Abstract
Local gravitational theories with more than four derivatives can have remarkable quantum properties. Namely, they can be super-renormalizable and may be unitary in the Lee-Wick sense, if the massive poles of the propagator are complex. It is important, therefore, to also explore the classical aspects of these theories. In this talk we present recent results in this direction. Specifically, we discuss the effect that that higher-order terms can have on the Newtonian potential and related singularities.
Highlights
Higher-derivative extensions of general relativity (GR) have, recently, been the object of intensive investigation
GR is not perturbatively renormalizable, and fourth-order gravity contains a ghost in the spectrum; with six or more derivatives it is possible to restore the unitarity of the S-matrix if the ghost-like poles in the propagator are complex (Lee-Wick gravity) [1,2]
In the present work we review some results on a classical aspect of these higher-derivative gravity theories, namely the cancellation of the singularities in the linear regime
Summary
Higher-derivative extensions of general relativity (GR) have, recently, been the object of intensive investigation. GR is not perturbatively renormalizable, and fourth-order gravity contains a ghost in the spectrum; with six or more derivatives it is possible to restore the unitarity of the S-matrix if the ghost-like poles in the propagator are complex (Lee-Wick gravity) [1,2]. In the linear regime this is the most general local action with higher derivatives, and it includes as particular case the Lee-Wick gravity. Since the 1970s it is known that the case of trivial (constant non-null) polynomials yields a renormalizable theory with a finite modified Newtonian potential [8,15]. In what follows we summarize recent generalizations of these results to the case of the polynomial-derivative theory (1) in the weak-field approximation.
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