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▼❛❣♥❡t✐❝ ❇❧❛❝❦ ❍♦❧❡s ✇✐t❤ ❊❧❡❝tr♦✇❡❛❦✲❙②♠♠❡tr✐❝ ❈♦r♦♥❛s ❏♦s❤✉❛ ❇❡r❣❡r ❈♦❧♦r❛❞♦ ❙t❛t❡ ❯♥✐✈❡rs✐t② ❇❛✐✱ ❏❇✱ ❑♦r✇❛r✱ ❖r❧♦❢s❦② ❛r❳✐✈✿✷✵✵✼✳✵✸✼✵✸ ❙❡♣t❡♠❜❡r ✷✹✱ ✷✵✷✵ ❖❦❧❛❤♦♠❛ ❙t❛t❡ ❯♥✐✈❡rs✐t②

Pr❡❞✐❝t✐✈❡✳ ✳ ✳ ❊❛s② t♦ t❤✐♥❦ ✐t✬s ❛❧❧ ❝♦✈❡r❡❞ ❆ ♥❛rr♦✇ t❤❡r♠❛❧ ♣❛r❛❞✐❣♠ ▼❛ss ✶ ●❡❱ ✶✵✵ ❚❡❱ � Pr❡❞✐❝t✐✈❡✦ ❙✐❣♥❛❧s ♦❢ ◮ ❙♦❢t ♥✉❝❧❡❛r r❡❝♦✐❧ ✭❞✐r❡❝t ❞❡t❡❝t✐♦♥✮ ◮ ❆str♦♣❤②s✐❝❛❧ ❛♥♥✐❤✐❧❛t✐♦♥s ✭✐♥❞✐r❡❝t ❞❡t❡❝t✐♦♥✮ ◮ Pr♦❞✉❝t✐♦♥ ❛t ❚❡❱✲s❝❛❧❡ ❝♦❧❧✐❞❡rs ✷

❆ ♥❛rr♦✇ t❤❡r♠❛❧ ♣❛r❛❞✐❣♠ ▼❛ss ✶ ●❡❱ ✶✵✵ ❚❡❱ � Pr❡❞✐❝t✐✈❡✦ ❙✐❣♥❛❧s ♦❢ ◮ ❙♦❢t ♥✉❝❧❡❛r r❡❝♦✐❧ ✭❞✐r❡❝t ❞❡t❡❝t✐♦♥✮ ◮ ❆str♦♣❤②s✐❝❛❧ ❛♥♥✐❤✐❧❛t✐♦♥s ✭✐♥❞✐r❡❝t ❞❡t❡❝t✐♦♥✮ ◮ Pr♦❞✉❝t✐♦♥ ❛t ❚❡❱✲s❝❛❧❡ ❝♦❧❧✐❞❡rs X Pr❡❞✐❝t✐✈❡✳ ✳ ✳ ❊❛s② t♦ t❤✐♥❦ ✐t✬s ❛❧❧ ❝♦✈❡r❡❞ ✷

❆ ❜r♦❛❞ r❛♥❣❡ ♦❢ ♣♦ss✐❜✐❧✐t✐❡s ▼❛❝r♦s❝♦♣✐❝ ❲❛✈❡✲❧✐❦❡ ❲■▼P ❯❧tr❛✲❤❡❛✈② s✉❜✲●❡❱ ▼❛ss ✶✵ − ✷✷ ❡❱ ✶✵✵ M ⊙ ✶ ●❡❱ ✶✵✵ ❚❡❱ ▼❛♥② ♠♦r❡ ✐♥t❡r❡st✐♥❣✱ t❡st❛❜❧❡ ♣♦ss✐❜✐❧✐t✐❡s✦ ◮ ❲❛✈❡✲❧✐❦❡✿ ❆①✐♦♥s ✫ ❆▲Ps ◮ s✉❜✲●❡❱✿ ❇♦♦st❡❞ ❉▼ ❯❧tr❛✲❤❡❛✈②✿ ▼✉❧t✐✲s❝❛tt❡r✐♥❣ ◮ ◮ ▼❛❝r♦s❝♦♣✐❝✿ Pr✐♠♦r❞✐❛❧ ❜❧❛❝❦ ❤♦❧❡s ✸

