Bondi Accretion onto a Damour-Solodukhin Wormhole

Problem Statement
The Damour-Solodukhin wormhole (DSWH) is a theoretical spacetime metric known to mimic the horizon properties of a Schwarzschild black hole (SBH) under specific conditions. Traditionally, for the DSWH to act as an effective mimic, the dimensionless parameter $\lambda$ must be extremely small ($\lambda \sim 0$), ensuring that the coordinate time interval for light to travel from the throat to the asymptotic region is sufficiently large to render the two objects indistinguishable within observational timescales. However, previous literature (e.g., Lemos and Zaslavskii) has noted that in the limit $\lambda \to 0$, the DSWH exhibits divergent tidal forces at the throat, contrasting with the finite tidal effects at an SBH horizon, which could betray the mimicry. This paper investigates whether the requirement of $\lambda \sim 0$ is strictly necessary when considering Bondi accretion profiles. Specifically, it asks if the DSWH can mimic the SBH in terms of accretion dynamics even at considerably higher values of $\lambda$ (e.g., $\lambda \sim 1$).

Methodology
The authors analyze the steady-state, spherically symmetric Bondi accretion of perfect fluids onto a DSWH and compare these results with the standard SBH case ($\lambda = 0$). The study employs the following methodological framework:

• Metric: The DSWH metric is defined with a throat at $r_{th} = 2M$, differing from the SBH metric only in the $g_{00}$ component by the parameter $\lambda$.
• Fluid Dynamics: The accreting matter is treated as a perfect fluid with a barotropic equation of state $p = \omega\rho$. The study considers four cosmologically relevant types of matter: phantom ($\omega = -2$), quintessence ($\omega = -0.5$), dust ($\omega = 0$), and stiff matter ($\omega = 1$).
• Conservation Laws: The authors utilize the energy-momentum conservation law ($T^{\nu\mu}_{;\mu} = 0$) and the relativistic continuity equation to derive analytical expressions for radial velocity ($u$), energy density ($\rho$), and the rate of change of mass ($\dot{M}$).
• Critical Points: The analysis identifies critical (sonic) points where the fluid velocity equals the sound speed, determining the maximum accretion rate.
• Constraints: Integration constants are fixed based on physical conditions, ensuring the critical radius exceeds the throat/horizon radius and that density and velocity profiles remain physically valid for the chosen equation of state parameters.

Key Contributions and Results
The paper derives analytical solutions for the radial velocity, energy density, and mass accretion rate for both DSWH and SBH across the selected equations of state. The key findings include:

1. Velocity Profiles:

   • For non-phantom fluids (quintessence, dust, stiff matter), the radial velocity of the accreting fluid is lower for the DSWH compared to the SBH at all radii.
   • A distinct difference is observed at the horizon/throat ($r=2M$): For the SBH, the radial velocity approaches a finite non-zero value, whereas for the DSWH, the velocity drops to zero ($u=0$) at the throat.
   • Increasing the parameter $\lambda$ generally lowers the radial velocity for the DSWH.

2. Density Profiles:

   • The energy density for DSWH is generally higher than that of the SBH, though the profiles converge and coincide near $r = 2M$.
   • For phantom energy, the absolute density values increase near $r=2M$ for both objects, but the DSWH density remains lower than the SBH density.

3. Mass Accretion Rates:

   • Phantom Matter: Accretion leads to a decrease in the mass of both objects ($\dot{M} < 0$). For the DSWH, the rate of mass decrease increases as $\lambda$ increases.
   • Non-Phantom Matter: Accretion increases the mass of both objects ($\dot{M} > 0$). The profiles for the rate of mass change are nearly identical for DSWH and SBH in the vicinity of $r=2M$, regardless of the value of $\lambda$.

4. The Phantom Divide: The study confirms that dark energy with $\omega = -1$ cannot accrete onto the DSWH, as the equations yield divergences in velocity and zero density at this specific equation of state, consistent with known pathologies at the phantom divide.

Significance and Claims
The paper concludes that the restrictive requirement of $\lambda \sim 0$ for the DSWH to mimic an SBH may be too narrow when considering Bondi accretion. The comparative analysis reveals that the accretion profiles (velocity, density, and mass change rate) of the DSWH closely mimic those of the SBH in the immediate vicinity of the horizon/throat ($r \approx 2M$), even when $\lambda$ is significantly higher (up to $\lambda \sim 1$).

The authors assert that these results suggest the DSWH can function as a viable black hole mimicker in the context of accretion dynamics without necessitating the extreme fine-tuning of $\lambda$ required for light propagation arguments. The authors suggest these findings could aid in the interpretation of future observational data from projects such as Millimetron, though they do not propose specific experimental tests or applications beyond this interpretative potential.