Can Static Black Holes in Massive Gravity Serve as Candidates for Aschenbach-Like Phenomena?

TL;DR

The paper investigates whether Aschenbach-like non-monotonic orbital velocity can arise in static black holes by curvature-driven extrema outside the horizon, using black holes in Massive Gravity as a testing ground. It employs a topological photon-sphere framework with an effective potential $H(r,\theta)$ and a two-component vector field to assign photon-sphere charges, together with time-like circular-orbit analysis governed by the beta function $\beta$, to identify allowed regions for stable orbits. Across three Massive Gravity models (Bardeen AdS, nonlinear charged AdS, and ModMax-dRGT-like), the authors demonstrate parameter regimes in which exterior photon spheres and MSCO structures yield a non-monotonic $\Omega(r)$ outside the horizon, i.e., an Aschenbach-like effect without frame dragging. This shows curvature-induced dynamics alone can mimic aspects of relativistic orbital behavior and suggests a potential observational signature of general relativistic dynamics in static spacetimes. The work highlights how massive-gravity modifications shape horizon structure and light-ring topology, offering a curvature-based mechanism for relativistic orbital phenomena with possible astrophysical implications.

Abstract

The Aschenbach effect is widely regarded as a manifestation of two quintessential relativistic features: frame dragging and extreme spacetime curvature. Traditionally associated with rotating geometries, this non-monotonic behavior in orbital angular velocity challenges Newtonian intuition. In our previous work, however, we demonstrated that this velocity irregularity is not exclusive to spinning spacetimes. Specifically, we showed that the presence of a stable minimum in the gravitational potential, corresponding to a stable photon sphere, can reproduce Aschenbach-like behavior in static black holes as well. This observation suggests that, even in the absence of rotational frame dragging, curvature alone (if encoded through appropriate geometric extrema) may be sufficient to induce non-monotonic velocity profiles. In this study, we build upon that foundation to investigate whether black hole architectures in theories of Massive Gravity can inherently support the emergence of Aschenbach-like phenomena. Furthermore, can this Aschenbach-like phenomenon in static configurations be considered as an observable signature in the dynamics of general relativity, similar to the original Aschenbach effect in rotating spacetimes?

Figures (15)

• Figure 1: Metric function Fig (1a): With $l = 1, q = 0.5, C = 1, c_{1} = -1, c_{2} = 1, m_{g} = 0.5$ with different M , (1b): With $l = 1, M = 10, C = 1, c_{1} = -1, c_{2} = 1, m_{g} = 0.5$ with different q (1c): With $M = 2, q = 0.5, C = 1, c_{1} = -1, c_{2} = 1, m_{g} = 0.5$ with different l (1d): With $M = 2, l = 1, q = 0.5, C = 1, c_{1} = -1, c_{2} = 1$ with different $m_{g}$ (1e): With $M = 2, l = 1, q = 0.5, C = 1, c_{2} = 1, m_{g} = 0.5$ with different $c_{1}$ for Bardeen black holes in massive gravity
• Figure 2: The heat capacity with $M = 2, l = 1, q = 0.5, C = 1, c_{1} = -1, c_{2} = 1, m_{g} = 0.5$ for Bardeen black holes in massive gravity
• Figure 3: (3a): The photon spheres location at $(r, \theta)=(7.7667, 1.57)$ and $(r, \theta)=(12.0996, 1.57)$ with respect to $M = 2, l = 1, q = 0.5, C = 1, c_{1} = -1, c_{2} = 1, m_{g} = 0.5$ in the $(r-\theta)$ plane of the normal vector field $n$ , (3b): the topological potential H(r) for Bardeen black holes in massive gravity
• Figure 4: (4a): $\beta$ diagram (4b):MSCO localization and space classification for the Bardeen black holes in massive gravity
• Figure 5: Angular velocity VS r with $M = 2, l = 1, q = 0.5, C = 1, c_{1} = -1, c_{2} = 1, m_{g} = 0.5$ for the Bardeen black holes in massive gravity