Can branes travel beyond CTC horizon in Godel Universe?

TL;DR

This paper investigates whether M-branes can traverse the CTC horizon in Godel universe, revealing classical gyrating orbits influenced by charge and energy, and quantum self-similar wave functions akin to Landau levels.

Contribution

It demonstrates that M2-branes can classically move beyond the CTC horizon and analyzes their quantum behavior, extending understanding of probe dynamics in Godel universe.

Findings

M2-branes can travel outside the CTC horizon classically.

Probe orbits depend on energy, charge, and angular momentum.

Quantum states exhibit self-similarity and Landau-level analogy.

Abstract

Godel universe in M-theory is a supersymmetric and homogeneous background with rotation and four-form magnetic flux. It is known that, as seen in inertial frame of co-moving observer, all geodesics with zero orbital angular momentum orbit inside `surface of light velocity' (CTC horizon). To learn if other probes can travel beyond the CTC horizon, we study dynamics of M-graviton and, in particular, M2-brane, whose motion is affected by Lorentz force exerted by the four-form magnetic flux and by nonzero orbital angular momentum. Classically, we find that both probes gyrate closed orbits, but diameter and center of gyration depends on sign and magnitude of probe's energy, charge and orbital angular momentum. For M2-brane, orbits in general travel outside the CTC horizon. Quantum-mechanically, we find that wave function and excitation energy levels are all self-similar. We draw analogy of probe's dynamics with Landau problem for charged particle in magnetic field.