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2013

What is the Schwarzschild radius of a quantum mechanical particle?

Casadio, R.

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Understand

A localised particle in Quantum Mechanics is described by a wave packet in position space, regardless of its energy.

However, from the point of view of General Relativity, if the particle's energy density exceeds a certain threshold, it should be a black hole.
In order to combine these two pictures, we introduce a horizon wave-function determined by the position wave-function, which yields the probability that the particle is a black hole.
The existence of a (fuzzy) minimum mass for black holes naturally follows, and we also show that our construction entails an effective Generalised Uncertainty Principle simply obtained by adding the uncertainties coming from the two wave-functions.

What is the Schwarzschild radius of a quantum mechanical particle? · Around

Built on

T.D. Newton and E.P. Wigner, Rev. Mod. Phys. 3
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K.S. Thorne, “Nonspherical Gravitational Collapse: A Short Review,” in J.R. Klauder, Magic Without Magic,
1972
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P.D. D’Eath and P.N. Payne, Phys. Rev. D 46
1992
Earlier work this paper cites.

Similar

T. Banks and W. Fischler, “A Model for high-energy scattering in quantum gravity,” hep-th/9906038; D.M. Eardley and S.B. Giddings, Phys. Rev. D 66
2002
Cited alongside, same era.
X. Calmet, D. Fragkakis and N. Gausmann, Eur. Phys. J. C 71
2008
Cited alongside, same era.
R. Casadio, “Localised particles and fuzzy horizons: A tool for probing Quantum Black Holes,” arXiv:1305.3195 [gr-qc]; R. Casadio and F. Scardigli, “Horizon wave-function for single localized particles: GUP and quantum black hole decay,” arXiv:1306.5298 [gr-qc]
Original
Cited in the paper.

Then

M. Maggiore, Phys. Lett. B 319
2009
Later among the works it cites.
G.L. Alberghi, R. Casadio, O. Micu and A. Orlandi, JHEP 1109
2011
Later among the works it cites.

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