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2020

Collective scalarization or tachyonization: when averaging fails

Cardoso, Vitor, Foschi, Arianna, Zilhao, Miguel

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Certain scalar-tensor theories of gravity provide negative-energy, tachyonic modes to a fundamental scalar inside matter, giving rise to non-perturbative phenomena around compact stars.

Studies of this and other tachyonic instabilities always average over local matter properties.
We use elementary, flat space models to understand possible collective effects and the accuracy of the averaging procedure.
In particular, we consider bodies made of elementary constituents which do not, in isolation, scalarize because their compactness ${\cal C}$ is too small, ${\cal C}\lesssim {\cal C}_{\rm crit}$.

Collective scalarization or tachyonization: when averaging fails · Around

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This is a special case of a more general result: the polarizability of a sphere of radius R R in this theory, defined as the ratio between the external and induced ℓ − \ell- pole, is R 2 ℓ + 1 J ℓ + 3 / 2 ( R μ ) / J ℓ − 1 / 2 ( R μ ) R^{2\ell+1}J_{\ell+3/2}(R\mu)/J_{\ell-1/2}(R\mu) with J ⁡ ( x ) J(x) a Bessel function. For ℓ = 0 \ell=0 there’s a pole at R μ = π / 2 R\mu=\pi/2 signaling a new regular solution

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