Kinetic screening in nonlinear stellar oscillations and gravitational
  collapse
  We consider k-essence, a scalar-tensor theory with first-order derivative
self-interactions that can screen local scales from scalar fifth forces, while
allowing for sizeable deviations from General Relativity on cosmological
scales. We construct fully nonlinear static stellar solutions that show the
presence of this screening mechanism, and we use them as initial data for
simulations of stellar oscillations and gravitational collapse in spherical
symmetry. We find that for k-essence theories of relevance for cosmology, the
screening mechanism works in the case of stellar oscillation and suppresses the
monopole scalar emission to undetectable levels. In collapsing stars, we find
that the Cauchy problem, although locally well posed, can lead to diverging
characteristic speeds for the scalar field. By introducing a ''fixing
equation'' in the spirit of J. Cayuso, N. Ortiz, and L. Lehner [Phys. Rev. D
96, 084043 (2017)], inspired in turn by dissipative relativistic hydrodynamics,
we manage to evolve collapsing neutron stars past the divergence of the
characteristic speeds. We show that, in these systems, the screening mechanism
is less efficient than for oscillating and static stars, because the collapsing
star must shed away all of its scalar hair before forming a black hole. For
k-essence theories of relevance for cosmology, the characteristic frequency of
the resulting scalar monopole signal is too low for terrestrial detectors, but
we conjecture that space-borne interferometers such as LISA might detect it if
a supernova explodes in the Galaxy.
