Additional parameters can eliminate closed timelike curves in modified gravity

A recent study has investigated the existence of closed timelike curves (CTCs) in three rotating black hole models arising from modified theories of gravity. CTCs are hypothetical regions of spacetime where an object's trajectory can return to its starting point in time, implying the possibility of time travel to the past and chronological paradoxes. The researchers have shown that additional parameters inherent in these modified theories can control the extent of these causality-violating regions, and even eliminate them entirely under certain configurations. The models analyzed include the tidally charged braneworld black hole, the Kerr-Newman black hole in Rastall gravity, and the charged Johannsen-Psaltis spacetime. For each, the sign of the gφφ component of the metric tensor on the equatorial plane was examined, as this is a key indicator of the presence of CTCs. It was found that, in all cases, the new parameters introduced by modified gravity theories offer a mechanism to influence spacetime geometry in such a way that CTCs can be suppressed or confined. In the braneworld black hole case, the CTC region only exists for a positive tidal charge, disappearing if it is zero or negative. For Rastall gravity, the Rastall coupling and surrounding matter jointly determine the extent of the CTC region, and a finite range of coupling values was identified for which CTCs are absent. Finally, in the Johannsen-Psaltis spacetime, the deformation parameter can either increase or decrease the gφφ metric, and a window of values for this parameter was derived that removes CTCs from the considered radial domain. These findings suggest that modified theories of gravity could offer solutions to the temporal paradoxes predicted by General Relativity under certain extreme conditions.

New technique reveals transient resonances in relativistic chaotic orbits

Researchers have developed a new technique, called Sliding-Window Frequency Ratio (SWFR), to identify and analyze transient resonances in chaotic orbits within relativistic spacetimes. Traditionally, long-term Poincaré sections tend to blur chaotic orbits, obscuring the sequence in which an orbit explores its local structures. The SWFR method overcomes this limitation by reconstructing the temporal order of the orbit, revealing periods where chaotic motion temporarily approximates resonant behavior. The SWFR technique is constructed solely from radial and polar turning events of the orbit. By analyzing these events within sliding windows of a fixed number of radial cycles, the method counts polar events while keeping track of event times. This allows for the extraction and analysis of any candidate interval as its own Poincaré section. Unlike other methods, SWFR requires no spectra, reference centers, or basis functions, simplifying its application. In tests with integrable Kerr benchmarks, the technique successfully recovered known frequency ratios, and for regular motion, the counting error bound falls off as O(W⁻¹), where W is the window size. The primary application of SWFR lies in the analysis of chaotic orbits. For instance, in magnetized Kerr spacetime, a charged orbit was observed to dwell near 3/5 and later near 4/7 frequency ratios, with corresponding Poincaré sections exhibiting fivefold and sevenfold patterns. Another orbit showed a temporary residence near 1/2 with two lobes. In Schwarzschild-Melvin spacetime, a photon held a 4/5 ratio across a fivefold pattern. In every case, phase-space geometry and the integer counts from SWFR agreed that globally chaotic orbits are temporarily visiting resonances, opening new avenues for understanding complex dynamics in strong gravitational fields.

Automatic Differentiation Optimizes Critical Solution Search in Numerical Relativity

Researchers have demonstrated how automatic differentiation can significantly accelerate the identification of critical dynamical solutions in numerical relativity. This advancement is crucial because simulations of Einstein's equations are computationally very expensive, and the complexity of the parameter space, coupled with the nonlinear sensitivity of the solutions, makes finding specific outcomes of interest challenging. The new methodology offers a more efficient tool for exploring these complex solution landscapes. The team used the classic problem of scalar critical collapse as a proof of concept. They successfully located a line of critical solutions in a 2D parameter space with only 35 runs, a drastically smaller number compared to the 270 runs that would be required to find 10 critical points using the bisection method. Furthermore, automatic differentiation allowed for the direct calculation of the unstable mode, confirming its universality along the identified line of solutions. This method not only reduces computational cost but is also straightforwardly extendable to higher-dimensional parameter spaces. This makes it a promising technique for tackling more complex problems in strong dynamical gravity regimes, where identifying specific solutions is fundamental to understanding extreme astrophysical phenomena, such as black hole formation or the merger of compact objects.