❲❤② ✭♠❛❣♥❡t✐❝✮ ❜❧❛❝❦ ❤♦❧❡s❄ ◮ ❇❡❝❛✉s❡ ❛❧❧ t❤❡ ✐♥❣r❡❞✐❡♥ts ❛r❡ ❛❧r❡❛❞② ✐♥ t❤❡ ❙▼ ◆♦ ♥❡❡❞ ❢♦r ❧♦✇ E ❇❙▼✿ ♥❛t✉r❛❧❧② ❝♦♥s✐st❡♥t ✇✐t❤ ❡①♣✳ ◮ ❇❡❝❛✉s❡ ✐t✬s ♥♦✇ t❡st❛❜❧❡ ▼✐❝r♦❧❡♥s✐♥❣✱ ❣r❛✈✐t❛t✐♦♥❛❧ ✇❛✈❡s✱ ❡t❝✳ ◮ ❇❡❝❛✉s❡ ✐t✬s ❝♦♦❧❄ ❊①♦t✐❝ ♦❜❥❡❝ts✱ ✐♥t❡r❡st✐♥❣ ♣❤②s✐❝❛❧ s✐t✉❛t✐♦♥s ✹

❚❤❡ ❜✐❣ ♣✐❝t✉r❡✿ ❊❲❙ P▼❇❍s ❙▼✰❣r❛✈✐t② ❛❞♠✐ts ♠❛❣♥❡t✐❝❛❧❧② ❝❤❛r❣❡❞ ❇❍ s♦❧✉t✐♦♥s ◮ ◮ Pr✐♠♦r❞✐❛❧ ▼❇❍ ❝♦✉❧❞ ❜❡ ❛ ❝♦♠♣♦♥❡♥t ♦❢ ❉▼ ◮ ❆t ❧❛r❣❡ Q ✱ t❤❡ ❊❲ ✈❛❝✉✉♠ ✐s ❞❡st❛❜✐❧✐③❡❞ ❛♥❞ ❛ r❡❣✐♦♥ ♦❢ ❊❲ r❡st♦r❛t✐♦♥ ❢♦r♠s ❛r♦✉♥❞ t❤❡ ▼❇❍ ▼❛❧❞❛❝❡♥❛✿ ❛r❳✐✈✿✷✵✵✹✳✵✻✵✽✹ ◮ ❆♥② s✉❝❤ ▼❇❍ t❤❛t ❢♦r♠s q✉✐❝❦❧② r❛❞✐❛t❡s ❞♦✇♥ t♦ ❛♥ ❡①tr❡♠❛❧ st❛t❡✱ ✇❤✐❝❤ ❝❛♥ ❜❡ ✈❡r② st❛❜❧❡ ◮ ❈♦♥str❛✐♥ts ♦♥ P▼❇❍s ✐♥ ❣❛❧❛①✐❡s✱ st❛rs✱ ♣❧❛♥❡ts r❡str✐❝t t❤❡✐r ❛❜✉♥❞❛♥❝❡ ✭✶✵ − ✼ t♦ ✶✵ − ✸ ♦❢ ❉▼ ❛❜✉♥❞❛♥❝❡✮ ✺

❖✉t❧✐♥❡ ◮ ▼❛❣♥❡t✐❝ ❜❧❛❝❦ ❤♦❧❡ ♣r♦♣❡rt✐❡s P❛r❦❡r ❧✐♠✐ts ❢r♦♠ ❣❛❧❛❝t✐❝ ♠❛❣♥❡t✐❝ ✜❡❧❞s ◮ ◮ ▲✐♠✐ts ❢r♦♠ s♦❧❛r ♥❡✉tr✐♥♦ ♣r♦❞✉❝t✐♦♥ ◮ ▲✐♠✐ts ❢r♦♠ ❡♠✐ss✐♦♥s ✐♥ t❤❡ ❊❛rt❤ ▲✐♠✐ts ❢r♦♠ ❤❡❛t✐♥❣ ♥❡✉tr♦♥ st❛rs ◮ ◮ ❙✉♠♠❛r② ❛♥❞ ♦✉t❧♦♦❦ ✻

