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Degeneracy forces zero mass when global Komar transport applies

Statement

For the normalized nonrotating horizon data of Normalized Komar data on a nonrotating horizon section, assume the additional, separately established global identity $M_{K} = Q_{C} [T]$ . If $κ = 0$ , then $M_{K} = 0$ . In particular, an independent theorem forbidding zero mass in the specified black-hole class excludes such a configuration. The local horizon evaluation is Constant surface gravity gives the normalized horizon integral; this lemma does not establish the global identity, an admissible completion for positive mass, or the exclusion theorem.

Facts & Assumptions

[F1]

Use the normalized functional and its constant-gravity evaluation. The exterior identity and any zero-mass exclusion are separate explicit hypotheses, not consequences of a local cross-section calculation. Normalized Komar data on a nonrotating horizon section Constant surface gravity gives the normalized horizon integral

Proof

**Given:**The local data, $M_{K} = Q_{C} [T]$ and degeneracy $κ = 0$ .

Goal: Derive the stated conditional zero-mass implication.

1.1givenF1

The constant-gravity integral yields $Q_{C} [T] = 0 \cdot A_{C} / (4 π) = 0$ . The supplied equality then gives $M_{K} = 0$ .

2.1givenF1step 1.1∎

If a separately applicable theorem excludes zero mass for the specified black-hole class, the equality in step 1.1 contradicts that theorem. This is a conditional implication and leaves every global applicability obligation with that separately supplied theorem.

Depends on

Used by · 1

Analytic connected-horizon uniqueness including the degenerate case

Dependency tree · 2 levels

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