Sunday, June 14, 2015

reissner nordstrom metric - Can a nearly-extremal black hole be stable against Schwinger vacuum breakdown?


I was doing some basic algebra to estimate the range of possible masses M and electric charge Q for a nearly extremal Reissner-Noström black hole. I want to see if the logic is correct


the electric field near the event horizon of such a black hole would be


E=14πϵ0qr2=14πϵ0qc4G2M2=1066Volt Kg2m CoulqM2


since Schwinger-pair vacuum breakdown occurs at 1018Voltm, it implies that



qM2<1048CoulKg2


Would be a bound that guarantees electromagnetic vacuum stability


Question: can a charged black hole that is stable against this breakdown still be nearly extremal?


well, it seems so, because the extremality condition:


rQ=rs2


Implies that


QG4πϵ0c4=GMc2


QM1016CoulKg


So the above two relations would imply that a black hole with a mass


M>1032Kg100 Solar masses



Can be both stable (against the specific Schwinger-pair decay) and extremal.


In particular, if the mass is 1032 kilograms, a charge around 1016 Coulomb would make the black hole arbitrarily close to extremal as one might want, and is not at all clear that it would decay from the extremality state


But probably i'm overlooking other ways than the extremality of the black hole can decay (in particular, i'm ignorant about how Hawking radiation will contribute in here, specially if the temperature is below 511 KeV). Any insights into this would be greatly appreciated




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