Static stable timelike circular orbits and Aschenbach effect in horizonless solutions of Einstein cubic gravity

Abstract

In the spacetime of horizonless compact objects described by Einsteinian cubic gravity (ECG), we demonstrate the existence of static stable timelike circular orbits on which massive particles remain at rest relative to distant observers. These static orbits are further identified as the innermost stable circular orbits (ISCOs) in this spacetime. If such static orbits form part of an accretion disk, they would give rise to a ring-like structure that is unaffected by Doppler shifts. Moreover, the Aschenbach effect is shown to be present: the orbital velocity of particles on timelike circular orbits, as measured by a zero angular momentum observer (ZAMO), displays a non-monotonic dependence on the radial coordinate. Additionally, the regions supporting stable circular orbits can be discontinuous, and particles on stable orbits near the center can possess specific energies greater than one ($E > 1$).

Figures (8)

• Figure 1: Solutions of $f(r)$ for (a) $f_0 = 0.9$ and (b) $f_0 = 0.5$. Curves with the same $\lambda$ value correspond to the same color, where dashed and solid lines represent solutions in Branch 1 and Branch 2, respectively.
• Figure 2: Plots of function $D(r)$ for different values of $\lambda$. The left panel (a) corresponds to Branch 1, while the right panel (b) corresponds to Branch 2. The dashed lines represent the Schwarzschild case, and the solid lines represent the ECG case with parameters $f_0 = 0.9$ and different values of $\lambda$.
• Figure 3: The region where circular orbits exist (green). The corresponding solution comes from Branch 2, with parameters $f_0 = 0.9$ and $\lambda = 0.7$. Here, $f'(r) < 0$ and $D(r) < 0$ are marked in red and orange, respectively, with the black dashed circle serving as a reference, and the numbers indicate its value of radius.
• Figure 4: Effective potential for particles with zero angular velocity $\Omega = 0$. The corresponding solution come from Branch 1, with parameters $f_0 = 0.9$ and $\lambda = 10$. The blue star ($\star$) marks the location of the minimum of the effective potential. The vertical red dashed line indicates the location of the minimum of effective potential.
• Figure 5: (a) The particle trajectory diagram, where the dashed reference circle has a radius of $4.065175$, the solid orange circle represents the starting position, the solid square represents the ending position. The initial conditions are: radial coordinate $r_0 = 4.065175$, angular velocity $\Omega_0$, and zero radial velocity. (b) The radial deviation as a function of proper time. The solution is from Branch 1, with parameters $f_0=0.9$ and $\lambda=10.0$.