▼❛❣♥❡t✐❝ ❜❧❛❝❦ ❤♦❧❡ ♣r♦♣❡rt✐❡s ✼

❘❡✐ss♥❡r✲◆♦r❞strö♠ ♣✐❝t✉r❡ ◮ ✭▼❛❣♥❡t✐❝❛❧❧②✮ ❝❤❛r❣❡❞ ❇❍ ❞❡s❝r✐❜❡❞ ❜② t❤❡ ♠❡tr✐❝ r + r ✷ ds ✷ = f ( r ) dt ✷ − dr ✷ f ( r ) = ✶ − r s f ( r ) − r ✷ d Ω ✷ , Q r ✷ r s = ✷ G M ✿ ❙❝❤✇❛r③s❝❤✐❧❞ r❛❞✐✉s ◮ r Q = π Q ✷ G / e ✷ ❢♦r ♠❛❣♥❡t✐❝❛❧❧② ❝❤❛r❣❡❞ ❜❧❛❝❦ ◮ � s − ✹ r ✷ ◮ ❚✇♦ ❤♦r✐③♦♥s ✐♥ ❣❡♥❡r❛❧✿ r ± = ( r s ± r ✷ Q ) / ✷ ❲❤❡♥ t❤❡ t✇♦ ❝♦✐♥❝✐❞❡ ✭✹ r Q = r s ✮✿ ❊①tr❡♠❛❧ ❜❧❛❝❦ ❤♦❧❡ ◮ ✽

Pr♦♣❡rt✐❡s ♦❢ ❡①tr❡♠❛❧ ♠❛❣♥❡t✐❝ ❇❍ ◮ ▼❛ss ❛♥❞ r❛❞✐✉s✿ √ π | Q | √ π | Q | ✶ M ❡❇❍ = M ♣❧ , R ❡❇❍ = e e M ♣❧ ◮ ▼❛❣♥❡t✐❝ ✜❡❧❞✿ = e M ✷ Q Q ♣❧ B = ✷ e r ✷ → ✷ e R ✷ ✷ π Q ❡❇❍ ◮ ■♥ ❛♥ ❡①tr❡♠❛❧ st❛t❡✱ ♥♦ ❍❛✇❦✐♥❣ r❛❞✐❛t✐♦♥ M ✷ − M ✷ T = M ✷ � ♣❧ ❡❇❍ M ✷ − M ✷ ✷ π � M + ❡❇❍ ✾

❱❛❝✉✉♠ ❛t ❤✐❣❤ B ◮ ❙❤♦✇♥ t❤❛t ❛t ❤✐❣❤ B ✱ m W → ✵ ❛t � B w ∼ m ✷ ✶ Q W e , r w ∼ ✷ m W ◮ ❙✉❜s❡q✉❡♥t❧②✱ ❊❲ s②♠♠❡tr② ✐s r❡st♦r❡❞ ❛t � B h ∼ m ✷ ✶ Q h e , R ❊❲ = r h ∼ ✷ m h ❆♠❜❥♦r♥✱ ❖❧❡s❡♥✿ ❤❡♣✲♣❤✴✾✸✵✹✷✷✵ ◮ ❍②♣♦t❤❡s✐③❡❞ t❤❛t ♥♦♥✲st❛♥❞❛r❞ ◗❈❉ ♣❤❛s❡ ❛t B ◗❈❉ ∼ Λ ✷ � ✶ Q ◗❈❉ , R ◗❈❉ ∼ ✷ Λ ◗❈❉ e ❑❤❛r③❡❡✈✱ ▲❛♥❞st❡✐♥❡r✱ ❙❝❤♠✐tt✱ ❨❡❡✿ ✶✷✶✶✳✻✷✹✺ ✶✵

❙tr✉❝t✉r❡ ♦❢ ❊❲ ❝♦r♦♥❛ ❇❍ ❍✐❣❣s ❝♦♥✜❣✉r❛t✐♦♥ ❛❝q✉✐r❡s ♥♦♥✲s♣❤❡r✐❝❛❧ ❛t B ∼ m ✷ W ❘❡❣✐♦♥ ❜❡t✇❡❡♥ r h ✫ r w ❞✉❜❜❡❞ ✏❊❲ ❝♦r♦♥❛✑ ✭ ∗ • ✮ ▼❛❧❞❛❝❡♥❛✿ ❛r❳✐✈✿✷✵✵✹✳✵✻✵✽✹ ✶✶

