  A well-known result in general relativity is that the tidal Love numbers of
black holes vanish. In contrast, different configurations to a black hole may
have non-vanishing Love numbers. For instance, it has been conjectured recently
that the Love number of generic exotic compact objects (ECOs) shows a
logarithmic behavior. Here we analyze the ultracompact Schwarzschild star which
allows the compactness to cross and go beyond the Buchdahl limit. This
Schwarzschild star has been shown to be a good black hole mimicker, moreover,
it has been found that the Love number of these objects approaches zero as
their compactness approaches the black hole limit. Here we complement those
results, by showing that the Love number for these configurations follows an
exponentially decaying behavior rather than the logarithmic behavior proposed
for generic ECOs.
