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I often read that there is no known mechanism that prevents a charged black hole, if the charge is high enough compared to its irreducible mass, from forming a naked singularity. But I don't get how that is possible.

Imagine a sphere of charge $q$, with an “infinite” radius and “infinitesimal” mass. Imagine we start shrinking it. To do that we need to do work. That work will create mass, which will be added to the mass our sphere.

If we keep shrinking and shrinking, at some point we will reach a radius equal to

$$r = \sqrt{\frac{G q^2}{4 \pi \epsilon_0 c^4}}$$

At that point, the mass that we will have piled up through our shrinking will be equal to

$$m = \sqrt{\frac{q^2}{4 \pi \epsilon_0 G}}$$

Is that not a black hole with an event horizon (at half of its Schwarzschild radius, due to how Reissner-Nordström metric works)? What should I do to create a naked singularity?

P.S. For heuristic purposes I reduced to $1$ the $\frac{5}{3}$ factor that we normally use to calculate the energy of a charged sphere.

EDIT: Maybe my question is not clear enough, so I will try to formulate it better: In which way one could, theoretically, create a naked singularity – or, to put it differently, a black hole “with more charge than mass”? I can't find a way; so to me naked singularities seem mathematically impossible even just theoretically speaking.

I often read that there is no known mechanism that prevents a charged black hole, if the charge is high enough compared to its irreducible mass, from forming a naked singularity. But I don't get how that is possible.

Imagine a hollow sphere of charge $q$, with an “infinite” radius and “infinitesimal” mass. Imagine we start shrinking it. To do that we need to do work. That work will create mass, which will be added to the mass our sphere.

If we keep shrinking and shrinking, at some point we will reach a radius equal to

$$r = \sqrt{\frac{G q^2}{8 \pi \epsilon_0 c^4}}$$

At that point, the mass that we will have piled up through our shrinking will be equal to

$$m = \sqrt{\frac{q^2}{8 \pi \epsilon_0 G}}$$

Is that not a black hole with an event horizon (at half of its Schwarzschild radius, due to how Reissner-Nordström metric works)? What should I do to create a naked singularity?

EDIT: Maybe my question is not clear enough, so I will try to formulate it better: In which way one could, theoretically, create a naked singularity – or, to put it differently, a black hole “with more charge than mass”? I can't find a way; so to me naked singularities seem mathematically impossible even just theoretically speaking.

I often read that there is no known mechanism that prevents a charged black hole, if the charge is high enough compared to its irreducible mass, from forming a naked singularity. But I don't get how that is possible.

Imagine a sphere of charge $q$, with an “infinite” radius and “infinitesimal” mass. Imagine we start shrinking it. To do that we need to do work. That work will create mass, which will be added to the mass our sphere.

If we keep shrinking and shrinking, at some point we will reach a radius equal to

$$r = \sqrt{\frac{G q^2}{2 \pi \epsilon_0 c^4}}$$

At that point, the mass that we will have piled up through our shrinking will be equal to

$$m = \sqrt{\frac{q^2}{8 \pi \epsilon_0 G}}$$

Is that not a black hole with an event horizon? What should I do to create a naked singularity?

P.S. For heuristic purposes I reduced to $1$ the $\frac{5}{3}$ factor that we normally use to calculate the energy of a charged sphere.

I often read that there is no known mechanism that prevents a charged black hole, if the charge is high enough compared to its irreducible mass, from forming a naked singularity. But I don't get how that is possible.

Imagine a sphere of charge $q$, with an “infinite” radius and “infinitesimal” mass. Imagine we start shrinking it. To do that we need to do work. That work will create mass, which will be added to the mass our sphere.

If we keep shrinking and shrinking, at some point we will reach a radius equal to

$$r = \sqrt{\frac{G q^2}{4 \pi \epsilon_0 c^4}}$$

At that point, the mass that we will have piled up through our shrinking will be equal to

$$m = \sqrt{\frac{q^2}{4 \pi \epsilon_0 G}}$$

Is that not a black hole with an event horizon (at half of its Schwarzschild radius, due to how Reissner-Nordström metric works)? What should I do to create a naked singularity?

P.S. For heuristic purposes I reduced to $1$ the $\frac{5}{3}$ factor that we normally use to calculate the energy of a charged sphere.

EDIT: Maybe my question is not clear enough, so I will try to formulate it better: In which way one could, theoretically, create a naked singularity – or, to put it differently, a black hole “with more charge than mass”? I can't find a way; so to me naked singularities seem mathematically impossible even just theoretically speaking.