Problems about Rings due to Speed-up of Spinning Machines

Doubly Spinning Black Rings

We study a method to solve stationary axisymmetric vacuum Einstein equations numerically. As an illustration, the five-dimensional doubly spinning black rings that have two independent angular momenta are formulated in a way suitable for fully nonlinear numerical method. Expanding for small second angular velocity, the formulation is solved perturbatively upto second order involving the backrea...

Sliding Rings and Spinning Holes

We construct smooth supergravity solutions describing a BPS black ring with a BPS black hole centered at an arbitrary distance above the ring. We find that as one moves the black hole the entropy of the ring remains constant, but the angular momentum coming from the supergravity fluxes changes. Our solutions also show that in order to merge a BPS black ring with a BPS black hole one has to incr...

Linear Speed-Up, Information Vicinity, and Finite-State Machines

Connections are shown between two properties of a machine model: linear speed-up and polynomial vicinity . In the context of the author’s Block Move (BM) model, these relate to: “How long does it take to simulate a finite transducer S on a given input z?” This question is related to the century-old problem of finding economical representations for finite groups. Under some cost measures for com...

Spinning Strings as Small Black Rings

Certain supersymmetric elementary string states with spin can be viewed as small black rings whose horizon has the topology of S 1 × S d−3 in a d-dimensional string theory. By analyzing the singular black ring solution in the supergravity approximation, and using various symmetries of the α ′ corrected effective action we argue that the Bekenstein-Hawking-Wald entropy of the black string soluti...

Machines Reasoning About Machines: 2015