**1. Introduction**

In the research presented in the works [1–3], it has been suggested that Primordial Black Holes make up a significant fraction of dark matter. Microscopic Black Holes (MBH) can also be formed within stars by coalescence of dark matter composed of weakly interacting massive particles [4, 5]. According to the plot in ([3], p. 14), considerations other than stellar capture constrain the masses of MBH as a dark matter to the range of 1016 kg–<sup>5</sup> <sup>10</sup><sup>21</sup> kg*:*

Up to now, researchers believed that all MBH captured by a star would be slowed down within stellar material until they settle in the stellar center [1, 2]. In the present work, we explore the possibility of MBH accelerating during their passage through stellar matter at low Mach numbers. As MBH passes through matter, it accretes material at a rate we denote *M*\_ . Some of the mass accreted by MBH is turned into energy. This energy escapes the MBH in the form of protons and gamma rays. These rays heat the surrounding material, causing its rarefaction. The rarefied material behind the moving MBH exerts a lower gravitational pull on the MBH than the dense material in front of it. *Moving MBH experiences a net forward force.* This force is called **MBH ramjet** force. The effect is illustrated in **Figure 1**.

The conditions under which MBH accelerates within the stellar material are derived in this work. In order to define these conditions, three efficiencies must be

**Figure 1.** *MBH passage through matter.*

defined. These are gas redistribution efficiency, radiative efficiency, and accretion efficiency. **Gas redistribution efficiency**, *ηG*, is the ratio of the accelerating force caused by gas rarefaction behind the MBH to the theoretical maximum of such force. The exact definition starts at paragraph containing Eq. (9) and ends with a paragraph containing Eq. (11). **Radiative efficiency**, *η*Γ, is the ratio of the total power radiated by MBH to the power *Mc* \_ <sup>2</sup> of the mass falling into MBH. It is expressed in Eq. (12). **Accretion efficiency**, *ηA*, is the ratio of the actual and the zero-radiation mass capture rates. It is defined in Eq. (16).

We show that in the case of MBH moving through stellar material at supersonic (supersonic MBH) speed, the condition for MBH acceleration is given in Eq. (29):

$$\mathcal{N} = \frac{\eta\_A \eta\_\Gamma \eta\_{G\_2}}{T\_6} \gtrsim 4 \cdot 10^{-4} \cdot \left(1 + \mathcal{M}^{-2}\right)^{3/2},\tag{1}$$

where *T*<sup>6</sup> is the temperature of the stellar material in millions Kelvin. Even though we do not have precise values for efficiencies *ηA*, *η*Γ, and *ηG*, we are almost certain that for supersonic MBH, condition Eq. (1) is never met. In the case of MBH moving through stellar material at a subsonic speed (subsonic MBH), the condition for MBH acceleration is given in Eq. (33):

$$\mathcal{N} = \frac{\eta\_A \eta\_\Gamma \eta\_{G\_2}}{T\_6} \gtrsim 9 \cdot 10^{-7} \mathcal{M}^3 \mathfrak{F}(\mathcal{M}, \eta\_A), \tag{2}$$

where M is the Mach number and Fð Þ M, *η<sup>A</sup>* > 0*:*11 is given in Eq (34). Supersonic MBH always experiences deceleration within stellar material. Subsonic MBH experiences acceleration when the Mach number exceeds M<sup>0</sup> (the equilibrium Mach number) and deceleration when the Mach number is below M0. Eventually the MBH settles into an intrastellar orbit with Mach number M0. The value of M<sup>0</sup> can be obtained by solving Eq. (2) as an equality.

In Appendix A, a minimal value of *η<sup>G</sup>* for subsonic MBH is estimated. Estimating *η<sup>G</sup>* for supersonic MBH remains an open problem. Calculating the values of *η<sup>A</sup>* and *η*<sup>Γ</sup> also remain open problems. As we discuss later in this work, different theorists obtained different results for *η*Γ.

We briefly outline the content of the present chapter. In Section 2, we calculate forces acting on MBH. We also derive conditions for MBH acceleration at subsonic and supersonic speed. In Section 3, we present estimates for *η<sup>A</sup>* and *η*Γ. In Section 4, we present an empirical discussion of possible behaviors of MBH within stellar material. In Section 5, the problems remaining after this work are briefly described.
