Primordial regular black holes as all the dark matter. I. Time-radial-symmetric metrics
Marco Calzà, Davide Pedrotti, Sunny Vagnozzi
备注：
22 pages, 9 figures. M.C. and D.P. contributed equally to this work. v2: changed name of one of the metrics from "GCSV" to "CGSV" to properly acknowledge earlier work. v3: several additional references added, removed Hayward-like BH, added figure comparing GBFs, discussed time-evolution, clarified some technical aspects. Version accepted for publication in PRD. Companion paper in arXiv:2409.02807
Primordial black holes (PBHs) are usually assumed to be described by the Schwarzschild or Kerr metrics, which however feature unwelcome singularities. We study the possibility that PBHs are non-singular objects, considering three phenomenological, regular tr (time-radial)-symmetric space-times (including the well-known Bardeen and Hayward ones), featuring either de Sitter or Minkowski cores. We characterize the evaporation of these PBHs and constrain their abundance from $γ$-ray observations. For all three metrics we find that constraints on $f_{\text{pbh}}$, the fraction of dark matter (DM) in the form of PBHs, weaken with respect to the Schwarzschild limits, because of modifications to the PBH temperature and greybody factors. This moves the lower edge of the asteroid mass window down by potentially an order of magnitude or more, leading to a much larger region of parameter space where PBHs can make up all the DM. A companion paper is devoted to non-\textit{tr}-symmetric metrics, including loop quantum gravity-inspired ones. Our work provides a proof-of-principle for the interface between the DM and singularity problems being a promising arena with a rich phenomenology.
The Eddington-inspired-Born-Infeld (EiBI) model is reformulated within the mimetic approach. In the presence of a mimetic field, the model contains non-trivial vacuum solutions which could be free of spacetime singularity because of the Born-Infeld nature of the theory. We study a realistic primordial vacuum universe and prove the existence of regular solutions, such as primordial inflationary solutions of de Sitter type or bouncing solutions. Besides, the linear instabilities present in the EiBI model are found to be avoidable for some interesting bouncing solutions in which the physical metr…
The possibility that dark matter particles could be constituted by extreme regular primordial black holes is discussed. Extreme black holes have zero surface temperature, and are not subjected to the Hawking evaporation process. Assuming that the common horizon radius of these black holes is fixed by the minimum distance that is derived from the Riemann invariant computed from loop quantum gravity, the masses of these non-singular stable black holes are of the order of the Planck mass. However, if they are formed just after inflation, during reheating, their initial masses are about six orders…
We numerically study the primordial black hole (PBH) formation by an isocurvature perturbation of a massless scalar field on super Hubble scales in the radiation-dominated universe. As a first step we perform simulations of spherically symmetric configurations. For the initial condition, we employ the spatial gradient expansion and provide the general form of the growing mode solutions valid up through the second order in this expansion. The initial scalar field profile is assumed to be Gaussian with a characteristic comoving wavenumber $k$; $\sim\exp(-k^2R^2)$, where $R$ is the radial coordin…
A primordial black hole (PBH) is thought to be made of the regular matter or ordinary mass ($M$) only, and hence could have already been decayed due to the Hawking radiation if its initial ordinary mass were $\lesssim 5 \times 10^{11}$ kg. Here, we study the role of gravitomagnetic monopole for the evaporation of PBHs, and propose that the lower energy PBHs (equivalent to ordinary mass $M << 5\times 10^{11}$ kg) could still exist in our present Universe, if it has gravitomagnetic monopole. If a PBH was initially made of both regular matter and gravitomagnetic monopole, the regular matter could…
We derive the equation governing the axial-perturbations in the space-time of a non-rotating uncharged primordial black hole (PBH), produced in early Universe, whose metric is taken as the generalized McVittie metric. The generalized McVittie metric is a cosmological black hole metric, proposed by V. Faraoni and A. Jacques in 2007 [Phys. Rev. D 76, 063510 (2007)]. This describes the space-time of a Schwarzschild black hole embedded in FLRW-Universe, while allowing its mass-change. Our derivation has basic similarities with the procedure of derivation of S. Chandrasekhar, for deriving the Regge…
One-loop renormalised quantum effective action for gravity contains quadratic in curvature terms. We have found an approximate analytic black hole solution in quadratic gravity by keeping only the radial spherically symmetric fluctuations and dimensionally reducing the 4-dimensional (4D) theory down to the 2-dimensional (2D) dilaton gravity with a potential. The solution reduces to the Schwarzschild black hole in the limit of Einstein's gravity, but otherwise admits non-negative Arnowitt-Deser-Misner (ADM) and positive quasi-local Misner-Sharp masses that can differ significantly. We then stud…
We investigate the consequences of different regularizations and ambiguities in loop cosmological models on the predictions in the scalar and tensor primordial spectrum of the cosmic microwave background using the dressed metric approach. Three models, standard loop quantum cosmology (LQC), and two modified loop quantum cosmologies (mLQC-I and mLQC-II) arising from different regularizations of the Lorentzian term in the classical Hamiltonian constraint are explored for chaotic inflation in spatially-flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. In each model, two different treatmen…
The stability of a class of electrically charged fluid spheres under radial perturbations is studied. Among these spheres there are regular stars, overcharged tension stars, regular black holes, quasiblack holes, and quasinonblack holes, all of which have a Reissner-Nordström exterior. We formulate the dynamical perturbed equations by following the Chandrasekhar approach and investigate the stability against radial perturbations through numerical methods. It is found that (i) under certain conditions that depend on the adiabatic index of the radial perturbation, there are stable charged stars …
We have proposed a model geometry for the interior of a regular black hole mimicker, the frozen star, whose most startling feature is that each spherical shell in its interior is a surface of infinite redshift. The geometry is a solution of the Einstein equations which is sourced by an exotic matter with maximally negative radial pressure. The frozen star geometry was previously presented in singular coordinates for which $-g_{tt}$ and $g^{rr}$ vanish in the bulk and connect smoothly to the Schwarzschild exterior. Additionally, the geometry was mildly singular in the center of the star. Here, …
We investigate the Dirac and Klein-Gordon equations, as well as greybody radiation, for the Hayward black hole (BH) spacetime. We first consider the Dirac equation using a null tetrad in the Newman- Penrose (NP) formalism. The equations are then separated into angular and radial parts. A pair of one-dimensional Schrödinger like wave equations with effective potentials is obtained from the radial part. In order to examine the behavior of potentials, they are plotted with respect to radial distances. Additionally, the Klein-Gordon equation is considered in the Hayward BH spacetime. At the end, w…
Slowly rotating traversable wormholes supported by radially varying string-fluid matter: From regular geometries to photon trajectories
University of KwaZulu-Natal（夸祖鲁-纳塔尔大学）；Khazar University（哈扎尔大学）；Central Asian University（中亚大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Ulugh Beg Astronomical Institute（乌鲁格别克天文研究所）；Imam Mohammad Ibn Saud Islamic University (IMSIU)（伊玛目穆罕默德·伊本·沙特伊斯兰大学）；Kimyo International University in Tashkent（塔什干化学国际大学）；Samarkand State University of Architecture and Construction（撒马尔罕建筑与建设国立大学）；Urgench State Pedagogical Institute（乌根奇国立师范学院）
