The progress of mini black holes: principles and analytical astronomical observation techniques

Mini-black hole (MBH) is a concept first proposed by Stephen Hawking in the 1970s. Normally, exploring MBHs will enhance the understanding of quantum theory and gravity theory as well as be helpful in predicting the configuration of the early universe. Based on information retrieval, this paper summarizes the progress of MBHs and takes three major aspects: background, models, practical methods for observations, and analysis. Specifically, the descriptive equations are derived, and different models are discussed separately. These results shed light on the prospective development of quantum field theorem, general relativity, and string theory.

Sterile neutrinos, black hole vacuum and holographic principle

We construct an effective field theory (EFT) model that describes matter field interactions with Schwarzschild mini-black-holes (SBH’s), treated as a scalar field, $$B_0(x)$$ B 0 ( x ) . Fermion interactions with SBH’s require a complex spurion field, $$\theta _{ij}$$ θ ij , which we interpret as the EFT description of “holographic information,” which is correlated with the SBH as a composite system. We consider Hawking’s virtual black hole vacuum (VBH) as a Higgs phase, $$\langle B_0 \rangle =V$$ ⟨ B 0 ⟩ = V . Integrating sterile neutrino loops, the information field $$\theta _{ij}$$ θ ij is promoted to a dynamical field, necessarily developing a tachyonic instability and acquiring a VEV of order the Planck scale. For N sterile neutrinos this breaks the vacuum to $$SU(N)\times U(1)/SO(N)$$ S U ( N ) × U ( 1 ) / S O ( N ) with N degenerate Majorana masses, and $$\frac{1}{2}N(N+1)$$ 1 2 N ( N + 1 ) Nambu-Goldstone neutrino-Majorons. The model suggests many scalars fields, corresponding to all fermion bilinears, may exist bound nonperturbatively by gravity.

Thermal relativity, modified Hawking radiation, and the generalized uncertainty principle

After a brief review of the thermal relativistic corrections to the Schwarzschild black hole entropy, it is shown how the Stefan–Boltzman law furnishes large modifications to the evaporation times of Planck-size mini-black holes, and which might furnish important clues to the nature of dark matter and dark energy since one of the novel consequences of thermal relativity is that black holes do not completely evaporate but leave a Planck size remnant. Equating the expression for the modified entropy (due to thermal relativity corrections) with Wald’s entropy should, in principle, determine the functional form of the modified gravitational Lagrangian [Formula: see text]. We proceed to derive the generalized uncertainty relation which corresponds to the effective temperature [Formula: see text] associated with thermal relativity and given in terms of the Hawking ([Formula: see text]) and Planck ([Formula: see text]) temperature, respectively. Such modified uncertainty relation agrees with the one provided by string theory up to first order in the expansion in powers of [Formula: see text]. Both lead to a minimal length (Planck size) uncertainty. Finally, an explicit analytical expression is found for the modifications to the purely thermal spectrum of Hawking radiation which could cast some light into the resolution of the black hole information paradox.

Regimes of mini black hole abandoned to accretion

Being inspired by the Eddington’s idea, along with other auxiliary arguments, it is unveiled that there exist regimes of a black hole that would prohibit accretion of ordinary energy. In explicit words, there exists a lower bound to black hole mass below which matter accretion process does not run for black holes. Not merely the baryonic matter, but, in regimes, also the massless photons could get prohibited from rushing into a black hole. However, unlike the baryon accretion abandoned black hole regime, the mass-regime of a black hole prohibiting accretion of radiation could vary along with its ambient temperature. For example, we discuss that earlier to [Formula: see text] s after the big-bang, as the cosmological temperature of the Universe grew above [Formula: see text] K, the mass range of black hole designating the radiation accretion abandoned regime, had to be in varying state being connected with the instantaneous age of the evolving Universe by an “one half” power law. It happens to be a fact that a black hole holding regimes prohibiting accretion of energy is gigantic by its size in comparison to the Planck length-scale. Hence the emergence of these regimes demands mini black holes for not being viable as profound suckers of energy. Consideration of accretion abandoned regimes could be crucial for constraining or judging the evolution of primordial black holes over the age of the Universe.