Closed timelike curves in general relativity

Because closed timelike curves are consistent with general relativity, many have asserted that time travel into the past is physically possible if not technologically infeasible. However, the possibility of time travel into the past rests on the unstated and false assumption that zero change to the past implies zero change to the present. I show that this assumption is logically inconsistent; as such, it renders time travel into the past both unscientific and pseudoscientific...

In a recent paper, Mallett found a solution of the Einstein equations in which closed timelike curves (CTC's) are present in the empty space outside an infinitely long cylinder of light moving in circular paths around an axis. Here we show that, for physically realistic energy densities, the CTC's occur at distances from the axis greater than the radius of the visible universe by an immense factor. We then show that Mallett's solution has a curvature singularity on the axis, ...

Einstein's general relativity is the best available theory of gravity. In recent years, spectacular proofs of Einstein's theory have been conducted, which have aroused interest that goes far beyond the narrow circle of specialists. The aim of this work is to offer an elementary introduction to general relativity. In this first part, we introduce the geometric concepts that constitute the basis of Einstein's theory. In the second part we will use these concepts to explore the ...

There are many spacetime geometries in general relativity which contain closed timelike curves. A layperson might say that retrograde time travel is possible in such spacetimes. To date no one has discovered a spacetime geometry which emulates what a layperson would describe as a time machine. The purpose of this paper is to propose such a space-time geometry. In our geometry, a bubble of curvature travels along a closed trajectory. The inside of the bubble is Rindler space...

Intrinsic time quantum geometrodynamics resolved `the problem of time' and bridged the deep divide between quantum mechanics and canonical quantum gravity with a Schrodinger equation which describes evolution in intrinsic time variable. In this formalism, Einstein's general relativity is a particular realization of a wider class of theories. Explicit classical black hole and cosmological solutions and the motion of test particles are derived and analyzed in this work in the c...

The theory of general relativity predicts the existence of closed time-like curves (CTCs), which theoretically would allow an observer to travel back in time and interact with their past self. This raises the question of whether this could create a grandfather paradox, in which the observer interacts in such a way to prevent their own time travel. Previous research has proposed a framework for deterministic, reversible, dynamics compatible with non-trivial time travel, where ...

The linear stability of closed timelike geodesics (CTGs) is analyzed in two spacetimes with cylindrical sources, an infinite rotating dust cylinder, and a cylindrical cloud of static cosmic strings with a central spinning string. We also study the existence and linear stability of closed timelike curves in spacetimes that share some common features with the G\"odel universe (G\"odel-type spacetimes). In this case the existence of CTGs depends on the `background' metric. The C...

In a large class of nonlocal as well as local higher derivative theories minimally coupled to the matter sector, we investigate the exactness of two different classes of homogeneous G\"{o}del-type solutions, which may or may not allow closed time-like curves (CTC). Our analysis is limited to spacetimes solving the Einstein's EoM, thus we can not exclude the presence of other G\"{o}del-type solutions solving the EoM of local and nonlocal higher derivative theories but not the ...

The initial value problem is well-defined on a class of spacetimes broader than the globally hyperbolic geometries for which existence and uniqueness theorems are traditionally proved. Simple examples are the time-nonorientable spacetimes whose orientable double cover is globally hyperbolic. These spacetimes have generalized Cauchy surfaces on which smooth initial data sets yield unique solutions. A more difficult problem is to characterize the class of spacetimes with closed...

In this comment on S.Lloyd, et al, Phys.Rev.Lett. 106, 040403 (2011), we show that modelling closed timelike curves (CTCs) as post-selected teleportation allows signalling to past times before the creation of the CTC and allows information paradoxes to form.