  The recently proposed formalism of extended Jordan-Brans-Dicke gravity makes
it possible to calculate energy loss rate due to both gravitational wave and
scalar field (giving the origin of dark energy) wave emission at merger of a
black hole and a neutron star; a binary system of no scalar hair and a star
with the scalar charge. The scalar field emission changes orbit parameters of
the binary system, thereby changes detectable gravitational wave emission. When
neutron stars carry significantly large scalar charge, significant dark wave
(namely, scalar field wave) emission occurs at the same time of gravitational
wave emission. It is found that solutions of coupled differential equations
predict non-vanishing remnant dark charge after the gravitational collapse.
This gives two interesting possibilities: (1) the no-hair conjecture of black
hole is violated, or (2) a bosonic cloud is formed outside the event horizon of
black hole. The bosonic cloud proposed in the literature is a gigantic atom
made of gravitationally bound dark energy quanta surrounding a black hole. One
can either constrain, or even determine, parameters of extended
Jordan-Brans-Dicke gravity from accumulated gravitational wave observations of
merging black hole and neutron star.
