shouldn't it be dM/dt = a M^2 T^4? Where M^2 is proportional to the surface area (remembering R is proportional to M for black holes).
Show threadOscar Cunningham7h ago
@sjb @apsmith @gjm Well M is inversely proportional to T, so M²T⁴ and T² are proportional.