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Bose-Einstein graviton condensate in a Schwarzschild black hole | | Jorge Alfaro
; Domènec Espriu
; Luciano Gabbanelli
; | | Date: |
6 Sep 2016 | | Abstract: | We analyze in detail a previous proposal by Dvali and G’omez that black
holes could be treated as consisting of a Bose-Einstein condensate of
gravitons. In order to do so we extend the Einstein-Hilbert action with a
chemical potential-like term, thus placing ourselves in a grand-canonical
ensemble. The form and characteristics of this chemical potential-like piece
are discussed in some detail. After this, we proceed to expand the ensuing
equations of motion up to second order around the classical Schwarzschild
metric so that some non-linear terms in the metric fluctuation are kept. We
argue that the resulting equations could be interpreted as the Gross-Pitaevskii
equation describing a graviton Bose-Einstein condensate trapped by the black
hole gravitational field. Next we search for solutions and, modulo some very
plausible assumptions, we find out that the condensate vanishes outside the
horizon but is non-zero in its interior. Based on hints from a numerical
integration of the equations we formulate an ansatz and eventually find an
exact non-trivial solution for a mean-field wave-function describing the
graviton Bose-Einstein condensate in the black hole interior. Based on this we
can rederive some of the relations involving the number of gravitons $N$ and
the black hole characteristics, summarized in its Schwarzschild radius, along
the lines suggested by Dvali and G’omez. These relations are parametrized by a
single parameter ---a dimensionless chemical potential. | | Source: | arXiv, 1609.1639 | | Services: | Forum | Review | PDF | Favorites | |
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