Earth: 15 Million Years Ago

In Einstein’s general relativity theory the metric component gxx in the direction of motion (x-direction) of the sun deviates from unity due to a tensor potential caused by the black hole existing around the center of the galaxy. Because the solar system is orbiting around the galactic center at 200 km/s, the theory shows that the Newtonian gravitational potential due to the sun is not quite radial. At the present time, the ecliptic plane is almost perpendicular to the galactic plane, consistent with this modification of the Newtonian gravitational force. The ecliptic plane is assumed to maintain this orientation in the galactic space as it orbits around the galactic center, but the rotational angular momentum of the earth around its own axis can be assumed to be conserved. The earth is between the sun and the galactic center at the summer solstice all the time. As a consequence, the rotational axis of the earth would be parallel to the axis of the orbital rotation of the earth 15 million years ago, if the solar system has been orbiting around the galactic center at 200 km/s. The present theory concludes that the earth did not have seasons 15 million years ago. Therefore, the water on the earth was accumulated near the poles as ice and the sea level was very low. Geological evidence exist that confirms this effect. The resulting global ice-melting started 15 million years ago and is ending now. Subect heading: General Relativity, Solar System, Milky Way Galaxy 1 ar X iv :0 81 0. 22 71 v1 [ ph ys ic s. ge nph ] 1 3 O ct 2 00 8 If we take gij = g (◦) ij + hij, (1) where g (◦) 00 = 1, g (◦) α0 = 0, g (◦) αβ = −δαβ, (2) α = 1, 2, 3, for the general relativistic metric (ds) = gijdx dx, (3) and assume that the hij are all so small that their powers higher than the first are negligible, Einstein’s general relativistic field equations can be simplified into those of the linearized Einstein theory. Introducing hij = φij − 1 2 φg (◦) ij (4) where φ = φi, and φ i j = g φkj, and assuming that ∂φj ∂xi = 0, (5) we see that Einstein’s field equation can be approximated as ( ∂ ∂x2 − 1 c2 ∂ ∂t2 ) φj = 16πG c4 T i j . (6) In eq. (6), T i j is a component of the mass energy-momentum tensor such that T 0 0 = μc 2 . It is easy to solve eq. (6), because it is mathematically identical to the Maxwell field equations, to obtain φ00 = −Σa 4GMa cra |t′ , (7a) φα0 = Σa 4GMava,α cra |t′ , (7b) φαβ = −Σa 4GMava,αva,β cra |t′ , (7c) where Ma is the mass of a point source located at a distance ra from the observation point, and va,α is the α-component of its velocity. Because eq. (6) is linear in μ, the mass density, we see that the right-hand sides of eqs, (7a) through (7c) are given by the sum over existing point masses Ma. Quantities on the right-hand side of eqs. (7a) through (7c) are to be evaluated at the retardation time t′, but the retardation effect can be