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 Q≈3×1053 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 zb≈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 zb. 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 Mc2 and be as large as 1.34 Mc2. This result, though surprising, follows from an 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 ∼ 2.1 Mc2 Thus, in principle, formation of an UCO of a few solar masses (M⊙) might release an energy Q∼1055 erg.

Keywords

• Supernova SN 1987A
• general relativity
• compact objects
• anisotropic stars