P.D.E.’s which Imply the Penrose Conjecture
نویسندگان
چکیده
In this paper, we show how to reduce the Penrose conjecture to the known Riemannian Penrose inequality case whenever certain geometrically motivated systems of equations can be solved. Whether or not these special systems of equations have general existence theories is therefore an important open problem. The key tool in our method is the derivation of a new identity which we call the generalized Schoen-Yau identity, which is of independent interest. Using a generalized Jang equation, we propose canonical embeddings of Cauchy data into corresponding static spacetimes. In addition, our techniques suggest a more general Penrose conjecture and generalized notions of apparent horizons and trapped surfaces, which are also of independent interest.
منابع مشابه
9 M ar 2 00 9 Birkhoff ’ s invariant and Thorne ’ s Hoop
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 ≤ 4πMADM. 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 c...
متن کاملThe reverse order law for Moore-Penrose inverses of operators on Hilbert C*-modules
Suppose $T$ and $S$ are Moore-Penrose invertible operators betweenHilbert C*-module. Some necessary and sufficient conditions are given for thereverse order law $(TS)^{ dag} =S^{ dag} T^{ dag}$ to hold.In particular, we show that the equality holds if and only if $Ran(T^{*}TS) subseteq Ran(S)$ and $Ran(SS^{*}T^{*}) subseteq Ran(T^{*}),$ which was studied first by Greville [{it SIAM Rev. 8 (1966...
متن کاملL S Penrose's limit theorem: Tests by simulation
L S Penrose’s Limit Theorem – which is implicit in Penrose [7, p. 72] and for which he gave no rigorous proof – says that, in simple weighted voting games, if the number of voters increases indefinitely and the relative quota is pegged, then – under certain conditions – the ratio between the voting powers of any two voters converges to the ratio between their weights. Lindner and Machover [4] p...
متن کاملProof of the Riemannian Penrose Inequality Using the Positive Mass Theorem
We prove the Riemannian Penrose Conjecture, an important case of a conjecture [41] made by Roger Penrose in 1973, by defining a new flow of metrics. This flow of metrics stays inside the class of asymptotically flat Riemannian 3-manifolds with nonnegative scalar curvature which contain minimal spheres. In particular, if we consider a Riemannian 3-manifold as a totally geodesic submanifold of a ...
متن کامل( refereed ) L . S . Penrose ' s limit theorem : proof of some special cases . Ines Lindner and
LS Penrose was the first to propose a measure of voting power (which later came to be known as ‘the [absolute] Banzhaf index’). His limit theorem – which is implicit in Penrose (1952) and for which he gave no rigorous proof – says that, in simple weighted voting games, if the number of voters increases indefinitely while the quota is pegged at half the total weight, then – under certain conditi...
متن کامل