New Horizons in Mathematical Physics

3

Authors: Vasiliy K. Balkhanov

The article found that quasi-classic quantum approach allows to calculate temperature and entropy of black holes. Installed border applicability of quasi classical approximation: the mass of the black hole must be greater than the Planck mass.

7

Authors: V.G.Mete, V.D.Elkar, Poonam P. Kadu

An attempt has been taken to study the minimally interacting fields, dark matter and holographic dark energy in scalar tensor theory formulated by Saez and Ballester. The exact solution of the field equations is obtained by using the fact that the scalar expansion of the universe is proportional to the shear scalar. Some physical and geometrical aspects of the model are also discussed.

12

Authors: Maria F. Correia, Christopher Cox, Hong-Kun Zhang

We investigate a three-parameter family of billiard tables with circular arc boundaries. These umbrella-shaped billiards may be viewed as a generalization of two-parameter moon and asymmetric lemon billiards, in which the latter classes comprise instances where the new parameter is 0. Like those two previously studied classes, for certain parameters umbrella billiards exhibit evidence of chaotic behavior despite failing to meet certain criteria for defocusing or dispersing, the two most well understood mechanisms for generating ergodicity and hyperbolicity. For some parameters corresponding to non-ergodic lemon and moon billiards, small increases in the new parameter transform elliptic 2-periodic points into a cascade of higher order elliptic points. These may either stabilize or dissipate as the new parameter is increased. We characterize the periodic points and present evidence of new ergodic examples.