Can branes travel beyond CTC horizon in Godel Universe?

TL;DR

This work investigates whether probes in the Gödel universe of M-theory can traverse the CTC horizon. By analyzing classical dynamics of an M-graviton and an M2-brane, the authors reveal Landau-like gyration on two rotating planes, with the M2-brane able to cross the CTC horizon depending on energy and charge, while the M-graviton geodesics remain inside. Quantum mechanically, the wavefunctions and excitation spectra form discrete, self-similar ladders analogous to Landau levels, with a single characteristic frequency set by the rotation parameter $|\mu|$. The Type IIB uplift shows the same spectral structure, reinforcing a universal Landau-like picture; the results illuminate chronology-related puzzles in Gödel spacetime and motivate further study of holography and backreaction in non-globally-hyperbolic backgrounds.

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.

Figures (3)

• Figure 1: Trajectory of the probe with zero angular momenta, passing through co-moving observer located at O. The probe traces the Larmor orbit, whose radius is $R$ and gyration speed is $\sqrt{E^2 - m^2}$.
• Figure 2: Trajectories of various probes. The inner circle refers to the CTC horizon as seen in the inertial frame of comoving observer at the center, outside which closed time-like curves are present. Geodesics of M-graviton, shown in the left for three different angular initial conditions, are confined inside the CTC horizon. Trajectory of M2-branes with $E>0$ are shown in the right for $q>0$ and $q<0$, respectively. Notice that $q>0$ orbit is always inside the CTC horizon, while $q<0$ orbit extends beyond the CTC horizon.
• Figure 3: Energy spectrum of massless (left) and massive (right) M-theory gravitons. Horizontal axis refer to different multiplicities associated with ${\bf n_1, n_2, m_1, m_2}$. The energy gap is denoted as $E_0 = 4 \vert \mu \vert$.