I study six novel observational tests of general relativity. First, I show
    that a gravitational wave pulse from a major merger of massive black holes at
    the Galactic center induces a permanent increase in the Earth-Moon separation.
    For black holes of a few million solar masses, the shift in the local
    gravitational potential is comparable to the Earth-Moon potential, leading to
    the Moon being perturbed relative to the Earth during the passage of the pulse.
    The permanent increase in the Earth-Moon separation is a fraction of a
    millimeter, measurable by lunar ranging for future merger events. Second, I
    show that General Relativity sets an absolute upper limit on the energy flux
    observed from a cosmological source as a function of its redshift. Third, I
    consider the implications of modified inertia at low accelerations for rockets.
    An attractive interpretation of MOdified Newtonian Dynamics (MOND) as an
    alternative to dark matter, changes the inertia of matter at accelerations
    a<a_0=1.2×10^{-8} cm/s^2. I show that if inertia is modified rockets operating
    at a<<a_0 might allow intergalactic travel with a modest fuel-to-payload mass
    ratio. Fourth, I show that in MOND the amplitude of the observed dipole of the
    Cosmic Microwave Background (CMB) can originate from the primordial fluctuation
    amplitude on the scale of the cosmic horizon. Fifth, I show that the tidal
    gravitational potential of the Milky-Way galaxy removes fuzzy dark matter from
    its satellite dwarf galaxies through quantum-mechanical tunneling. Sixth, I
    show that a charged particle can be accelerated to arbitrarily high energies by
    maintaining a permanent resonance with the phase of a planar gravitational wave
    propagating along a uniform magnetic field. The Doppler-shifted cyclotron
    autoresonance could potentially result in electromagnetic afterglows near
    gravitational-wave sources.

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