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 (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.
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Notes
The cosmological term (both in de Sitter and anti-de Sitter regimes) is characterized by the equation of state \(p= -\varepsilon \), while minimal scalar field (both in standard and antiscalar regimes) corresponds to \(p=\varepsilon \) for time-like gradient, and to \(p = -\varepsilon /3\) for space-like gradient.
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Acknowledgements
The research was performed within the program No. BR05236322 by the Ministry of Education and Science of the Republic of Kazakhstan.
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Makukov, M., Mychelkin, E. Triple Path to the Exponential Metric. Found Phys 50, 1346–1355 (2020). https://doi.org/10.1007/s10701-020-00384-y
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DOI: https://doi.org/10.1007/s10701-020-00384-y