Triple Path to the Exponential Metric
Abstract
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 spacetime 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. https://doi.org/10.1103/PhysRevLett.20.878, 1968), and Xanthopoulos and Zannias (Phys Rev D 40(8):2564, 1989), we prove that all three reduce to the same exponential metric provided that scalar charge is equal to central mass, thereby suggesting the universal character of such background scalar field.
 Publication:

Foundations of Physics
 Pub Date:
 November 2020
 DOI:
 10.1007/s1070102000384y
 arXiv:
 arXiv:2009.08655
 Bibcode:
 2020FoPh...50.1346M
 Keywords:

 Exponential metric;
 Scalar field;
 JanisNewmanWinicour solution;
 Scalar charge;
 General Relativity and Quantum Cosmology
 EPrint:
 Accepted in Foundations of Physics