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15 - Relativistic hydrodynamics and thermodynamics

from Part II - The theory of gravitation

Published online by Cambridge University Press:  30 May 2024

Jerzy Plebanski
Affiliation:
National Polytechnic Institute of Mexico
Andrzej Krasinski
Affiliation:
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences
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Summary

The description of motion of a continuous medium in curved spacetime is introduced and related to the corresponding Newtonian description. Expansion, acceleration, shear and rotation of the medium are defined and interpreted. The Raychaudhuri equation and other evolution equations of hydrodynamical quantities are derived. A simple example of a singularity theorem is presented. Relativistic thermodynamics is introduced and it is shown that a thermodynamical scheme is guaranteed to exist only in such spacetimes that have an at least 2-dimensional symmetry group.

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Publisher: Cambridge University Press
Print publication year: 2024

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