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Il Nuovo Cimento B (1971-1996)

, Volume 25, Issue 2, pp 757–785 | Cite as

Strong and weak gravity: A class of generally covariant mixing models of spin-2 neutral fields: Linearization

  • W. C. Hammel
Article

Summary

By linearizing, in an unorthodox way, the nonlinear partial differential equation system proposed to describe the interaction of a massless and massive graviton, it is discovered that the equations yield a variety of theories with different structure. The general system of equations which results from this linearization is a Lorentz-covariant system of coupled equations in two symmetric Lorentz tensor fields. We distinguish between situations where the system may be uncoupled by a linear transformation of the tensor fields, thus permitting the definition of diagonalizing fields, and those situations where this is not possible. The diagonalizable cases are examined for mass and spin structure, and are divided into perturbative and nonperturbative cases. One of the perturbative cases contains the theory of Aichelburg and Mansouri. Finally we discuss the procedure for solving the explicitly coupled equations.

Riassunto

Linearizzando, con procedimento non ortodosso, il sistema non lineare di equazioni differenziali parziali che è stato proposto per descrivere l’interazione fra un gravitone dotato di massa e uno privo di massa, si è scoperto che le equazioni producono una varietà di teorie con strutture diverse. Il sistema generale di equazioni che si ottiene da questa linearizzazione è un sistema covariante di Lorentz di equazioni accoppiate in due campi tensoriali simmetrici di Lorentz. Si fa distinzione fra casi in cui si può disaccoppiare il sistema per mezzo di una trasformazione, lineare dei campi tensoriali, permettendo così la definizione di campi diagonalizzanti, e casi in cui ciò non è possibile. Si esamina la massa e la struttura dello spin nei casi in cui si hanno campi diagonalizzabili e si distingue ulteriormente fra casi perturbativi e non perturbativi. Uno dei casi perturbativi comprende la teoria di Aichelburg e Mansouri. Infine si discute il procedimento per risolvere le equazioni accoppiate esplicitamente.

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Copyright information

© Società Italiana di Fisica 1975

Authors and Affiliations

  • W. C. Hammel
    • 1
  1. 1.Department of PhysicsUniversity of Wisconsin-MilwaukeeMilwaukee

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