Abstract
This analysis considers our universe as a closed Friedmann universe, dominated by vacuum energy in the form of a cosmological constant, with cosmological parameters obtained from full mission Planck satellite observations. A few simple assumptions lead to straightforward calculation of general features of large scale structures in the universe and minimum stellar mass as a function of redshift. Those assumptions also generate upper and lower bounds on supermassive black hole mass in relation to total stellar mass of the host galaxy, consistent with observations across four orders of magnitude of black hole mass and five orders of magnitude of galactic stellar mass. The results are based only on fundamental constants and measured cosmological parameters. No arbitrary parameters are involved.
Highlights
How supermassive black holes “... form and evolve inside galaxies is one of the most fascinating mysteries in modern astrophysics” [1]
The upper bound is consistent with two important test cases involving observations of the supermassive black hole with mass 3.6 × 10−6 times the galactic mass in Sagittarius A* near the center of our Milky Way and the 2 × 109 solar mass black hole in the quasar ULAS J112001.48 + 064124.3 at redshift z = 7.085
This analysis addresses that issue with a holographic model [2] for large scale structure in the universe, based on the holographic principle [3] resulting from the theory of gravitation expressed by general relativity
Summary
How supermassive black holes “... form and evolve inside galaxies is one of the most fascinating mysteries in modern astrophysics” [1]. Form and evolve inside galaxies is one of the most fascinating mysteries in modern astrophysics” [1]. This analysis addresses that issue with a holographic model [2] for large scale structure in the universe, based on the holographic principle [3] resulting from the theory of gravitation expressed by general relativity. The internal dynamics of large scale structures is analyzed using classical Newtonian gravity to describe the motion of sub-elements within the structures and general relativity to describe the supermassive black holes at their centers. Consistency of the results with test cases across the range of large scale structures and redshifts makes it difficult to ascribe those results to numerical coincidences
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