Extremal isolated horizons: a local uniqueness theorem
نویسندگان
چکیده
We derive all the axi-symmetric, vacuum and electrovac extremal isolated horizons. It turns out that for every horizon in this class, the induced metric tensor, the rotation 1-form potential and the pullback of the electromagnetic field necessarily coincide with those induced by the monopolar, extremal Kerr– Newman solution on the event horizon. We also discuss the general case of a symmetric, extremal isolated horizon. In particular, we analyse the case of a two-dimensional symmetry group generated by two null vector fields. Its relevance to the classification of all the symmetric isolated horizons, including the non-extremal ones, is explained. PACS numbers: 04.20.Ex, 04.70.Bw
منابع مشابه
Random differential inequalities and comparison principles for nonlinear hybrid random differential equations
In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities have been proved for an IVP of first order hybrid random differential equations with the linear perturbation of second type. A comparison theorem is proved and applied to prove the uniqueness of random solution for the considered perturbed random differential eq...
متن کاملGeneric weak isolated horizons
Isolated horizons [1], much like Killing horizons [2], were introduced in order to deal with the more practical problems involving black holes. Both formulations are local, in contrast with the global nature of event horizons [3]. However, isolated horizons, unlike Killing horizons, do not require a Killing vector field in their neighbourhood. Thus, isolated horizons are characterized by a weak...
متن کاملA Uniqueness Theorem of the Solution of an Inverse Spectral Problem
This paper is devoted to the proof of the unique solvability ofthe inverse problems for second-order differential operators withregular singularities. It is shown that the potential functioncan be determined from spectral data, also we prove a uniquenesstheorem in the inverse problem.
متن کاملHair from the Isolated Horizon Perspective
The recently introduced Isolated Horizons (IH) formalism has become a powerful tool for realistic black hole physics. In particular, it generalizes the zeroth and first laws of black hole mechanics in terms of quasi-local quantities and serves as a starting point for quantum entropy calculations. In this note we consider theories which admit hair, and analyze some new results that the IH provid...
متن کاملExistence and uniqueness results for a nonlinear differential equations of arbitrary order
This paper studies a fractional boundary value problem of nonlinear differential equations of arbitrary orders. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. In order to clarify our results, some illustrative examples are also presented.
متن کامل