Pr♦♣❡rt✐❡s ♦❢ ❊❲ ❝♦r♦♥❛ ❇❍ ◮ ❯♣♣❡r Q ✿ ❡①✐st❡♥❝❡ ♦❢ ❊❲❙ ❝♦r♦♥❛ ◮ ▲♦✇❡r Q ✿ ❙❝❤✇✐♥❣❡r ❞✐s❝❤❛r❣❡ ❜② ●❯❚ ♠♦♥♦♣♦❧❡s Q ♠❛① ≈ e ✷ M ✷ M ♣❧ ♣❧ = ✶ . ✹ × ✶✵ ✸✷ , ∼ ✺ × ✶✵ ✸ Q ♠✐♥ ≈ ✷ π m ✷ π M ●❯❚ h ◦ M Mass in kg 10 0 10 4 10 8 10 12 10 16 10 20 10 24 10 28 10 0 10 - 5 Radius in meters 10 - 10 Black hole radius EW corona radius 10 - 15 QCD radius 10 - 20 10 - 25 10 - 30 10 6 10 10 10 14 10 18 10 22 10 26 10 30 10 34 ▼❛❧❞❛❝❡♥❛✿ ❛r❳✐✈✿✷✵✵✹✳✵✻✵✽✹ Charge Q ✶✷

◆♦♥✲❡①tr❡♠❛❧ ❇❍ r❛❞✐❛t✐♦♥ ◮ ❊①tr❡♠❛❧ ❇❍ ❛r❡ ✈❡r② st❛❜❧❡✱ ❜✉t ❛♥② ❛❞❞✐t✐♦♥❛❧ ♠❛ss ❜❡②♦♥❞ ❡①tr❡♠❛❧✐t② ✐s ✉♥st❛❜❧❡ ◮ ❋♦r r < r h ✿ ❉♦♠✐♥❛♥t ♠♦❞❡s ❛r❡ ✷ d ♠❛ss❧❡ss ❢❡r♠✐♦♥s ❋❡r♠✐♦♥s tr❛✈❡❧ ❛❧♦♥❣ ✏✇✐r❡s✑ ♦❢ ♠❛❣♥❡t✐❝ ✜❡❧❞ ❧✐♥❡s ❖♥❧② ❊▼ ❝❤❛r❣❡❞ ❢❡r♠✐♦♥s ✇✴ m � T ❡s❝❛♣❡ ❝♦r♦♥❛ ◮ ❈❤❛r❣❡❞ ♠❛ss❧❡ss ❜♦s♦♥s ❣❡t ♠❛ss sq✉❛r❡❞ ∼ B ◮ ❚❤❡ ♣♦✇❡r r❛❞✐❛t❡❞ ✐s ❣✐✈❡♥ ❜② ✷✹ T ✷ ≫ g ∗ π ✷ P ✷ = g ∗ π ✶✷✵ ( ✹ π r ✷ + ) T ✹ ✶✸

◆♦♥✲❡①tr❡♠❛❧ ❇❍ r❛❞✐❛t✐♦♥✱ ♣❛rt ■■ ◮ ■❢ T � m e ✱ ✷ d ♠♦❞❡s ❝❛♥✬t ❡s❝❛♣❡ ❊❲❙ r❡❣✐♦♥ s❤♦✉❧❞ t❤❡r♠❛❧✐③❡ ❛♥❞ r❛❞✐❛t❡ P ✹ = g ∗ π ✷ ✶✷✵ ( ✹ π R ✷ ❊❲ ) T ✹ ◮ ❆❢t❡r ♠❡r❣❡r ♦❢ t✇♦ ▼❇❍✱ ✷ d r❛❞✐❛t✐♦♥ q✉✐❝❦❧② ♠❛❦❡s r❡s✉❧t✐♥❣ ❇❍ ♥❡❛r❧② ❡①tr❡♠❛❧ τ ❇❍ ≈ ✸✵✵✵ π ✸ / ✷ c W M ✷ ∗ • = ( ✶ . ✽ × ✶✵ − ✷✺ s ) M ✷ ✷✻ M ✸ e ♣❧ ✶✹