Submissions from D. P. H. Almasy
 [1] faKiv:2002.07518 [pdf]

A cosmological model for the Minkowski VacuaComments: 9 pages, 1 figure
We argue that the Minkowski vacua of the Planck and MAC models can be modified in the vacuum geometry to the Schwarzschild analogue. We present a cosmological model in order to study the vacuum state of the Planck and MAC models. The model is a macroscopically flat model which can be realized as a black hole in the presence of a gravitational field. The black hole can be made to collapse to a vacuum state in the presence of a gravitational field. The vacuum state of the Schwarzschild model is the selfinteracting graviton, which can be systematically investigated. The cosmological models are created on a spacelike manifold with a nonvanishing $U(1)$ gauge group. We also show that the Minkowski vacua of the MAC models are compatible with the Schwarzschild analogue. The results obtained in this paper can be used to determine the Hawking temperature of black holes.
 [2] faKiv:2002.07519 [pdf]

A cosmological model with a black hole in the backgroundComments: 8 pages
We study the cosmological model with a black hole in the background. We show that the black holes are not necessarily black and that the cosmological constant is always positive. We also show that the cosmological constant is always positive when the black hole is removed. We show that the cosmological constant can be reduced to the cfield in the background of the black holes.