General Relativity and Gravitation

, Volume 9, Issue 4, pp 353–371 | Cite as

Classical gravity with higher derivatives

  • K. S. Stelle
Research Articles


Inclusion of the four-derivative terms ∫R μν R μν (−g)1/2 and ∫R2(−g)1/2 into the gravitational action gives a class of effectively multimass models of gravity. In addition to the usual massless excitations of the field, there are now, for general amounts of the two new terms, massive spin-two and massive scalar excitations, with a total of eight degrees of freedom. The massive spin-two part of the field has negative energy. Specific ratios of the two new terms give models with either the massive tensor or the massive scalar missing, with correspondingly fewer degrees of freedom. The static, linearized solutions of the field equations are combinations of Newtonian and Yukawa potentials. Owing to the Yukawa form of the corrections, observational evidence sets only very weak restrictions on the new masses. The acceptable static metric solutions in the full nonlinear theory are regular at the origin. The dynamical content of the linearized field is analyzed by reducing the fourth-order field equations to separated second-order equations, related by coupling to external sources in a fixed ratio. This analysis is carried out into the various helicity components using the transverse-traceless decomposition of the metric.


Field Equation Massive Scalar Nonlinear Theory Weak Restriction Linearize Solution 
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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • K. S. Stelle
    • 1
  1. 1.Department of PhysicsBrandeis UniversityWaltham

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