Spherically symmetric black holes and wormholes in hybrid
  metric-Palatini gravity
  The so-called hybrid metric-Palatini theory of gravity (HMPG), proposed in
2012 by T. Harko et al., is known to successfully describe both local
(solar-system) and cosmological observations. This paper gives a complete
description of static, spherically vacuum solutions of HMPG in the simplest
case where its scalar-tensor representation has a zero scalar field potential
$V(\phi)$, and both Riemannian ($R$) and Palatini ($\cal R$) Ricci scalars are
zero. Such a scalar-tensor theory coincides with general relativity with a
phantom conformally coupled scalar field as a source of gravity. Generic
asymptotically flat solutions either contain naked central singularities or
describe traversable wormholes, and there is a special two-parameter family of
globally regular black hole solutions with extremal horizons. In addition,
there is a one-parameter family of solutions with an infinite number of
extremal horizons between static regions and a spherical radius monotonically
changing from region to region. It is argued that the obtained black hole and
wormhole solutions are unstable under monopole perturbations. As a by-product,
it is shown that a scalar-tensor theory with $V(\phi)=0$, in which there is at
least one nontrivial ($\phi \ne \rm const$) vacuum solution with $R\equiv 0$,
necessarily reduces to a theory with a conformal scalar field (the latter may
be usual or phantom).
