The minimum mass of a charged spherically symmetric object in $D$ dimensions, its implications for fundamental particles, and holography
The European Physical Journal C, 76(3), 1-22 (2016) We obtain bounds for the minimum and maximum mass/radius ratio of a stable, charged, spherically symmetric compact object in a $D$-dimensional space-time in the framework of general relativity, and in the presence of dark energy. The total energy,...
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Main Authors | , , , |
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Format | Journal Article |
Language | English |
Published |
23.12.2015
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Subjects | |
Online Access | Get full text |
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Summary: | The European Physical Journal C, 76(3), 1-22 (2016) We obtain bounds for the minimum and maximum mass/radius ratio of a stable,
charged, spherically symmetric compact object in a $D$-dimensional space-time
in the framework of general relativity, and in the presence of dark energy. The
total energy, including the gravitational component, and the stability of
objects with minimum mass/radius ratio is also investigated. The minimum energy
condition leads to a representation of the mass and radius of the charged
objects with minimum mass/radius ratio in terms of the charge and vacuum energy
only. As applied to the electron in the four-dimensional case, this procedure
allows one to re-obtain the classical electron radius from purely general
relativistic considerations. By combining the lower mass bound, in four
space-time dimensions, with minimum length uncertainty relations (MLUR)
motivated by quantum gravity, we obtain an alternative bound for the maximum
charge/mass ratio of a stable, gravitating, charged quantum mechanical object,
expressed in terms of fundamental constants. Evaluating this limit numerically,
we obtain again the correct order of magnitude value for the charge/mass ratio
of the electron, as required by the stability conditions. This suggests that,
if the electron were either less massive (with the same charge) or if its
charge were any higher (for fixed mass), a combination of electrostatic and
dark energy repulsion would destabilize the Compton radius. In other words, the
electron would blow itself apart. Our results suggest the existence of a deep
connection between gravity, the presence of the cosmological constant, and the
stability of fundamental particles. |
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DOI: | 10.48550/arxiv.1512.07413 |