Submissions from C. J. M. Dabrowski
 [1] faKiv:2104.08149 [pdf]

On the existence of nonperturbative gravitational waves on spacetime boundariesComments: 35 pages, 1 figure, LaTeX2e
We consider the existence of nonperturbative gravitational waves on spacetime boundaries of a Schwarzschild black hole. The solution to the Einstein equations for the black hole is found to be nonperturbative, i.e. it is proportional to the square of the horizon radius. The existence of gravitational waves over the horizon radius is known to be of the same type as the existence of gravitational waves on the original horizon. The problems of mixing and scattering of gravitational waves are solved in the same way, i.e. the effect of gravitational waves is determined by the position of the black hole. We find that the spacetime boundary cannot contain gravitational waves, but it does contain the gravitational waves. The result shows that if the spacetime boundary is a flat space, the gravitational waves cannot be present on spacetime.
 [2] faKiv:2104.08199 [pdf]

The first law of thermodynamics: a formalismComments: 19 pages, 4 figures, 3 tables
We provide a formalism for the first law of thermodynamics: an invariant quantity of an object on a sphere. We obtain a universal formula for the thermodynamic quantities of Minkowski vacuum, Quarkgluon plasma and FriedmanRobertsonWalker vacuum, which is invariant under the first law. We show that the equation of state equation for Minkowski vacuum is solved in the largest dimension, and the equation of state equation for Quarkgluon plasma is solved in the smallest dimension, and that the thermodynamic quantities of Minkowski vacuum, Quarkgluon plasma and FriedmanRobertsonWalker are the same as those of the thermodynamical quantities of Quarkgluon plasma. The latter were originally obtained in volume and mass formulas and have been generalized to multiple dimensions. We discuss the relation to the first law of thermodynamics and provide a formula for the thermodynamic quantities of Minkowski vacuum, Quarkgluon plasma and FriedmanRobertsonWalker. This formula is invariant under the first law of thermodynamics. We present the formula for the thermodynamic quantities of Minkowski vacuum, Quarkgluon plasma and FriedmanRobertsonWalker; it is invariant under the first law of thermodynamics.