There and back again -- Closed timelike curves as EFT selection principle

TL;DR

The paper proposes a causal EFT selection principle: modified gravity should render closed timelike curves harder to realize than in General Relativity. Using Horndeski gravity, it builds perturbative rotating black-hole solutions in two EFT subsets, k-essence and Einstein–dilaton Gauss–Bonnet (EdGB), deriving bounds on EFT coefficients that avoid CTCs and ensure stability. It demonstrates how CTC-avoidance translates into constraints on the EFT parameter space and shows that gravitational-wave echoes can serve as observational probes of near-horizon causality, relating echo timing to the effective cosmological constant generated by the EFT sector. The work bridges geometric and field-theoretic notions of causality, offering a perturbative framework to diagnose causality in modified gravity and to extract phenomenological implications for next-generation gravitational-wave data.

Abstract

Modified gravity is often approached in the context of effective-field theory (EFT), with the view that the EFT corrections permit a more desirable theory. In this paper, we posit that this should extend to the causal structure of curved spacetime in addition to the standard demands such that of flat spacetime positivity and unitarity. We propose a new guiding principle for modified-gravity theories, namely that closed timelike curves should always be {\it harder} to obtain than in General Relativity. By demanding this, one can place powerful constraints on modified gravity. To elucidate this claim, we investigate modified-gravity EFTs on rotating black-hole backgrounds, focusing on the appearance/disappearance of closed timelike curves, and provide parameter bounds which only partly overlap with other approaches based on time delay. We construct perturbative rotating black-hole solutions in modified-gravity EFTs based on the Horndeski class and provide parameter bounds necessary to preserve causality and stability. Finally, we present a novel probe for the existence of closed timelike curves through quasinormal modes and black-hole echoes. This can be used to diagnose spacetime causality once next-generation gravitational-wave data becomes available.

Figures (10)

• Figure 1: Rotating cylinder and the appearance of the closed timelike curve (inner circle), represented by the tilted lightcones with the curve in its causal future.
• Figure 2: CTC regions for an infinite rotating cylinder for different values of $q$. The boundary line between the regions is impacted when matter is added.
• Figure 3: Causality parameter space for zero-change k-essence. CTCs only appear in the red region in the third quadrant. The dashed line indices the boundary between the causal and acausal region of parameter space, which is shown for different values of $M$ and $M_\ast$ in Figure \ref{['fig:kessencectc']}.
• Figure 4: CTC regions for zero-charge k-essence for different values of $M$ and $M_\ast$ using $\varepsilon_a=0.4$ and $\theta=\pi/2$ (third quadrant of Figure \ref{['fig:kessencectc_allregions']}). CTCs appear to the left of any curve. The region to the right is chronologically safe shrinks with increasing $M$ and $M_\ast$ in general. The region where $\alpha$ and $\tilde{\beta}$ are both positive is always chronologically safe, and when either $\alpha$ or $\tilde{\beta}$ is negative, there is no real solution for the scalar field.
• Figure 5: CTC regions for non zero-charge k-essence for different values of spin $\varepsilon_a$, matter coupling $\varepsilon_q$, and equatorial angle $\theta$ when using $M_\ast=M_{\rm Pl}/100$ and $M=1000M_{\rm Pl}$. CTCs appear in the top left region, and the lower right region is chronologically safe and which shrinks with increasing angular momentum and matter coupling strength. The region $\{\alpha>0,\tilde{\beta}>0\}$ is always chronologically safe. In the regions where either $\alpha$ or $\tilde{\beta}$ is negative, the scalar field has no real solution.