On the Maximum Energy Release from Formation of Static Compact Objects

Abstract

Type II Supernova 1987A (SN 1987A), observed in 1987, released an energy of \mbox{$Q\approx 3\times 10^{53}$ erg}}. This huge energy is essentially the magnitude of gravitational potential or self-gravitational energy (PE) of a new born cold neutron star having a gravitational compactness or redshift $z_b\approx 0.15$. One may wonder what could be the upper limit on the amount of energy that might be released with the formation of a cold Ultra Compact Object (UCO) with an arbitrary high $z_b$. Accordingly, here, for the first time, we obtain an analytical expression for the PE of a homogeneous general relativistic UCO assuming it to be cold and static. It is found that the PE of a homogeneous UCO of mass $M$ may exceed Mc${}^2$ and be as large as 1.34 Mc${}^2$. This result, though surprising, follows from an \textit{exact and correct} analytical calculation based on the standard General Theory of Relativity (GTR). Further, UCOs supported by tangential stresses may be inhomogeneous and much more massive than neutron stars with PE $\sim$ 2.1 Mc${}^2$ Thus, in principle, formation of an UCO of a few solar masses ($M_{\odot }$) might release an energy $Q\sim 10^{55}$ erg.

arXiv comment8 Pages, 1 Figure, Galaxies 2023, 11, 116

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