Generalized Landau-Pollak Uncertainty Relation

The Landau-Pollak uncertainty relation treats a pair of rank one projection valued measures and imposes a restriction on their probability distributions. It gives a nontrivial bound for summation of their maximum values. We give a generalization of this bound (weak version of the Landau-Pollak uncertainty relation). Our generalization covers a pair of positive operator valued measures. A nontrivial but slightly weak inequality that can treat an arbitrary number of positive operator valued measures is also presented.Comment: Simplified the proofs. To be published in Phys.Rev.

Wigner-Araki-Yanase theorem on Distinguishability

The presence of an additive conserved quantity imposes a limitation on the measurement process. According to the Wigner-Araki-Yanase theorem, the perfect repeatability and the distinguishability on the apparatus cannot be attained simultaneously. Instead of the repeatability, in this paper, the distinguishability on both systems is examined. We derive a trade-off inequality between the distinguishability of the final states on the system and the one on the apparatus. The inequality shows that the perfect distinguishability of both systems cannot be attained simultaneously.Comment: To be published in Phys.Rev.

New Charged Black Holes with Conformal Scalar Hair

A new class of four-dimensional, hairy, stationary solutions of the Einstein-Maxwell-Lambda system with a conformally coupled scalar field is constructed in this paper. The metric belongs to the Plebanski-Demianski family and hence its static limit has the form of the charged C-metric. It is shown that, in the static case, a new family of hairy black holes arises. They turn out to be cohomogeneity-two, with horizons that are neither Einstein nor homogenous manifolds. The conical singularities in the C-metric can be removed due to the back reaction of the scalar field providing a new kind of regular, radiative spacetime. The scalar field carries a continuous parameter proportional to the usual acceleration present in the C-metric. In the zero-acceleration limit, the static solution reduces to the dyonic Bocharova-Bronnikov-Melnikov-Bekenstein solution or the dyonic extension of the Martinez-Troncoso-Zanelli black holes, depending on the value of the cosmological constant.Comment: Published versio

Static and symmetric wormholes respecting energy conditions in Einstein-Gauss-Bonnet gravity

Properties of $n(\ge 5)$-dimensional static wormhole solutions are investigated in Einstein-Gauss-Bonnet gravity with or without a cosmological constant $\Lambda$. We assume that the spacetime has symmetries corresponding to the isometries of an $(n-2)$-dimensional maximally symmetric space with the sectional curvature $k=\pm 1, 0$. It is also assumed that the metric is at least $C^{2}$ and the $(n-2)$-dimensional maximally symmetric subspace is compact. Depending on the existence or absence of the general relativistic limit $\alpha \to 0$, solutions are classified into general relativistic (GR) and non-GR branches, respectively, where $\alpha$ is the Gauss-Bonnet coupling constant. We show that a wormhole throat respecting the dominant energy condition coincides with a branch surface in the GR branch, otherwise the null energy condition is violated there. In the non-GR branch, it is shown that there is no wormhole solution for $k\alpha \ge 0$. For the matter field with zero tangential pressure, it is also shown in the non-GR branch with $k\alpha<0$ and $\Lambda \le 0$ that the dominant energy condition holds at the wormhole throat if the radius of the throat satisfies some inequality. In the vacuum case, a fine-tuning of the coupling constants is shown to be necessary and the radius of a wormhole throat is fixed. Explicit wormhole solutions respecting the energy conditions in the whole spacetime are obtained in the vacuum and dust cases with $k=-1$ and $\alpha>0$.Comment: 10 pages, 2 tables; v2, typos corrected, references added; v3, interpretation of the solution for n=5 in section IV corrected; v4, a very final version to appear in Physical Review

