We adapt the horizon wave-function formalism to describe massive static spherically symmetric sources in a general (1+D)-dimensional space-time, for D>3 and including the D=1 case. We find that the probability PBH that such objects are (quantum) black holes behaves similarly to the probability in the (3+1) framework for D>3. In fact, for D≥3, the probability increases towards unity as the mass grows above the relevant D-dimensional Planck scale mD. At fixed mass, however, PBH decreases with increasing D, so that a particle with mass m≃mD has just about 10% probability to be a black hole in D=5, and smaller for larger D. This result has a potentially strong impact on estimates of black hole production in colliders. In contrast, for D=1, we find the probability is comparably larger for smaller masses, but PBH<0.5, suggesting that such lower dimensional black holes are purely quantum and not classical objects. This result is consistent with recent observations that sub-Planckian black holes are governed by an effective two-dimensional gravitation theory. Lastly, we derive Generalised Uncertainty Principle relations for the black holes under consideration, and find a minimum length corresponding to a characteristic energy scale of the order of the fundamental gravitational mass mD in D>3. For D=1 we instead find the uncertainty due to the horizon fluctuations has the same form as the usual Heisenberg contribution, and therefore no fundamental scale exists.

Horizon of quantum black holes in various dimensions / Casadio, Roberto; Cavalcanti, Rogerio T.; Giugno, Andrea; Mureika, Jonas. - In: PHYSICS LETTERS. SECTION B. - ISSN 0370-2693. - ELETTRONICO. - 760:(2016), pp. 36-44. [10.1016/j.physletb.2016.06.042]

Horizon of quantum black holes in various dimensions

CASADIO, ROBERTO;GIUGNO, ANDREA;
2016

Abstract

We adapt the horizon wave-function formalism to describe massive static spherically symmetric sources in a general (1+D)-dimensional space-time, for D>3 and including the D=1 case. We find that the probability PBH that such objects are (quantum) black holes behaves similarly to the probability in the (3+1) framework for D>3. In fact, for D≥3, the probability increases towards unity as the mass grows above the relevant D-dimensional Planck scale mD. At fixed mass, however, PBH decreases with increasing D, so that a particle with mass m≃mD has just about 10% probability to be a black hole in D=5, and smaller for larger D. This result has a potentially strong impact on estimates of black hole production in colliders. In contrast, for D=1, we find the probability is comparably larger for smaller masses, but PBH<0.5, suggesting that such lower dimensional black holes are purely quantum and not classical objects. This result is consistent with recent observations that sub-Planckian black holes are governed by an effective two-dimensional gravitation theory. Lastly, we derive Generalised Uncertainty Principle relations for the black holes under consideration, and find a minimum length corresponding to a characteristic energy scale of the order of the fundamental gravitational mass mD in D>3. For D=1 we instead find the uncertainty due to the horizon fluctuations has the same form as the usual Heisenberg contribution, and therefore no fundamental scale exists.
2016
Horizon of quantum black holes in various dimensions / Casadio, Roberto; Cavalcanti, Rogerio T.; Giugno, Andrea; Mureika, Jonas. - In: PHYSICS LETTERS. SECTION B. - ISSN 0370-2693. - ELETTRONICO. - 760:(2016), pp. 36-44. [10.1016/j.physletb.2016.06.042]
Casadio, Roberto; Cavalcanti, Rogerio T.; Giugno, Andrea; Mureika, Jonas
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/550655
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