Birkhoff's invariant and Thorne's Hoop Conjecture
| dc.creator | Gibbons, G. W. | |
| dc.date | 2009-03-09 | |
| dc.date.accessioned | 2026-07-07T12:50:31Z | |
| dc.date.available | 2026-07-07T12:50:31Z | |
| dc.description | I propose a sharp form of Thorne's hoop conjecture which relates Birkhoff's invariant $β$ for an outermost apparent horizon to its $ADM$ mass, $ β\le 4 πM_{ADM}$. I prove the conjecture in the case of collapsing null shells and provide further evidence from exact rotating black hole solutions. Since $β$ is bounded below by the length $l$ of the shortest non-trivial geodesic lying in the apparent horizon, the conjecture implies $l \le 4 πM_{ADM}$. The Penrose conjecture, $\sqrt{πA} \le 4 πM_{ADM}$, and Pu's theorem imply this latter consequence for horizons admitting an antipodal isometry. Quite generally, Penrose's inequality and Berger's isembolic inequality, $\sqrt{πA} \ge {2\over\sqrtπ} i$, where $i$ is the injectivity radius, imply $ 4c \le 2 i \le 4 πM_{ADM}$, where $c$ is the convexity radius. | |
| dc.identifier | https://arxiv.org/abs/0903.1580 | |
| dc.identifier | http://arxiv.org/abs/0903.1580 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222708 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Birkhoff's invariant and Thorne's Hoop Conjecture | |
| dc.type | text |