Christian Fronsdal

Hydrodynamics, Thermodynamics, General Relativity

Office: 4-941 PAB
Phone: (310) 825-3432       fronsdal@physics.ucla.edu

3 new papers appear here, with weights 0,1,2, all of them revolutionary.

      All are with referees.

Nr. 0 Calculates the speeds of second and fourth sounds in He-II with high accuracy.

Nr. 1 Gravitational Waves, shows how to do it with Hydrodynamics.  

           I cannot believe that all 80 observed events were produced by Colliding Black Holes

Nr. 2 Explains the rings around the minor planets


Current project: Confinement


To see the papers go to the bottom of this page

I am learning to do this. Lots of confusion from this point on.


My latest paper: " Hydrodynamic sources for Gravitational Waves "

has been added below for viewing.


The paper  "Metastable fluids, capillary  action and superfluids

includes decisive progress on superfluids" has been added; it is available here only, so far.


The paper "Classic Mistake...". With new title "Stability analysis for cylindrical Couette flow... ",

has been published in December 2020 in Physics of Fluids".


The paper "Rotating Planets ..." has been submitted for publications on 21 Feb.  There is no response from referees yet.


The book ""Adiabatic Thermodynamics ..." was published in Sept. 2020. It is available from Amazon and others.

Individual Chapters are below for viewing.


Next, I am going to finish the paper "Inide the meniscus.

Please comment or write to




Since 2007 I have been bringing together    General relativity, Hydrodynamics and Thermodynamics. 







Publications in order of appearance.  Under construction.

2007 arXiv :gr-qc/0606027   and Gen.Rel.Grav 39  1971 2000-2007,    "Ideal stars in General Relativity"

This was the begininning. The main point is to give a scalar field theory that reduces to (irrotational hydrodynamics in the non relativistic limit. From this time I work under the conviction that any continuous source for Einstein's equations must be formulated as an action principle.  I reject Tolman's phenomenological approach although it is only recently that i understand the full justification of this:  Tolman's approach has no predictive power. This paper introduces the action principle for irrotational hydrodynamics in a general metric background. It provides a source for Einstein's equation that respectes the Bianchi identitity.  The non relativistic limit is classical irrotational hydrodynamics with the Newtonian gravitational potential included.

2011 arXiv and Entropy   2014   16 1515-1546.       "Heat and Gravity. I. The Action Principle." 

I needed to understand relation between fluids in General Relativity. This paper starts with the action principle for irrotational hydrodynamics (preceding paper) and upgrades it to thermodynamics to make contact with Gibbs concepts of minimum energy andmaximal entropy.  This was only a beginning; it led to a book on Adiabatic Thermodynamics that is only now being published.

2019.  "Adiabatic Thermodynamics of fluids". World Scientific 2019.  Please see the Table of contents and the Introduction. This work provides a fully developed action principle for Hydrodynamics, and Thermodynamics. It goes far beyond classical, equilibrium thermodynamics. It includes a new approach to the thermodynamics of mixtures and provides a direct relation to general Relativity. An abstract is under preparation. The entire book is provided for copying below, chapter by chapter.  Chapters X is an exposition of Conservative Hydrodynamics of general flows with vorticity, the first progress in this field since 1760. applications include hydrodynamic stability and rotating planets with rings.


2018-2019.    As the book neared completion I found a more general action principle that includes vortex motion.  Four recent  papers  announce the first applications of this theory.

ArXiv 1803.10599.    "A Classical  Mistake and what we can learn from it".  Hydrodynamics based on the Navier - Stokes equation is severely criticized in the context of Couette flow. The new theory of conservative hydrodynamics gives a very successful account of cylindrical Couette flow.  It shows that the new elements in the theory provide an account of stresses in liquids.    Completely new version including new title uploaded May 29, 2020.

ArXiv 1803.09625   "Rotating planets in Newtonian gravity".  Planets and other celestial bodies arel rotating; they can be understood only in the context of a general action principle. To my great surprise i found that the theory includes planetary rings as well as certain features seen on the surface of Saturn.  

ArXiv   1910 "Inside the meniscus". This may be the first study of the dynamics of fluids that relates the surface menisci to the bulk dynamics. Iturns out that the new action principle relates this problem to the well known phenomenon of fluid stresses to provide a completely new account of metastable states in thermodynamics.  

Headed for arXiv   "Sources for Einstein's equations. The Noetherian field theories".  This paper gives a new account of the development of Einstein's metric theory under the influence of the ideas of Noether. It is found that there is a unique theory of relativistic hydrodynamics (and thermodynamics) that   extends the classical irrotational theory by including vorticity. 


  Comments are solicited and  received with thanks.   fronsdal@physics.ucla.edu

There may be difficulties seeing the files.  A VPN access may help.

Projects.  Superfluid Helium.  Sonoluminescence. Wind tunnels. Ocean waves. Quantum gravity.


  1. Relativistic Thermodynamics, a Lagrangian Field Theory
    for general flows including rotation arXive:  1106.2271V5[GR-QC], revised 2014.






Selected Recent Publications (link to LANL archive) the book chapters are being revised.

  1. Completion and Embedding of the Schwarzschild Solution, Phys. Rev. 116, 778 (1959).
  2. Simple Groups and Strong Interaction Symmetries (with R. E. Behrends, J. Dreitlein and B. W. Lee), Rev. Mod. Phys. 34, 1 (1962).
  3. Deformation Theory and Quantization.
    I. Deformations and Symplectic Structures (with F. Bayen, M. Flato, A. Lichnerowicz and D. Sternheimer), Ann. Phys. 111, 61 (1978).
    II. Physical Applications (with F. Bayen, M. Flato, A. Lichnerowicz and D. Sternheimer), Ann. Phys. 111, 111 (1978).
  4. Massless Fields with Integer Spin, Phys. Rev. D18, 3624 (1978).
  5. Massless Fields with Half-Integral Spin (with J. Fang), Phys. Rev. D 18, 3630 (1978).
  6. What is a Covariant Derivative?, JGP 7, 305-338 (1990).
  7. Growth of a Black Hole, J. Geom. Phys. 57, 167-177 (2006).
  8. Ideal Stars and General Relativity, Gen.Rel.Grav. 39 1971-2000 (2007).
  9. Cosmology with an Action Principle (in preparation).
  10. Stability of Polytropes, Phys.Rev. D 77 (2008).
  11. Reissner-Nordstrom and Charged Polytropes, Lett. Math.Phys. 82, 255-273 (2007)
  12. Heat and Gravitation. The Action Principle, Entropy 2014, 16(3), 1515-1546; doi:10.3390/e16031515
  13. Heat and Gravitation. II Stability Criteria. Published in General Relativity and Gravitation 2011.
  14. Action Principle for Hydrodynamics and Thermodynamics including general, rotational flows, arXive:1405.7138.
  15. Relativistic Thermodynamics, a Lagrangian Field Theory
    for general flows including rotation arXive:  1106.2271V5[GR-QC], revised 2014.



Book Title etc.pdf
Book Chapter 1.pdf
Book Chapter 2.pdf
Book Chapter 3.pdf
Book Chapter 4.pdf
Book Chapter 5.pdf
Book Chapter 6.pdf
Book Chapter 7.pdf
Book Chapter 8.pdf
Book Chapter 9.pdf
Book Chapter 10.pdf
Book Chapter 11.pdf
Book Chapter 12.pdf
Chapters 13and14.pdf
FinalNoetherDEfinitive 2.pdf