## Topics in Space-Time, Gravity and Cosmology

**Authors:** Miroslav Pardy

We derive the Poincar´e model of the Lobachevsky geometry from the Fermat
principle. The Lobachevsky geometry is interpreted as the
Lobachevsky-Beltrami-Fok velocity space geometry of moving particles. The relation
of this geometry to the decay of the neutral π-meson is considered. The
generalization of the Lobachevsky geometry is performed and the new angle of
parallelism is derived. Then, we determine nonlinear transformations between coordinate
systems which are mutually in a constant symmetrical accelerated motion.
The maximal acceleration limit follows from the kinematic origin. Maximal acceleration
is an analogue of the maximal velocity in special relativity. We derive the
dependence of mass, length, time, Doppler effect, on acceleration as an analogue
phenomena in special theory of relativity. We apply the derived nonlinear
Lorentz group to the so called Thomas precession. The total quantum energy loss
of binary is caused by the production of gravitons emitted by the rotation motion of
binary. We have calculated it in the framework of the Schwinger theory of gravity
for the situation where the gravitational propagator involves radiative corrections.
We also derive the finite-temperature gravitational Cherenkov radiation involving
radiative corrections. The graviton action in vacuum is generalized for the medium
with the constant gravitational index of refraction. From this generalized action
the power spectral formula of the Cherenkov radiation of gravitons is derived in
the framework of the Schwinger theory at zero and nonzero temperature. The next
text deals with non-relativistic quantum energy shift of H-atom electrons due to Gibbons-Hawking thermal bath. The seventh chapter deals with gravity as the
deformation of the space time and it involves the light deflection by the screw dislocation.
In conclusion, we consider the scientific and technological meaning and the
perspectives of the results derived. Some parts of the complex are published in the
reputable journals.
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**Comments:** 89 Pages. The original ideas published in reputable journals

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### Submission history

[v1] 2017-02-02 02:03:22

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