1,022 research outputs found
The Compton-Schwarzschild correspondence from extended de Broglie relations
The Compton wavelength gives the minimum radius within which the mass of a
particle may be localized due to quantum effects, while the Schwarzschild
radius gives the maximum radius within which the mass of a black hole may be
localized due to classial gravity. In a mass-radius diagram, the two lines
intersect near the Planck point , where quantum gravity effects
become significant. Since canonical (non-gravitational) quantum mechanics is
based on the concept of wave-particle duality, encapsulated in the de Broglie
relations, these relations should break down near . It is unclear
what physical interpretation can be given to quantum particles with energy , since they correspond to wavelengths or time
periods in the standard theory. We therefore propose a correction
to the standard de Broglie relations, which gives rise to a modified Schr{\"
o}dinger equation and a modified expression for the Compton wavelength, which
may be extended into the region . For the proposed modification,
we recover the expression for the Schwarzschild radius for and
the usual Compton formula for . The sign of the inequality
obtained from the uncertainty principle reverses at , so that
the Compton wavelength and event horizon size may be interpreted as minimum and
maximum radii, respectively. We interpret the additional terms in the modified
de Broglie relations as representing the self-gravitation of the wave packet.Comment: 40 pages, 7 figures, 2 appendices. Published version, with additional
minor typos corrected (v3
Primordial black holes from the QCD epoch: Linking dark matter, baryogenesis and anthropic selection
If primordial black holes (PBHs) formed at the quark-hadron epoch, their mass
must be close to the Chandrasekhar limit, this also being the characteristic
mass of stars. If they provide the dark matter (DM), the collapse fraction must
be of order the cosmological baryon-to-photon ratio , which
suggests a scenario in which a baryon asymmetry is produced efficiently in the
outgoing shock around each PBH and then propagates to the rest of the Universe.
We suggest that the temperature increase in the shock provides the ingredients
for hot spot electroweak baryogenesis. This also explains why baryons and DM
have comparable densities, the precise ratio depending on the size of the PBH
relative to the cosmological horizon at formation. The observed value of the
collapse fraction and baryon asymmetry depends on the amplitude of the
curvature fluctuations which generate the PBHs and may be explained by an
anthropic selection effect associated with the existence of galaxies. We
propose a scenario in which the quantum fluctuations of a light stochastic
spectator field during inflation generate large curvature fluctuations in some
regions, with the stochasticity of this field providing the basis for the
required selection. Finally, we identify several observational predictions of
our scenario that should be testable within the next few years. In particular,
the PBH mass function could extend to sufficiently high masses to explain the
black hole coalescences observed by LIGO/Virgo.Comment: 37 pages, 3 figures, published in MNRA
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