Tidal deformability of white dwarfs in Eddington-inspired Born-Infeld gravity

We compute the static quadrupole Love number $k_2$ and the dimensionless tidal deformability $\mathrm{\Lambda }$ of cold white dwarfs in Eddington-inspired Born-Infeld (EiBI) gravity. Matter couples to the physical metric while perturbation equations are solved in an auxiliary metric, so the physical tidal field near the surface depends on derivatives of the equation of state. This dependence is regular for a surface polytropic index $1<{\mathrm{\Gamma }}_{\mathrm{e}\mathrm{n}\mathrm{v}}<3\mathrm{/}2$, but not for the $\mathrm{\Gamma }=5\mathrm{/}3$ Chandrasekhar equation of state. The mechanism, an algebraic map between the metric that carries perturbations and the metric that matter feels, is common to Palatini-type theories, so the same type of surface condition should apply to tidal calculations in this wider class. We use thermodynamically consistent envelopes that exactly reach zero enthalpy. At five masses from $0.6$ to $1.3\text{Msun}$ and five sampled Born-Infeld couplings $\kappa$, with $\mathrm{\mid }\kappa \mathrm{\mid }\le 5\times {10}^6{\mathrm{m}}^2$, the EiBI-GR differences are approximately linear in $\kappa$. The largest absolute fractional shifts are $3.89\times {10}^{-5}$ in the stellar radius $R$, $4.09\times {10}^{-5}$ in $k_2$, and $2.36\times {10}^{-4}$ in $\mathrm{\Lambda }$. Across nine envelope models, half the spread of each quantity relative to the baseline envelope is at most $0.0186$ in $R$ and $0.0857$ in $k_2$, but only $3.02\times {10}^{-5}$ in $\mathrm{\Lambda }$ as the changes in $k_2$ and $R^5$ largely cancel. A high-precision calculation shows that the envelope dependence of the EiBI-GR difference in $\mathrm{\Lambda }$ is small. Half the spread of this difference ranges from $1.067\times {10}^{-12}$ to $6.208\times {10}^{-11}$ over the 20 nonzero mass-coupling points.