Subjects: Astronomy >> Astrophysical processes submitted time 2023-02-19
Abstract： We systematically study the top-down model of loop quantum black holes (LQBHs), recently derived by Alesci, Bahrami and Pranzetti (ABP). To understand the structure of the model, we first derive several well-known LQBH solutions by taking proper limits. These include the B\"ohmer-Vandersloot and Ashtekar-Olmedo-Singh models, which were all obtained by the so-called bottom-up polymerizations within the framework of the minisuperspace quantizations. Then, we study the ABP model, and find that the inverse volume corrections become important only when the radius of the two-sphere is of the Planck size. For macroscopic black holes, the minimal radius obtained at the transition surface is always much larger than the Planck scale, and hence these corrections are always sub-leading. The transition surface divides the whole spacetime into two regions, and in one of them the spacetime is asymptotically Schwarzschild-like, while in the other region, the asymptotical behavior sensitively depends on the ratio of two spin numbers involved in the model, and can be divided into three different classes. In one class, the spacetime in the 2-planes orthogonal to the two spheres is asymptotically flat, and in the second one it is not even conformally flat, while in the third one it can be asymptotically conformally flat by properly choosing the free parameters of the model. In the latter, it is asymptotically de Sitter. However, in any of these three classes, sharply in contrast to the models obtained by the bottom-up approach, the spacetime is already geodesically complete, and no additional extensions are needed in both sides of the transition surface. In particular, identical multiple black hole and white hole structures do not exist.
Peer Review Status:
Awaiting Review
Subjects: Astronomy >> Astrophysical processes submitted time 2023-02-19
Abstract： In this paper, we study the polarization of a gravitational wave (GW) emitted by an astrophysical source at a cosmic distance propagating through the Friedmann-Lema\^itre-Robertson-Walk universe. By considering the null geodesic deviations, we first provide a definition of the polarization of the GW in terms of the Weyl scalars with respect to a parallelly-transported frame along the null geodesics, and then show explicitly that, due to different effects of the expansion of the universe on the two polarization modes, the so-called "+" and "$\times$" modes, the polarization angle of the GW changes generically, when it is propagating through the curved background. By direct computations of the polarization angle, we show that different epochs, radiation-, matter- and $\Lambda$-dominated, have different effects on the polarization. In particular, for a GW emitted by a binary system, we find explicitly the relation between the change of the polarization angle $|\Delta \varphi|$ and the redshift $z_s$ of the source in different epochs. In the $\Lambda$CDM model, we find that the order of $|\Delta \varphi|{\eta_0 F}$ is typically $O(10^{-3})$ to $O(10^3)$, depending on the values of $z_s$, where $\eta_0$ is the (comoving) time of the current universe, and $F\equiv\Big(\frac{5}{256}\frac{1}{\tau_{obs}}\Big)^{3/8}\left(G_NM_c\right)^{-5/8}$ with $\tau_{obs}$ and $M_c$ being, respectively, the time to coalescence in the observer's frame and the chirp mass of the binary system.
Peer Review Status:Awaiting Review
Subjects: Astronomy >> Astrophysical processes submitted time 2023-02-19
Abstract： Primordial black holes (PBHs) could be formed if large perturbations are generated on small scales in inflation. We study a toy inflation model with a local minimum. The curvature perturbations are enhanced when the inflaton passes through the local minimum, with more efficient amplification rate than that of quasi-inflection point inflation, leading to the production of PBHs on small scales. For parameter spaces provided in this paper, the PBHs could comprise a fraction of the total dark matter around $0.1\%$--$1\%$.
Peer Review Status:Awaiting Review
Subjects: Astronomy >> Astrophysical processes submitted time 2023-02-19
Abstract： In this paper we systematically study a five-parameters class of spherically symmetric polymer black/white hole solutions, and find that only three independent combinations are physical and uniquely determine the spacetime properties. After exploring the whole 3-dimensional (3D) phase space, we find that the model has very rich physics, and depending on the choice of these parameters, various possibilities exist, including: (i) spacetimes that have the standard black/white hole structures, that is, spacetimes that are free of spacetime curvature singularities and possess two asymptotically flat regions, which are connected by a transition surface (throat) with a finite and non-zero geometric radius. The black/white hole masses measured by observers in the two asymptotically flat regions are all positive, and the surface gravity of the black (white) hole is positive (negative). (ii) Spacetimes that have wormhole-like structures, in which the two masses are all positive, but no horizons exist.(iii) Spacetimes that still possess curvature singularities, which can be either hidden inside trapped regions or naked. However, such spacetimes correspond to only some limit cases, and the necessary (but not sufficient) condition is that at least one of the two "polymerization" parameters vanishes. In addition, even for solar mass black/white holes, quantum gravitational effects can be still very large at the black/white hole horizons, again depending on the choice of the parameters.
Peer Review Status:Awaiting Review
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