Gravitational Entropy and Hawking Temperature from the Killing Norm: A Local Covariant Formulation
Fuente:
Zenodo
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Recurso digital |
| Veröffentlicht: |
Zenodo
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866901891436249088 |
|---|---|
| author | Uzundemir, İlyas |
| author_facet | Uzundemir, İlyas |
| contents | <p class="MsoNormal">The Bekenstein-Hawking entropy S_BH = k_B c³ A/(4Gℏ) [4,5] and Hawking temperature T_H = ℏc²/(4πk_B r_s) are foundational results of black hole thermodynamics. The standard surface gravity κ = √(−½ ∇_μξ_ν ∇µξν) is already a local Killing horizon property in GR; however, its standard form requires a normalization condition on the Killing vector that is fixed at asymptotic infinity. This Letter demonstrates that within the C̃(r) ≡ √(−g_μνξµξν) framework [1,2], surface gravity takes the transparent form κ = c²/2 × |d(C̃²)/dr|_{r=r_s}, a gradient of the Killing norm squared evaluated locally at the horizon, without requiring asymptotic normalization. The Hawking temperature T_H = ℏκ/(2πk_B) follows directly. The Bekenstein-Hawking entropy is recast as S_BH = 4πk_B GM²/(ℏc) in terms of the Killing norm structure. A local gravitational entropy density s_C(r) = k_B r_s⁴/(4Gℏr⁴) is proposed as a natural companion to the energy density u_C(r) = GM²/(16πr⁴) from Letter 1 [1]; its surface integral reproduces S_BH in the brick-wall regularisation (detailed in Section IV). At C̃ = 0, vanishing Killing norm, diverging energy density u_C, and diverging entropy density s_C coincide — providing a unified scalar description of black hole thermodynamics that makes explicit what standard GR expresses through separate formalisms. This construction introduces no new dynamical degrees of freedom and is consistent with all standard GR thermodynamic results.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20240274 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Gravitational Entropy and Hawking Temperature from the Killing Norm: A Local Covariant Formulation Uzundemir, İlyas Bekenstein-Hawking entropy Hawking temperature Killing norm surface gravity gravitational thermodynamics information-carrying capacity black hole stationary spacetimes <p class="MsoNormal">The Bekenstein-Hawking entropy S_BH = k_B c³ A/(4Gℏ) [4,5] and Hawking temperature T_H = ℏc²/(4πk_B r_s) are foundational results of black hole thermodynamics. The standard surface gravity κ = √(−½ ∇_μξ_ν ∇µξν) is already a local Killing horizon property in GR; however, its standard form requires a normalization condition on the Killing vector that is fixed at asymptotic infinity. This Letter demonstrates that within the C̃(r) ≡ √(−g_μνξµξν) framework [1,2], surface gravity takes the transparent form κ = c²/2 × |d(C̃²)/dr|_{r=r_s}, a gradient of the Killing norm squared evaluated locally at the horizon, without requiring asymptotic normalization. The Hawking temperature T_H = ℏκ/(2πk_B) follows directly. The Bekenstein-Hawking entropy is recast as S_BH = 4πk_B GM²/(ℏc) in terms of the Killing norm structure. A local gravitational entropy density s_C(r) = k_B r_s⁴/(4Gℏr⁴) is proposed as a natural companion to the energy density u_C(r) = GM²/(16πr⁴) from Letter 1 [1]; its surface integral reproduces S_BH in the brick-wall regularisation (detailed in Section IV). At C̃ = 0, vanishing Killing norm, diverging energy density u_C, and diverging entropy density s_C coincide — providing a unified scalar description of black hole thermodynamics that makes explicit what standard GR expresses through separate formalisms. This construction introduces no new dynamical degrees of freedom and is consistent with all standard GR thermodynamic results.</p> |
| title | Gravitational Entropy and Hawking Temperature from the Killing Norm: A Local Covariant Formulation |
| topic | Bekenstein-Hawking entropy Hawking temperature Killing norm surface gravity gravitational thermodynamics information-carrying capacity black hole stationary spacetimes |
| url | https://doi.org/10.5281/zenodo.20240274 |