  The Janis-Newman-Winicour and Papapetrou metrics represent counterparts to
the Schwarzschild black hole with scalar and antiscalar background fields,
correspondingly (where "anti" is to be understood as in "anti-de Sitter").
There is also a scalar counterpart (the Krori-Bhattacharjee metric) to the Kerr
black hole. Here we study analytical connections between these solutions and
obtain the exact rotational generalization of the antiscalar Papapetrou
spacetime as a viable alternative to the Kerr black hole. The antiscalar
metrics appear to be the simplest ones as they do not reveal event horizons and
ergospheres, and they do not involve an extra parameter for scalar charge.
Static antiscalar field is thermodynamically stable and self-consistent, but
this is not the case for the scalar Janis-Newman-Winicour solution; besides,
antiscalar thermodynamics is reducible to black-hole thermodynamics. Lensing,
geodetic and Lense-Thirring effects are found to be practically
indistinguishable between antiscalar and vacuum solutions in weak fields. Only
strong-field observations might provide a test for the existence of antiscalar
background. In particular, the antiscalar solution predicts 5% larger shadows
of supermassive compact objects, as compared to the vacuum solution. Another
measurable aspect is the 6.92% difference in the frequency of the innermost
stable circular orbit, characterizing the upper cut-off in the gravitational
wave spectrum.
