Extended time-travelling objects in Misner space

Abstract

Misner space is a two-dimensional (2D) locally-flat spacetime which elegantly demonstrates the emergence of closed timelike curves from causally well-behaved initial conditions. Here we explore the motion of rigid extended objects in this time-machine spacetime. This kind of 2D time-travel is found to be risky due to inevitable self-collisions (i.e. collisions of the object with itself). However, in a straightforward four-dimensional generalization of Misner space (a physically more relevant spacetime obviously), we find a wide range of safe time-travel orbits free of any self-collisions.

Quantum mechanics of the interior of radiating 2D black holes

“…Singularity resolution, is self-evident in this case, since the wall is a perfect reflector for all values of the extension parameter [10]. The interesting feature that emerges, one that was not touched upon in ( [6,7]), is that for each λ < 0 there exists a unique normalizable bound state with probability amplitude peaked close to the singularity:…”

“…The latter is a necessary condition for the solution to start peaked near a black hole horizon [6,7]. Singularity resolution, is self-evident in this case, since the wall is a perfect reflector for all values of the extension parameter [10].…”

“…Using this as the starting point we investigated the dynamics of the dilaton in terms of conformal time and derived an effective Hamiltonian in which the dilaton was decoupled from the other modes apart from a time dependent coefficient in the potential. Finally, following Levanony and Ori([6]) and ( [7]) we quantized the near singularity behaviour of the dilaton, paying close attention to boundary conditions. The Hamiltonian allowed a one parameter family of self-adjoint extensions that resolved the singularity.…”

“…In what follows, we re-examine the homogeneous black hole interiors of the radiating 2-D black hole along the lines of [6,7] but with some modifications and extensions. Specifically, we look at the RST model as opposed to the CGHS model.…”

“…Levanony and Ori (LO) [6,7] have studied the CGHS model arguing that near the singularity the spacetime would be nearly homogeneous. They examined the corresponding near singularity dynamics classically and quantum mechanically, verifying that the singularity was indeed resolved in the quantum version of their model.…”