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2010

Instability of the Noncommutative Geometry Inspired Black Hole

Brown, Eric, Mann, Robert B.

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Non-commutative geometries have been proposed as an approach to quantum gravity and have led to the construction of non-commutative black holes, whose interior singularities are purportedly eliminated due to quantum effects.

Here we find evidence that these black holes are in fact unstable, with infalling matter near the Cauchy (inner) horizon being subject to an infinite blueshift of the type that has been repeatedly demonstrated for the Reissner-Nordstr\(\ddot{\text{o}}\)m black hole.
This instability is present even when an ultraviolet cutoff (induced by anticipated non-commutative geometric effects) to a field propagating in that spacetime is included.
We demonstrate this by following an analogous argument made for Reissner-Nordstr\(\ddot{\text{o}}\)m black holes, and conclude that stability is dependent on the surface gravities \(\kappa_-\) and \(\kappa_+\) of the inner and outer horizons respectively.

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Similar

Madore, J. An Introduction to Noncommutative Geometry. Springer Berlin / Heidelberg, Lecture Notes in Physics, (2000)
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Then

Modesto, L. arXiv:0811.2196 [gr-qc] (2008)
Original
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Nicolini, P. Int. J. Phys. A 24
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Batic, D., Nicolini, P. arXiv: 1001,1158v1 [gr-qc] (2010)
2010
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Brown, E., Mann, R., Modesta, L. arXiv:1006.4164 [gr-qc] (2010)
Original
2010
Closest in time.

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