Origin of matter out of pure curvature

We propose a mechanism for origin of matter in the universe in the framework of Einstein-Gauss-Bonnet gravity in higher dimensions. The recently discovered new static black hole solution by the authors \cite{md2006} with the Kaluza-Klein split up of spacetime as a product of the usual {\ma M}^4 with a space of negative constant curvature is indeed a pure gravitational creation of a black hole which is also endowed with a Maxwell-like {\it gravitational charge} in four-dimensional vacuum spacetime. Further it could be envisioned as being formed from anti-de Sitter spacetime by collapse of radially inflowing charged null dust. It thus establishes the remarkable reciprocity between matter and gravity - as matter produces gravity (curvature), gravity too produces matter.Comment: 8 pages, 1 Fig, Received Honorable Mention in 2007 GRF Essay Competition, Summary of the talk given at Himalayan Relativity Dialogue at Mirik, April 18-20, 200

No-Cloning Theorem on Quantum Logics

This paper discusses the no-cloning theorem in a logico-algebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result indicating a relation between cloning on effect algebras and hidden variables.Comment: To appear in J. Math. Phy

Gauss-Bonnet black holes with non-constant curvature horizons

We investigate static and dynamical n(\ge 6)-dimensional black holes in Einstein-Gauss-Bonnet gravity of which horizons have the isometries of an (n-2)-dimensional Einstein space with a condition on its Weyl tensor originally given by Dotti and Gleiser. Defining a generalized Misner-Sharp quasi-local mass that satisfies the unified first law, we show that most of the properties of the quasi-local mass and the trapping horizon are shared with the case with horizons of constant curvature. It is shown that the Dotti-Gleiser solution is the unique vacuum solution if the warp factor on the (n-2)-dimensional Einstein space is non-constant. The quasi-local mass becomes constant for the Dotti-Gleiser black hole and satisfies the first law of the black-hole thermodynamics with its Wald entropy. In the non-negative curvature case with positive Gauss-Bonnet constant and zero cosmological constant, it is shown that the Dotti-Gleiser black hole is thermodynamically unstable. Even if it becomes locally stable for the non-zero cosmological constant, it cannot be globally stable for the positive cosmological constant.Comment: 15 pages, 1 figure; v2, discussion clarified and references added; v3, published version; v4, Eqs.(4.22)-(4.24) corrected, which do not change Eqs.(4.25)-(4.27

Gravitational wave forms for a three-body system in Lagrange's orbit: parameter determinations and a binary source test

Continuing work initiated in an earlier publication [Torigoe et al. Phys. Rev. Lett. {\bf 102}, 251101 (2009)], gravitational wave forms for a three-body system in Lagrange's orbit are considered especially in an analytic method. First, we derive an expression of the three-body wave forms at the mass quadrupole, octupole and current quadrupole orders. By using the expressions, we solve a gravitational-wave {\it inverse} problem of determining the source parameters to this particular configuration (three masses, a distance of the source to an observer, and the orbital inclination angle to the line of sight) through observations of the gravitational wave forms alone. For this purpose, the chirp mass to a three-body system in the particular configuration is expressed in terms of only the mass ratios by deleting initial angle positions. We discuss also whether and how a binary source can be distinguished from a three-body system in Lagrange's orbit or others.Comment: 21 pages, 3 figures, 1 table; text improved, typos corrected; accepted for publication in PR

Exact dynamical AdS black holes and wormholes with a Klein-Gordon field

We present several classes of exact solutions in the Einstein-Klein-Gordon system with a cosmological constant. The spacetime has spherical, plane, or hyperbolic symmetry and the higher-dimensional solutions are obtained in a closed form only in the plane symmetric case. Among them, the class-I solution represents an asymptotically locally anti-de Sitter (AdS) dynamical black hole or wormhole. In four and higher dimensions, the generalized Misner-Sharp quasi-local mass blows up at AdS infinity, inferring that the spacetime is only locally AdS. In three dimensions, the scalar field becomes trivial and the solution reduces to the BTZ black hole.Comment: 11 pages, 2 figures, 2 tables; v2, results strengthened, argument on trapping horizon corrected; v3, argument on locally AdS property added, accepted for publication in Physical Review