In general relativity, the Wahlquist fluid is an exact rotating perfect fluid solution to Einstein's equation with equation of state corresponding to constant gravitational mass density.

Introduction

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The Wahlquist fluid was first discovered by Hugo D. Wahlquist in 1968.[1] It is one of few known exact rotating perfect fluid solutions in general relativity. The solution reduces to the static Whittaker metric in the limit of zero rotation.

Metric

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The metric of a Wahlquist fluid is given by

 

where

 
 
 
 

and   is defined by  . It is a solution with equation of state   where   is a constant.

Properties

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The pressure and density of the Wahlquist fluid are given by

 
 

The vanishing pressure surface of the fluid is prolate, in contrast to physical rotating stars, which are oblate. It has been shown that the Wahlquist fluid can not be matched to an asymptotically flat region of spacetime.[2]

References

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  1. ^ Wahlquist, Hugo D. (1968). "Interior Solution for a Finite Rotating Body of Perfect Fluid". Physical Review. 172 (5): 1291–1296. Bibcode:1968PhRv..172.1291W. doi:10.1103/PhysRev.172.1291.
  2. ^ Bradley, Michael; Fodor, Gyula; Marklund, Mattias; Perjés, Zoltán (2000). "The Wahlquist metric cannot describe an isolated rotating body". Classical and Quantum Gravity. 17 (2): 351–359. arXiv:gr-qc/9910001. Bibcode:2000CQGra..17..351B. doi:10.1088/0264-9381/17/2/306. S2CID 2911496.