Diffusion in the general theory of relativity - General Relativity and Quantum CosmologyReport as inadecuate




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Abstract: The Markovian diffusion theory in the phase space is generalized within theframework of the general theory of relativity. The introduction of movingorthonormal frame vectors both for the position as well the velocity spaceenables to bypass difficulties in the general relativistic stochastic calculus.The general relativistic Kramers equation in the phase space is derived both inthe parametrization of phase space proper time and the coordinate time. Thetransformation of the obtained diffusion equation under hypersurface-preservingcoordinate transformations is analyzed and diffusion in the expanding universeis studied. It is shown that the validity of the fluctuation-dissipationtheorem ensures that in the quasi-steady state regime the result of the deriveddiffusion equation is consistent with the kinetic theory in thermodynamicequilibrium.



Author: Joachim Herrmann

Source: https://arxiv.org/



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