Renormalizability, van Dam-Veltman-Zakharov discontinuity, and Newtonian singularity in higher-derivative gravity

Abstract

It was proposed that if a higher-derivative gravity is renormalizable, it implies necessarily a finite Newtonian potential at the origin, but the reverse of this statement is not true. Here we show that the reverse is true when taking into account the vDVZ discontinuity which states that the theory obtained from massive one by taking zero mass limit is not equivalent to the theory obtained in the zero mass case. The surviving degree of freedom in the zero mass limit is an extra scalar which does not affect the light bending angle, but affects the Newtonian potential. This asserts that in order to make the singularity cancellation, the number of massive ghost and healthy tensors matches with that of massive ghost and healthy scalars. a ysmyung@inje.ac.kr

On the vDVZ Discontinuity in Massive Conformal Gravity

“…Recently, it was proposed that the vDVZ discontinuity of a local gravitational theory is closely related to the finiteness of the gravitational potential at the origin [13]. If this proposal is valid then the MCG potential should have a singularity at the origin, which we will show that is not true in the next section.…”

Canonical quantization of massive symmetric rank-two tensor in string theory

“…Accordingly, the propagator for the massive spin-two field of Fierz-Pauli theory also diverges and does not reduce to that of the massless graviton of Einstein's gravity in the massless limit: this gives rise to the vDVZ discontinuity [24,25], which has been studied in detail in Refs. [32][33][34][35].…”