What is it about?

This article displays a new class of solutions to Einstein's equations of general relativity, describing the spacetime generated inside a rotating cylinder of ordinary matter as mostly found in the Universe. The solutions are written with the use of standard mathematical functions and they satisfy the main physical properties usually ascribed to astrophysical objects of the type, which are analyzed carefully here.

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Why is it important?

Exact fully specified solutions describing the geometry and dynamics of the inside of a gravitating object are very few, contrary to solutions for the vacuum exterior of these sources. Often, the published solutions are not completely caracterized and are described by a mere system of simplified but not fully solved equations. This is due to the fact that the resolution of the corresponding equations is much mathematically involved and that, even when a solution is found, its physical interpretation is not straightforward. Hence, the importance of the results here displayed is that, not only a rare kind of complete mathematical solutions is exhibited but its physical properties allow them to describe a large class of astrophysical and physical objects, such as black holes, a number of stellar and cosmological systems and more fundamental phenomenons occuring in the physics bestiary. Moreover the results displayed here have been obtained through the use of a particularly efficient mathematical recipe previously developed by the same author and described here at lenght for the application to the considered case.


Exact solutions to the equations of general relativity are much valuable. Either they are directly used as models for representing some phenomenons whose physics corresponds to that of the given solution, or they may be used as a seed to some numerical description. Therefore, this solution will be be applied to increasing our knowledge of any astrophysical object exhibiting some cylindrical symmetry. Moreover, it is usual that the display of a new solution boosts the interest of the research community and is followed by the finding of new others. Indeed, due to the powerfulness of the mathematical method used here and which has already been employed by the same author to solve similar cases, it will certainly be a very useful tool in the framework of other similar problems, some being already considered in works in progress.

Marie-Noelle Celerier
Observatoire de Paris

Read the Original

This page is a summary of: Fully integrated interior solutions of GR for stationary rigidly rotating cylindrical perfect fluids, Journal of Mathematical Physics, February 2023, American Institute of Physics, DOI: 10.1063/5.0131945.
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