# 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: I am engaged in writing a book on Thermodynamics. This work has some controversial elements and departs from traditional views and methods in many ways. For example, I emphasize the lagrangian approach, which is a very strong constraint since, for a given system, one lagrangian density has to be effective in all contexts. I propose an improvement of Landau's two-fluid theory of superfluids and I take a controversial approach to (mixed) atmospheres. For mixtures I recognize all the natural degrees of freedom but do not use molar fractions. Entropy is very central to my approach. A full integration of thermodynamics with General Relativity is proposed and now included in the book, a significant improvement over the much used method of Tolman. There is a chapter on phase transitions and another on mixtures, including some chemical reactions. I am very unhappy with the method invented by Tolman and think that I have improved on it. But to justify my suggestions with respect to this topic I have had to make a strong effort to learn thermodynamics; the book is the result. A working and preliminary copy of the book can be seen here. Comments to

## fronsdal@physics.ucla.edu

## are received with thanks.

Update 12/1/15. The papers

- 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 presented in a preliminary form in the book, Section XI.7. 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.

The book is taking shape, now up to over 300 pages.

**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.