309 research outputs found
On prescribed change of profile for solutions of parabolic equations
Parabolic equations with homogeneous Dirichlet conditions on the boundary are
studied in a setting where the solutions are required to have a prescribed
change of the profile in fixed time, instead of a Cauchy condition. It is shown
that this problem is well-posed in L_2-setting. Existence and regularity
results are established, as well as an analog of the maximum principle
Black hole atom as a dark matter particle candidate
We propose the new dark matter particle candidate - the "black hole atom",
which is an atom with the charged black hole as an atomic nucleus and electrons
in the bound internal quantum states. As a simplified model we consider the the
central Reissner-Nordstrom black hole with the electric charge neutralized by
the internal electrons in bound quantum states. For the external observers
these objects would look like the electrically neutral Schwarzschild black
holes. We suppose the prolific production of black hole atoms under specific
conditions in the early universe.Comment: 5 pages, 1 figures, with additional reference
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