Triple Path to the Exponential Metric

@article{Makukov2020TriplePT,
  title={Triple Path to the Exponential Metric},
  author={Maxim Makukov and Eduard G. Mychelkin},
  journal={Foundations of Physics},
  year={2020},
  volume={50},
  pages={1346 - 1355}
}
The exponential Papapetrou metric induced by scalar field conforms to observational data not worse than the vacuum Schwarzschild solution. Here, we analyze the origin of this metric as a peculiar space-time within a wide class of scalar and antiscalar solutions of the Einstein equations parameterized by scalar charge. Generalizing the three families of static solutions obtained by Fisher (Zhurnal Experimental’noj i Teoreticheskoj Fiziki 18:636, 1948), Janis et al. (Phys Rev Lett 20(16):878… 
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