Triple path to the exponential metric

TL;DR

This paper demonstrates that a specific exponential metric derived from scalar fields fits observational data as well as the Schwarzschild solution and reveals its universal origin from a class of scalar solutions in Einstein's equations.

Contribution

It generalizes three classical static solutions to show they converge to the same exponential metric under certain conditions, highlighting its universal nature.

Findings

Exponential Papapetrou metric fits observational data as well as Schwarzschild.

All three classical solutions reduce to the same exponential metric.

Scalar charge equals central mass in these solutions.

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 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 (1948), Janis, Newman & Winicour (1968), and Xanthopoulos & Zannias (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.