@peter jeffrey cobb,
Peter, actually, it can be shown that an interaction between dark matter and dark energy is favored by the most recent large scale structure observations. The result presented by the BOSS-SDSS collaboration measuring the baryon acoustic oscillations of the Ly-α forest from high redshift quasars indicates a 2.5σ departure from the standard ΛCDM model. This is the first time that the evolution of dark energy at high redshifts has been measured and the current results cannot be explained by simple generalizations of the cosmological constant. We show here that a simple phenomenological interaction in the dark sector provides a good explanation for this deviation, naturally accommodating the Hubble parameter obtained by BOSS, H(z=2.34)=222±7 km s−1 Mpc−1, for two of the proposed models with a positive coupling constant and rejecting the null interaction at more than 2σ. For this we used the adjusted values of the cosmological parameters for the interacting models from the current observational data sets. This small and positive value of the coupling constant also helps alleviate the coincidence problem.
In 1916, Karl Schwarzschild obtained an exact solution[2][3] to Einstein's field equations for the gravitational field outside a non-rotating, spherically symmetric body (see Schwarzschild metric). Using the definition M=\frac {Gm} {c^2}, the solution contained a term of the form \frac {1} {2M-r}; where the value of r making this term singular has come to be known as the Schwarzschild radius. The physical significance of this singularity, and whether this singularity could ever occur in nature, was debated for many decades; a general acceptance of the possibility of a black hole did not occur until the second half of the 20th century.
Parameters[edit]
The Schwarzschild radius of an object is proportional to the mass. Accordingly, the Sun has a Schwarzschild radius of approximately 3.0 km (1.9 mi) while the Earth's is only about 9.0 mm, the size of a peanut. The observable universe's mass has a Schwarzschild radius of approximately 13.7 billion light years.[4][5]
\text{radius}_s (m)
\text{density}_s (g/cm3)
Universe 4.46×1025[citation needed] (~4.7 Gly) 8×10−29[citation needed] (9.9×10−30[6])
Milky Way 2.08×1015 (~0.2 ly) 3.72×10−8
Sun 2.95×103 1.84×1016
Earth 8.87×10−3 2.04×1027
Formula[edit]
The Schwarzschild radius is proportional to the mass with a proportionality constant involving the gravitational constant and the speed of light:
r_\mathrm{s} = \frac{2 G m}{c^2},
where:
rs is the Schwarzschild radius;G is the gravitational constant;m is the mass of the object;c is the speed of light in vacuum.
The proportionality constant, 2G/c2, is approximately 1.48×10−27 m/kg, or 2.95 km/M☉.
An object of any density can be large enough to fall within its own Schwarzschild radius,
V_\mathrm{s} \propto \rho^{-3/2},
where:
V_\mathrm{s}\! = \frac{4 \pi}{3} r_\mathrm{s}^3 is the volume of the object;\rho\! = \frac{ m }{ V_\mathrm{s} } is its density.
However if you figure in neutrino mass or positive lack of mass to be more exact, then it follows that.
Are you following still, because there is more
The Sudbury Neutrino Observatory (SNO) is a water Čerenkov detector located in INCO’s Creighton mine near Sudbury, Ontario, Canada.14 The SNO consists of a sphere, 12 m in diameter, filled with heavy water (D2O),15 and surrounded by light water (H2O)—to provide shielding from non-neutrino sources such as radioactivity.16 When a neutrino interacts with the heavy water, the Čerenkov photons generated within the sphere are detected by an array of 9,456 photomultiplier tubes placed around the sphere.
SNO can detect neutrinos in three different ways: the charged current (CC) reaction,17 the elastic scattering (ES) reaction,18 and the neutral current (NC) reaction.19 The CC reaction can detect only electron neutrinos (νe). The ES reaction can detect all neutrino flavours, but with reduced sensitivity to νµ and ντ . The NC reaction detects all neutrino flavours with equal sensitivity. By comparing the measured rates of the three reactions, it is possible to determine if any neutrinos are of a non-electron flavour. The reactions are listed below. The d represents a deuteron.20 The p, n, and e– are a proton, neutron, and electron, respectively. The νx indicates that all flavours of neutrinos can undergo the reaction.
Equation 2
The latest SNO results are now examined21 and compared with predictions. Using the standard solar model, Bahcall, Pinsonneault, and Basu have predicted22 a total neutrino flux (φ) for the 8B solar neutrinos23 at Equation 5 which can be compared with the observed values for each of the three reactions.24 In the measured values shown below, the first error bars are statistical and the second are systematic. The results are normalized for the 8B neutrino spectrum with an energy threshold of 5 MeV. All values are in units of 106 cm–2 s–1.
Equation 3
The NC reaction (which detects all neutrino flavours equally) is consistent with the standard solar model predictions. It does not show a deficit of neutrinos, yet it exceeds the fluxes of the other reactions that detect electron neutrinos preferentially (the ES reaction has been normalized assuming only electron neutrinos), or exclusively (as with the CC reaction). This is compelling support for neutrino oscillations. It is not consistent with a ⅓ fusion and ⅔ gravitational collapse power source. If the sun were simply producing fewer neutrinos than predicted, then all three fluxes should be reduced equally—the same as the CC flux. Less fusion would mean fewer neutrinos ‘across the board’; only oscillations to other flavours can readily explain the differences in the measured fluxes. The SNO data are demonstrated visually in the accompanying figure.
The electron, and non-electron components can be derived from the above fluxes:
Equation 4
The flux values for the non-electron neutrinos are 5.3 standard deviations above zero (combining the uncertainties). This detection of non-electron solar neutrinos makes a very compelling case for neutrino oscillations.
So if you can tie these ideas together, with the right strings, the unified theory should at least be near, however the missing neutrino mass is what throws me off every time.