A rigidity property of asymptotically simple spacetimes arising from conformally flat data

Given a time symmetric initial data set for the vacuum Einstein field equations which is conformally flat near infinity, it is shown that the solutions to the regular finite initial value problem at spatial infinity extend smoothly through the critical sets where null infinity touches spatial infinity if and only if the initial data coincides with Schwarzschild data near infinity.Comment: 37 page

Nonexistence of marginally trapped surfaces and geons in 2+1 gravity

We use existence results for Jang's equation and marginally outer trapped surfaces (MOTSs) in 2+1 gravity to obtain nonexistence of geons in 2+1 gravity. In particular, our results show that any 2+1 initial data set, which obeys the dominant energy condition with cosmological constant \Lambda \geq 0 and which satisfies a mild asymptotic condition, must have trivial topology. Moreover, any data set obeying these conditions cannot contain a MOTS. The asymptotic condition involves a cutoff at a finite boundary at which a null mean convexity condition is assumed to hold; this null mean convexity condition is satisfied by all the standard asymptotic boundary conditions. The results presented here strengthen various aspects of previous related results in the literature. These results not only have implications for classical 2+1 gravity but also apply to quantum 2+1 gravity when formulated using Witten's solution space quantization.Comment: v3: Elements from the original two proofs of the main result have been combined to give a single proof, thereby circumventing an issue with the second proof associated with potential blow-ups of solutions to Jang's equation. To appear in Commun. Math. Phy

Gravitational Geons on the Brane

In this paper, we examine the possibility of static, spherically symmetric gravitational geons on a 3 dimensional brane embedded in a 4+1 dimensional space-time. We choose a specific g_tt for the brane-world space-time metric. We then calculate g_rr analytically in the weak field limit and numerically for stronger fields. We show that the induced field equations on the brane do admit gravitational geon solutions.Comment: 14 pages with 9 figures. To appear in General Relativity and Gravitatio

Equatorial circular orbits in the Kerr-de Sitter spacetimes

Equatorial motion of test particles in the Kerr-de Sitter spacetimes is considered. Circular orbits are determined, their properties are discussed for both the black-hole and naked-singularity spacetimes, and their relevance for thin accretion discs is established.Comment: 24 pages, 19 figures, REVTeX

Expanding and Collapsing Scalar Field Thin Shell

This paper deals with the dynamics of scalar field thin shell in the Reissner-Nordstr$\ddot{o}$m geometry. The Israel junction conditions between Reissner-Nordstr$\ddot{o}$m spacetimes are derived, which lead to the equation of motion of scalar field shell and Klien-Gordon equation. These equations are solved numerically by taking scalar field model with the quadratic scalar potential. It is found that solution represents the expanding and collapsing scalar field shell. For the better understanding of this problem, we investigate the case of massless scalar field (by taking the scalar field potential zero). Also, we evaluate the scalar field potential when $p$ is an explicit function of $R$. We conclude that both massless as well as massive scalar field shell can expand to infinity at constant rate or collapse to zero size forming a curvature singularity or bounce under suitable conditions.Comment: 15 pages, 11 figure

A switchable controlled-NOT gate in a spin-chain NMR quantum computer

A method of switching a controlled-NOT gate in a solid-stae NMR quantum computer is presented. Qubits of I=1/2 nuclear spins are placed periodically along a quantum spin chain (1-D antiferromagnet) having a singlet ground state with a finite spin gap to the lowest excited state caused by some quantum effect. Irradiation of a microwave tuned to the spin gap energy excites a packet of triplet magnons at a specific part of the chain where control and target qubits are involved. The packet switches on the Suhl-Nakamura interaction between the qubits, which serves as a controlled NOT gate. The qubit initialization is achieved by a qubit initializer consisting of semiconducting sheets attached to the spin chain, where spin polarizations created by the optical pumping method in the semiconductors are transferred to the spin chain. The scheme allows us to separate the initialization process from the computation, so that one can optimize the computation part without being restricted by the initialization scheme, which provides us with a wide selection of materials for a quantum computer.Comment: 8 pages, 5 figure

On Physical Equivalence between Nonlinear Gravity Theories

We argue that in a nonlinear gravity theory, which according to well-known results is dynamically equivalent to a self-gravitating scalar field in General Relativity, the true physical variables are exactly those which describe the equivalent general-relativistic model (these variables are known as Einstein frame). Whenever such variables cannot be defined, there are strong indications that the original theory is unphysical. We explicitly show how to map, in the presence of matter, the Jordan frame to the Einstein one and backwards. We study energetics for asymptotically flat solutions. This is based on the second-order dynamics obtained, without changing the metric, by the use of a Helmholtz Lagrangian. We prove for a large class of these Lagrangians that the ADM energy is positive for solutions close to flat space. The proof of this Positive Energy Theorem relies on the existence of the Einstein frame, since in the (Helmholtz--)Jordan frame the Dominant Energy Condition does not hold and the field variables are unrelated to the total energy of the system.Comment: 37 pp., TO-JLL-P 3/93 Dec 199

Scattering of elastic waves by periodic arrays of spherical bodies

We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lam\'e coefficients which may be complex and frequency dependent, arranged periodically in a host medium with different mass density and Lam\'e coefficients. We view the crystal as a sequence of planes of spheres, parallel to and having the two dimensional periodicity of a given crystallographic plane, and obtain the complex band structure of the infinite crystal associated with this plane. The method allows one to calculate, also, the transmission, reflection, and absorption coefficients for an elastic wave (longitudinal or transverse) incident, at any angle, on a slab of the crystal of finite thickness. We demonstrate the efficiency of the method by applying it to a specific example.Comment: 19 pages, 5 figures, Phys. Rev. B (in press

The Superspace of Geometrodynamics

Wheeler's Superspace is the arena in which Geometrodynamics takes place. I review some aspects of its geometrical and topological structure that Wheeler urged us to take seriously in the context of canonical quantum gravity.Comment: 29 pages, 8 figures. To appear in the Wheeler memorial volume of General Relativity and Gravitatio