Editing Relativistic Euler equations (section)

== Motivation ==
For most fluids observable on Earth, traditional fluid mechanics based on Newtonian mechanics is sufficient. However, as the fluid velocity approaches the speed of light or moves through strong gravitational fields, or the pressure approaches the energy density (<math>P\sim\rho</math>), these equations are no longer valid.<ref name=":1">{{Cite book|last1=Thorne|first1=Kip S.|title=Modern Classical Physics|last2=Blandford|first2=Roger D.|publisher=Princeton University Press|year=2017|isbn=9780691159027|location=Princeton, New Jersey|pages=719–720}}</ref> Such situations occur frequently in astrophysical applications. For example, gamma-ray bursts often feature speeds only <math>0.01%</math> less than the speed of light,<ref>{{Cite journal|last1=Lithwick|first1=Yoram|last2=Sari|first2=Re'em|date=July 2001|title=Lower limits on Lorentz factors in gamma-ray bursts|journal=The Astrophysical Journal|volume=555|issue=1|pages=540–545|doi=10.1086/321455|arxiv=astro-ph/0011508|bibcode=2001ApJ...555..540L|s2cid=228707}}</ref> and neutron stars feature gravitational fields that are more than <math>10^{11}</math> times stronger than the Earth's.<ref>{{Cite book|title=An introduction to the sun and stars|date=2004|publisher=Open University|others=Green, S. F., Jones, Mark H. (Mark Henry), Burnell, S. Jocelyn.|isbn=0-521-83737-5|edition=Co-published|location=Cambridge|oclc=54663723}}</ref> Under these extreme circumstances, only a relativistic treatment of fluids will suffice.