Kavli Affiliate: Craig Hogan
| First 5 Authors: Kris Mackewicz, Craig Hogan, , ,
A linear analytical solution is derived for the gravitational shock wave
produced by a particle of mass $M$ that decays into a pair of null particles.
The resulting space-time is shown to be unperturbed and isotropic, except for a
discontinuous perturbation on a spherical null shell. Formulae are derived for
the perturbation as a function of polar angle, as measured by an observer at
the origin observing clocks on a sphere at distance $R$. The effect of the
shock is interpreted physically as an instantaneous displacement in time and
velocity when the shock passes the clocks. The time displacement is shown to be
anisotropic, dominated by a quadrupole harmonic aligned with the particle-decay
axis, with a magnitude $delta tausim GM/c^3$, independent of $R$. The
velocity displacement is isotropic. The solution is used to derive the
gravitational effect of a quantum state with a superposition of a large number
of randomly oriented, statistically isotropic particle decays. This approach is
shown to provide a well-controlled approximation to estimate the magnitude of
gravitational fluctuations in systems composed of null point particles up to
the Planck energy in a causal diamond of duration $tau= 2R/c$, as well as
quantum-gravitational fluctuations of black holes and cosmological horizons.
Coherent large-angle quantum distortions of macroscopic geometry from
fluctuations up to the Planck scale are shown to grow linearly with the
duration, with a variance $langle delta tau^2ranglesim tau t_P$ much
larger than that produced in models without causal quantum coherence.
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