Petrov type I spacetime curvature: Principal null vector spanning dimension

Sufficient Dimension Reduction via Principal L q Support Vector Machine ∗

Riemannian Curvature and the Petrov Classification

Let M be a Lorentzian space-time manifold. If p G 31, let TV(M) denote the tangent space to M at p and let I e Tp (M ) be a null vector. Because of the identification of radiation in General Relativity with null geodesic congruences of curves in M, one is led to study the geometrical properties of the wave surfaces of I. These are the two dimensional subspaces of TP(M), each member of which is ...

Pulsar Timing and Spacetime Curvature

We analyze the effect of weak field gravitational waves on the timing of pulsars, with particular attention to gauge invariance, that is, to the effects that are independent of the choice of coordinates. We find: (i) the Doppler shift cannot be separated into gauge invariant gravitational wave and kinetic contributions; (ii) a gauge invariant separation can be made for the time derivative of th...

Spin decoherence by spacetime curvature

A decoherence mechanism caused by spacetime curvature is discussed. The spin state of a particle is shown to decohere if only the particle moves in a curved spacetime. In particular, when a particle is near the event horizon of a black hole, an extremely rapid spin decoherence occurs for an observer who is static in a Killing time, however slow the particle’s motion is. PACS : 03.65.Ta, 03.67.-...

Null controllability of Grushin-type operators in dimension two

We study the null controllability of the parabolic equation associated with the Grushin-type operator A = ∂ x+|x|∂ y , (γ > 0), in the rectangle Ω = (−1, 1) × (0, 1), under an additive control supported in an open subset ω of Ω. We prove that the equation is null controllable in any positive time for γ < 1 and that there is no time for which it is null controllable for γ > 1. In the transition ...