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Inside the Vainshtein radius

${\displaystyle r_{V}=l_{\text{P}}\left({\frac {m_{\text{P}}^{3}M}{m_{G}^{4}}}\right)^{\frac {1}{5}}}$

with Planck length ${\displaystyle l_{\text{P}}}$ and Planck mass ${\displaystyle m_{\text{P}}}$

the gravitational field around a body of mass ${\displaystyle M}$ is the same in a theory where the graviton mass ${\displaystyle m_{G}}$ is zero and where it's very small because the helicity 0 degree of freedom becomes effective on distance scales ${\displaystyle r\gg r_{V}}$.

See also

• Massive gravity – Theory of gravity in which the graviton has nonzero mass

References

1. Vainshtein, Arkady (1972). "To the problem of nonvanishing gravitation mass". Physics Letters B. 39 (3): 393. Bibcode:1972PhLB...39..393V. doi:10.1016/0370-2693(72)90147-5.; see also Vainshtein; et al. (2001). "Nonperturbative Continuity in Graviton Mass versus Perturbative Discontinuity". Physical Review D. 65 (4): 044026. arXiv:hep-th/0106001. Bibcode:2002PhRvD..65d4026D. doi:10.1103/PhysRevD.65.044026.
2. Zee, Anthony. Quantum Field Theory in a Nutshell (2nd ed.). p. 440.

• Quantum gravity
• Radii