The Schwarzchild manifold of general relativity theory is unsatisfactory as a particle model because the singularity at the origin makes it geodesically incomplete. A coupling of the geometry of space-time to a scalar field φ produces in its stead a static, spherically symmetric, geodesically complete, horizonless space-time manifold with a topological hole, termed a drainhole, in its center. The coupling is Rμν=2φ,μφ,ν; its polarity is reversed from the usual to allow both the negative curvatures found in the drainhole and the completeness of the geodesics. The scalar field satisfies the scalar wave equation □φ=0 and has finite total energy whose magnitude, expressed as a length, is comparable to the drainhole radius. On one side of the drainhole the manifold is asymptotic to a Schwarzschild manifold with positive mass parameter m, on the other to a Schwarzschild manifold with negative mass parameter m̄, and − m̄ > m. The two-sided particle thus modeled attracts matter on the one side and, with greater strength, repels it on the other. If m is one proton mass, then − m̄/m ≈ 1+10−19 or 1+10−39, according as the drainhole radius is close to 10−33cm or close to 10−13 cm; the ratios of total scalar field energy to m in these instances are 1019 and 1039. A radially directed vector field which presents itself is interpreted, for purposes of conceptualization, as the velocity of a flowing ``substantial ether'' whose nonrigid motions manifest themselves as gravitational phenomena. When the ether is at rest, the two-sided particle has no mass on either side, but the drainhole remains open and is able to trap test particles for any finite length of time, then release them without ever accelerating them; some it can trap for all time without accelerating them. This massless, chargeless, spinless particle can, if disturbed, dematerialize into a scalar-field wave propagating at the wave speed characteristic of the space-time manifold.

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Proceeding from a solution of field equations that are improved versions of Einstein's nonvacuum gravitational field equations one is able to calculate precisely the trajectories of particles traveling inside a nonrotating, homogeneous, spherical body. Application of the results to the conditions of recent measurements of neutrino flight times between a source point A at CERN's European Laboratory for Particle Physics and a point B in either of two detectors (ICARUS or OPERA) at LNGS (Laboratori Nazionale del Gran Sasso), separated by a euclidean distance d(A, B) = 731 km, predicts for the flight time Tν from A to B of a 2 eV neutrino launched with energy 17 GeV that, as measured by a clock at B synchronized to a similar clock at A, Tν ≈ d/c + 9.3 × 10 −16 sec. But as measured by inertial observers along the path the flight time Tν ≈ d/c − 2.6 × 10 −9 sec and the path length Lν ≈ d − 8.4 × 10 −7 m, which yields Lν/ Tν ≈ c + 321 m/sec for the average inertially referenced speed of the neutrino from A to B.

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