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Dark stars and black holes both have a surface escape velocity equal or greater than lightspeed, and a critical radius of r ≤ 2M. However, the dark star is capable of emitting indirect radiation – outward-aimed light and matter can leave the r = 2M surface briefly before being recaptured, and while outside the critical surface, can interact ...
In general relativity, the Oppenheimer–Snyder model is a solution to the Einstein field equations based on the Schwarzschild metric describing the collapse of an object of extreme mass into a black hole. [1] It is named after physicists J. Robert Oppenheimer and Hartland Snyder, who published it in 1939. [2]
Dark star (Newtonian mechanics), a star that has a gravitational pull strong enough to trap light under Newtonian gravity Dark star (dark matter), a star heated by annihilation of dark matter particles within it
Under the above conditions, there exists a solution to the problem for any given set of data points {x k, y k} as long as N, the number of data points, is not larger than the number of coefficients in the polynomial, i.e., N ≤ 2K+1 (a solution may or may not exist if N>2K+1 depending upon the particular set of data points).
[1] [2] [3] In the unlikely event that dark stars have endured to the modern era, they could be detectable by their emissions of gamma rays, neutrinos, and antimatter and would be associated with clouds of cold molecular hydrogen gas that normally would not harbor such energetic, extreme, and rare particles. [4] [2]
Schwarzschild has 4 independent Killing vector fields, including a timelike one, and thus is a static metric, while Vaidya has only 3 independent Killing vector fields regarding the spherical symmetry, and consequently is nonstatic. Consequently, the Schwarzschild metric belongs to Weyl's class of solutions while the Vaidya metric does not.
r = | z | = √ x 2 + y 2 is the magnitude of z and; φ = arg z = atan2(y, x). φ is the argument of z, i.e., the angle between the x axis and the vector z measured counterclockwise in radians, which is defined up to addition of 2π. Many texts write φ = tan −1 y / x instead of φ = atan2(y, x), but the first equation needs ...
A solution to this conundrum is to hypothesize the existence of dark matter and to assume its distribution from the galaxy's center out to its halo. Thus the discrepancy between the two curves can be accounted for by adding a dark matter halo surrounding the galaxy.