Charged Dyson shells supported in curved spacetimes of spherically symmetric central compact objects

Abstract It is proved that charged thin shells (charged Dyson shells) can be supported in unstable static equilibrium states around spherically symmetric central compact objects. The regime of existence of the composed central-compact-object-static-charged-shell configurations is characterized by the inequalities $$\sqrt{m(m+2M)}&lt;|q|&lt;M+\sqrt{M^2+m^2}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> <mml:mi>M</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:msqrt> <mml:mo>&lt;</mml:mo> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>q</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>&lt;</mml:mo> <mml:mi>M</mml:mi> <mml:mo>+</mml:mo> <mml:msqrt> <mml:mrow> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mi>m</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:msqrt> </mml:mrow> </mml:math> , where $$\{m,q\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>{</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mi>q</mml:mi> <mml:mo>}</mml:mo> </mml:mrow> </mml:math> are respectively the proper mass and the electric charge of the supported shell and M is the mass of the central compact object (a black hole or an horizonless compact star). We reveal the physically interesting fact that the supported charged shells become marginally-stable in the $$|q|/\sqrt{m(m+2M)}\rightarrow 1^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mi>q</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> <mml:mo>/</mml:mo> <mml:msqrt> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> <mml:mi>M</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:msqrt> <mml:mo>→</mml:mo> <mml:msup> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:math> limit, in which case the lifetime (instability timescale) of the composed system can be made arbitrarily large. Our analysis goes beyond the test shell approximation by properly taking into account the exact gravitational and electromagnetic self-interaction energies of the spherically symmetric shell in the curved spacetime. In particular, the existence of the composed compact-object-charged-shell static configurations in the Einstein–Maxwell theory is attributed to the non-linear electromagnetic self-energy of the supported shell.