We examine particle production from spherical bodies collapsing into extremal Reissner-Nordstrom black holes. Kruskal coordinates become ill defined in the extremal case, but we are able to find a simple generalization of them that is good in this Limit. The extension allows us to calculate the late-time world Line of the center of the collapsing star, thus establishing a correspondence with a uniformly accelerated mirror in Minkowski spacetime. The spectrum of created particles associated with such uniform acceleration is nonthermal, indicating that a temperature is not defined. Moreover, the spectrum contains a constant that depends on the history of the collapsing object. At first sight this points to a violation of the no-hair theorems; however, the expectation value of the stress-energy-momentum tensor is zero and its variance vanishes as a power law at late times. Hence, both the no-hair theorems and the cosmic censorship conjecture are preserved. The power-law decay of the variance is in distinction to the exponential falloff of a nonextremal black hole. Therefore, although the vanishing of the stress tenser's expectation value is consistent with a thermal state at zero temperature, the incipient black hole does not behave as a thermal object at any time and cannot be regarded as the thermodynamic limit of a nonextremal black hole, regardless of the fact that the final product of collapse is quiescent.

Nonthermal nature of incipient extremal black holes

Liberati, Stefano;
2000-01-01

Abstract

We examine particle production from spherical bodies collapsing into extremal Reissner-Nordstrom black holes. Kruskal coordinates become ill defined in the extremal case, but we are able to find a simple generalization of them that is good in this Limit. The extension allows us to calculate the late-time world Line of the center of the collapsing star, thus establishing a correspondence with a uniformly accelerated mirror in Minkowski spacetime. The spectrum of created particles associated with such uniform acceleration is nonthermal, indicating that a temperature is not defined. Moreover, the spectrum contains a constant that depends on the history of the collapsing object. At first sight this points to a violation of the no-hair theorems; however, the expectation value of the stress-energy-momentum tensor is zero and its variance vanishes as a power law at late times. Hence, both the no-hair theorems and the cosmic censorship conjecture are preserved. The power-law decay of the variance is in distinction to the exponential falloff of a nonextremal black hole. Therefore, although the vanishing of the stress tenser's expectation value is consistent with a thermal state at zero temperature, the incipient black hole does not behave as a thermal object at any time and cannot be regarded as the thermodynamic limit of a nonextremal black hole, regardless of the fact that the final product of collapse is quiescent.
2000
62
2
Liberati, Stefano; Tony, Rothman; Sebestiano, Sonego
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/16631
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