Andrei Frolov
Email: frolov@cita.utoronto.ca
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Research Summary
[
Cosmology,
Early Universe and General Relativity
]
Andrei Frolov works on problems in general relativity and theoretical
cosmology. His recent topic of interest is brane-world models of the
Universe, in which our four-dimensional world is a surface (brane)
embedded in a higher dimensional bulk spacetime, and their observable
consequences. His other research interests include the early Universe,
exact solutions of general relativity, and black hole physics.
Research Projects:
(September 2002 - August 2003)
Thermodynamical aspects of quasi-de Sitter geometry
Andrei Frolov and Lev Kofman considered thermodynamical aspects of the
quasi-de Sitter geometry of the inflationary universe. They calculated
the energy flux of the slowly rolling background scalar field through
the quasi-de Sitter apparent horizon and set it equal to the change of
the entropy (1/4 of the area) multiplied by the temperature, dE=TdS.
Remarkably, this thermodynamic law reproduces the Friedmann equation
for the rolling scalar field. Next they added inflaton fluctuations
which generate scalar metric perturbations. Metric perturbations result
in a variation of the area entropy. Again, the equation dE=TdS with
fluctuations reproduces the linearized Einstein equations. In this
picture, as long as the Einstein equations hold, holography does not
put limits on the quantum field theory during inflation. Due to the
accumulating metric perturbations, the horizon area during inflation
randomly wiggles with dispersion increasing with time. They discussed
this in connection with the stochastic description of inflation.
Properties of Schwarzschild black holes
Andrei Frolov and Valeri Frolov (University of Alberta) investigated
properties of a 4-dimensional Schwarzschild black hole in a spacetime
where one of the spatial dimensions is compactified. As a result of the
compactification the event horizon of the black hole is distorted. They
used Weyl coordinates to obtain the solution describing such a
distorted black hole. This solution is a special case of the
Israel-Khan metric. They studied the properties of the compactified
Schwarzschild black hole, and developed an approximation which allows
one to find the size, shape, surface gravity and other characteristics
of the distorted horizon with a very high accuracy in a simple
analytical form. They also discussed possible instabilities of a black
hole in the compactified space.
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