# Homepage

http://fronsdal.physics.ucla.edu

# Christian Fronsdal

**Theoretical Elementary Particle**

Office: 4-941 PAB

Phone: (310) 825-3432

## Educational Background:

- Ph.D., UCLA, 1957

## Research Interest. Updated December 2017

Feb 16 2018. Here is an very big improvement of a paper that was posted on Feb 2 with a slightly different title. it is available below.

"A classical mistake and what it tells us.

How to do better with an action principle for Hydro and Thermo-dynamics"

I hope this is a definitive version. Comments are received with thanks.

## I am engaged in writing a book on Thermodynamics. An advanced working edition is avalable below.

## This work has some controversial elements and departs from traditional views and methods in many ways. For example, an action principle dominates the whole theory. This is a very strong constraint that greatly improves its predictive power since, for a given system, one Lagrangian density has to be effective in all contexts. The New Action Principle covers adiabatic thermodynamics, not just equilibria; it is a complete dynamical theory that embraces the classical theory of equilibria but also dynamical problems such as sound propagation and planetary dynamics. I propose an improvement of Landau's two-fluid theory of superfluids and I take a controversial approach to (mixed) atmospheres. Entropy of mixtures is a very vital part of the theory. There are chapters on superfluidity and cylindrical Couette flow, on sound propagation in mixtures and immiscible gases, and on the shapes of planets. The study of planets is of special interest and still ongoing. One of the radical elements is the hydrodynamical velocity fields. The familiar irrotational field, that is always needed to provide the equation of continuity, is supplemented by a vorticity field that is essential to rotational flow. The latter is subject to a constraint that reduces the total number of degrees of freedom in hydrodynamics to 4, as it must be.

The last section, a theory of rotating planets is a straightforward application off the same Lagrangian tp planetary shapes.

Unexpectively, the big planets have rings! This section will be updated weekly from now on.

## Comments are solicited and received with thanks.

The papers, this to be updated very soon.

- Relativistic Thermodynamics, a Lagrangian Field Theory

for general flows including rotation arXive: 1106.2271V5[GR-QC], revised 2014.

explains this breakthrough in the non relativistic context. See below "ActionGen.Flow.pp.copy.pdf" Further

developments in the book, Chapter XI.

The full relativistic generalization is also presented in in the book, Section X. The papers (the last two listed below)

Action Principle for Hydrodynamics and Thermodynamics including general, rotational flows, arXive:1405.7138.

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

are important improvement over an earlier paper with similar titles. (Submitted for publication.) They claim a theory of hydrodynamics and thermodynamics based on an action principle that allows for unrestricted flows. The step up from allowing just potential flows is the result of 7 years of labor. Many exciting application are accessible.

**Selected Recent Publications** (link to LANL archive)

- Completion and Embedding of the Schwarzschild Solution, Phys. Rev.
**116**, 778 (1959). - Simple Groups and Strong Interaction Symmetries (with R. E. Behrends, J. Dreitlein and B. W. Lee), Rev. Mod. Phys.
**34**, 1 (1962). - 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). - Massless Fields with Integer Spin, Phys. Rev. D
**18**, 3624 (1978). - Massless Fields with Half-Integral Spin (with J. Fang), Phys. Rev. D
**18**, 3630 (1978). - What is a Covariant Derivative?, JGP
**7**, 305-338 (1990). - Growth of a Black Hole, J. Geom. Phys.
**57**, 167-177 (2006). - Ideal Stars and General Relativity, Gen.Rel.Grav.
**39**1971-2000 (2007). - Cosmology with an Action Principle (in preparation).
- Stability of Polytropes, Phys.Rev. D
**77**(2008). - Reissner-Nordstrom and Charged Polytropes, Lett. Math.Phys.
**82**, 255-273 (2007) - Heat and Gravitation. The Action Principle,
*Entropy***2014**,*16*(3), 1515-1546; doi:10.3390/e16031515 - Heat and Gravitation. II Stability Criteria. Published in General Relativity and Gravitation 2011.
- Action Principle for Hydrodynamics and Thermodynamics including general, rotational flows, arXive:1405.7138.
- Relativistic Thermodynamics, a Lagrangian Field Theory

for general flows including rotation arXive: 1106.2271V5[GR-QC], revised 2014.