By adding an extra term to the Newtonian potential, matter outside the orbit of a star adds to the gravitational acceleration acting on that star. In this work, we solve the Poisson equation for non-Newtonian potentia...By adding an extra term to the Newtonian potential, matter outside the orbit of a star adds to the gravitational acceleration acting on that star. In this work, we solve the Poisson equation for non-Newtonian potentials of a spherically symmetric distribution of mass. We derive equations for calculating the centripetal acceleration and velocity of galactic disk stars that are due to the Newtonian and exponential potentials of the galaxy’s central bulge.展开更多
The prevailing cosmological constant and cold dark matter (ΛCDM) cosmic concordance model accounts for the radial expansion of the universe after the Big Bang. The model appears to be authoritative because it is base...The prevailing cosmological constant and cold dark matter (ΛCDM) cosmic concordance model accounts for the radial expansion of the universe after the Big Bang. The model appears to be authoritative because it is based on the Einstein gravitational field equation. However, a thorough scrutiny of the underlying theory calls into question the suitability of the field equation, which states that the Einstein tensor <strong><em>G</em></strong><span style="white-space:nowrap;"><sub><em><span style="white-space:nowrap;">μv</span></em></sub></span> is a constant multiple of the stress-energy tensor <em> <strong>T</strong></em><span style="white-space:nowrap;"><sub><em><span style="white-space:nowrap;">μv</span></em></sub> </span>when they both are evaluated at the same 4D space-time point: <strong style="white-space:normal;"><em>G</em></strong><sub><em><span style="white-space:nowrap;">μv</span> </em></sub>= 8<span style="white-space:nowrap;">π</span>k<strong style="white-space:normal;"><em>T</em></strong><sub><em><span style="white-space:nowrap;">μv</span></em></sub>, where k is the gravitational constant. Notwithstanding its venerable provenance, this equation is incorrect unless the cosmic pressure is <em>p</em> = 0;but then all that remains of the Einstein equation is the Poisson equation which models the Newtonian gravity field. This shortcoming is not resolved by adding the cosmological constant term to the field equation, <strong style="white-space:normal;"><em>G</em></strong><sub><em><span style="white-space:nowrap;">μv</span> </em></sub>+<span style="white-space:nowrap;">Λ</span> <strong style="white-space:normal;"><em>g</em></strong><sub><em><span style="white-space:nowrap;">μv</span> =<span style="white-space:normal;">8<span style="white-space:nowrap;">π</span></span><span style="white-space:normal;">k</span><strong style="white-space:normal;"><em>T</em></strong><sub style="white-space:normal;"><em><span style="white-space:nowrap;">μv</span></em></sub><span style="white-space:norma展开更多
文摘By adding an extra term to the Newtonian potential, matter outside the orbit of a star adds to the gravitational acceleration acting on that star. In this work, we solve the Poisson equation for non-Newtonian potentials of a spherically symmetric distribution of mass. We derive equations for calculating the centripetal acceleration and velocity of galactic disk stars that are due to the Newtonian and exponential potentials of the galaxy’s central bulge.
文摘The prevailing cosmological constant and cold dark matter (ΛCDM) cosmic concordance model accounts for the radial expansion of the universe after the Big Bang. The model appears to be authoritative because it is based on the Einstein gravitational field equation. However, a thorough scrutiny of the underlying theory calls into question the suitability of the field equation, which states that the Einstein tensor <strong><em>G</em></strong><span style="white-space:nowrap;"><sub><em><span style="white-space:nowrap;">μv</span></em></sub></span> is a constant multiple of the stress-energy tensor <em> <strong>T</strong></em><span style="white-space:nowrap;"><sub><em><span style="white-space:nowrap;">μv</span></em></sub> </span>when they both are evaluated at the same 4D space-time point: <strong style="white-space:normal;"><em>G</em></strong><sub><em><span style="white-space:nowrap;">μv</span> </em></sub>= 8<span style="white-space:nowrap;">π</span>k<strong style="white-space:normal;"><em>T</em></strong><sub><em><span style="white-space:nowrap;">μv</span></em></sub>, where k is the gravitational constant. Notwithstanding its venerable provenance, this equation is incorrect unless the cosmic pressure is <em>p</em> = 0;but then all that remains of the Einstein equation is the Poisson equation which models the Newtonian gravity field. This shortcoming is not resolved by adding the cosmological constant term to the field equation, <strong style="white-space:normal;"><em>G</em></strong><sub><em><span style="white-space:nowrap;">μv</span> </em></sub>+<span style="white-space:nowrap;">Λ</span> <strong style="white-space:normal;"><em>g</em></strong><sub><em><span style="white-space:nowrap;">μv</span> =<span style="white-space:normal;">8<span style="white-space:nowrap;">π</span></span><span style="white-space:normal;">k</span><strong style="white-space:normal;"><em>T</em></strong><sub style="white-space:normal;"><em><span style="white-space:nowrap;">μv</span></em></sub><span style="white-space:norma
