We derive the general conditions for a large family of shift symmetry breaking degenerate higher order scalar-tensor (DHOST) theories to admit stealth black hole solutions. Such black hole configurations correspond to vacuum solutions of general relativity and admit a scalar hair which does not gravitate, revealing itself only at the perturbative level. We focus our investigation on hairy Schwarzschild-(A)dS or pure Schwarzschild solutions, dressed with a linear time-dependent scalar hair, and assuming a constant kinetic term. We also discuss subclasses of this family which satisfy the observational constraint $c_{\mathrm{grav}}=c_{\text{light}}$, as well as the recent constraint ensuring the absence of graviton decay. We provide at the end concrete examples of DHOST Lagrangians satisfying our conditions. This work provides a first analysis of exact black hole solutions in shift symmetry breaking DHOST theories beyond Horndeski.

A new routine is proposed to relate loop quantum cosmology (LQC) to loop quantum gravity (LQG) from the perspective of effective dynamics. We derive the big-bang singularity resolution and big bounce from the first principle of full canonical LQG. Our results are obtained in the framework of the reduced phase space quantization of LQG. As a key step in our work, we derive with coherent states a new discrete path integral formula of the transition amplitude generated by the physical Hamiltonian. The semiclassical approximation of the path integral formula gives an interesting set of effective equations of motion (EOMs) for full LQG. When solving the EOMs with homogeneous and isotropic ansatz, we reproduce the LQC effective dynamics in the ${\mu }_0$-scheme. The solution replaces the big-bang singularity by a big bounce. In the end, we comment on the possible relation between the $\overline{\mu }$-scheme of effective dynamics and the continuum limit of the path integral formula.

We compute numerically the Lorentzian Engle-Pereira-Rovelli-Livine spinfoam propagator on a 4-simplex, by adapting the Lefschetz thimble and Markov chain Monte-Carlo methods to oscillatory spinfoam integrals. Our method can compute any spinfoam observables at relatively large spins. We obtain the numerical results of the propagators at different spins and demonstrate their consistency with the expected spinfoam semiclassical behavior in the large spin limit. Our results exhibit significant quantum corrections at smaller spins. Our method is reliable and thus can be employed to discover the semiclassical and quantum behaviors of the spinfoam model.

Based on the effective dynamics in the $\overline{\mu }$ scheme of the spherical symmetry reduced model in the reduced phase space formulation of loop quantum gravity (LQG), we investigate the gravitational collapse of a homogeneous dust cloud, with Gaussian dust serving as both the reference field and the source of the gravitational collapse. The effective dynamics from the considered model for a homogeneous dust cloud reduces precisely to the effective dynamics of loop quantum cosmology (LQC) with extrinsic curvature based K-quantization, indicating that the LQC effective dynamics lives as a subsector of the model presented here. In both the marginally bound and the bound cases of the collapse in effective dynamics, the singularity is resolved and replaced by a bounce. Though quantum geometric modification from spatial curvature is not directly included in the K-quantization it does affect the qualitative dynamics of the collapsing dust cloud in the sense that on the one hand for the marginally bound case, the dust cloud bounces once at fixed maximum energy density and on the other hand for the bound case, the dust cloud undergoes infinite cycles of contraction and expansion at energy densities dependent on the dust mass. Finally, the mass threshold for the formation of a trapped surface in each case is found and the matching conditions between the interior collapsing spacetime and an effective exterior static solution are discussed.

Based on modifications inspired from loop quantum gravity (LQG), spherically symmetric models have recently been explored to understand the resolution of classical singularities and the fate of the spacetime beyond. While such phenomenological studies have provided useful insights, questions remain on whether such models exhibit some of the desired properties such as consistent LTB conditions, covariance, and compatibility with the improved dynamics of loop quantum cosmology in the cosmological and LTB sector. We provide a systematic procedure to construct effective spherically symmetric models encoding LQG modifications as a $1+1$ field theory models encoding these properties following the analysis in our companion paper [K. Giesel et al., Embedding generalized LTB models in polymerized spherically symmetric spacetimes, Phys. Rev. D 110, 104017 (2024)]. As concrete examples of our generalized strategy, we obtain and compare with different phenomenological models, which have been investigated recently and demonstrate resolution of singularity by quantum geometry effects via a bounce. These include models with areal gauge fixing, a polymerized vacuum solution, polymerized junction conditions, and an Oppenheimer-Snyder dust collapse model. An important insight from our approach is that the dynamical equations care about the $\mathrm{det}(e)$ part rather than the square root of the determinant of the spatial metric. As a result, shock solutions that have been argued to exist in some models are found to be absent even if one considers coordinate transformations.

We propose a new model of the spherical symmetric quantum black hole in the reduced phase space formulation. We deparametrize gravity by coupling to the Gaussian dust which provides the material coordinates. The foliation by dust coordinates covers both the interior and exterior of the black hole. After the spherical symmetry reduction, our model is a 1 + 1 dimensional field theory containing infinitely many degrees of freedom. The effective dynamics of the quantum black hole is generated by an improved physical Hamiltonian H _Δ. The holonomy correction in H _Δ is implemented by the μ ¯ -scheme regularization with a Planckian area scale Δ (which often chosen as the minimal area gap in loop quantum gravity). The effective dynamics recovers the semiclassical Schwarzschild geometry at low curvature regime and resolves the black hole singularity with Planckian curvature, e.g. R _μνρσ R ^μνρσ ∼ 1/Δ². Our model predicts that the evolution of the black hole at late time reaches the charged Nariai geometry dS₂ × S ² with Planckian radii ∼ Δ . The Nariai geometry is stable under linear perturbations but may be unstable by nonperturbative quantum effects. Our model suggests the existence of quantum tunneling of the Nariai geometry and a scenario of black-hole-to-white-hole transition.