Kavli Affiliate: Craig Hogan

| First 5 Authors: Kris Mackewicz, Craig Hogan, , ,

| Summary:

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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