Submissions from C. J. M. Dabrowski

[1]  faKiv:2104.08149 [pdf]
On the existence of non-perturbative gravitational waves on space-time boundaries
Comments: 35 pages, 1 figure, LaTeX2e

We consider the existence of non-perturbative gravitational waves on space-time boundaries of a Schwarzschild black hole. The solution to the Einstein equations for the black hole is found to be non-perturbative, 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 space-time boundary cannot contain gravitational waves, but it does contain the gravitational waves. The result shows that if the space-time boundary is a flat space, the gravitational waves cannot be present on space-time.

[2]  faKiv:2104.08199 [pdf]
The first law of thermodynamics: a formalism
Comments: 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, Quark-gluon plasma and Friedman-Robertson-Walker 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 Quark-gluon plasma is solved in the smallest dimension, and that the thermodynamic quantities of Minkowski vacuum, Quark-gluon plasma and Friedman-Robertson-Walker are the same as those of the thermodynamical quantities of Quark-gluon 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, Quark-gluon plasma and Friedman-Robertson-Walker. This formula is invariant under the first law of thermodynamics. We present the formula for the thermodynamic quantities of Minkowski vacuum, Quark-gluon plasma and Friedman-Robertson-Walker; it is invariant under the first law of thermodynamics.