Обобщения модели Борна-Инфельда и некоторые их точные решения

• Автор: Сирило-Ломбардо Диего Хулио
• Шифр специальности: 01.04.02
• Научная степень: Кандидатская
• Год защиты: 2008
• Место защиты: Дубна
• Количество страниц: 126 с. : ил.

Joint institute for nuclear research Bogoliubov Laboratory of Theoretical Physics
Manuscript
Cirilo-Lombardo Diego Julio
Generalizations of the Born-Infeld model and exact solutions
PhD thesis
01.04.02 - theoretical physics
Dubna 2008

ABSTRACT Group theory and geometry play an increasing important role in modern theoretical and mathematical physics. Using the theory of the Lie groups as unifying vehicle, the Born-Infcld (BI) theory is reformulated. New non-abelian supersymmetric models, concepts and results of the BI theory in several fields of physics are expressed in an extremely economical way. Regular exact solutions of the BI theory in curved space-time within this mathematical framework are presented. Non-abelian super-generalization of the BI action independent of the gauge group are proposed in a language where the endomorphism algebras can replace the concept of principal fiber bundle and the gauge theories are included in the Riemannian structure. Finally, starting from the superparticle and the string models, the quantum problem of the theories with reparameterization invariant actions is analyzed, the mathematical tools involved are presented and the hints for the further quantum tretment of more complicated theories (e.g. d-branes) are given. The corresponding physical states and new relativistic wave equation from these toy models with they relation with the Harmonic Oscillator are shown on several examples.
Contents
I This is page iii i Printer: Opaque this
I Problems in Gravitation and Born-Infeld theory viii 1 New spherically symmetric monopole and regular solutions
in Einstein-Born-Infeld theories ix
1.1 Introduction and results: ix
1.2 The Born-Infeld theory: X
1.3 The regularity condition xi
1.4 Statement of the problem: xiii
1.5 Equations for the electromagnetic fields of Born-Infeld in the
tetrad XV
1.6 Reduction and solutions of the system of Einstein-Born-
Infeld equations 1.6.1 Analysis of the function T (r) from the physical point xvi
of view xvn
1.6.2 Interesting cases for particular values of n and m . . xix
1.7 Analysis of the metric XIX
1.8 Conclusions 1.8.1 Appendix: connections and curvature forms from the xxiii
geometrical Cartanfc formulation xxiii
1.8.2 References XXV
2 Rotating charged Black Holes in Einstein-Born-Infeld theories and their ADM mass. xxvii

3.7 References: xlix
where we defined

(-F13)~ — (J02)2 (^13-^02)
1 +
I ill V à
62 64 Finally, looking at (45), the components from Tg are
/ ip 2
T°o
t)’
(3.48)
= £b/ +
^3 = £bi +
(.F20?
4ttR 47rR
©3,)2
47tR “ 4?rR
(e20)2
4ttR 4ttR
{F31)2
4ttR ~~ 4ttR

(3.49)
From here we can easily see the typical structure of the energy-momentum tensor of Born Infeld in the tetrad that we used in the analysis of Sect. 4 [8,11,12]

-Too = T22 = — (1 - u)

Tn=T33=
(3.50)
where we defined the invariant quantity
(F31)2 +
with

1 - (Foa)

3.7 References:
[1] R. P. Kerr, Phys. Rev. Letters 11, 237 (1963).
[2] E. T. Newman and A. I. Janis, J. Math. Phys. 6, 915 (1965).
[3] E. T. Newman, E. Couch, K. Chinnapared, A. Exton, A. Prakash, and R. Torrence, J. Math. Phys. 6, 918 (1965).
[4] A. I. Janis and E. T. Newman, J. Math. Phys. 6, 902 (1965).
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