arXiv subjects

Robert Santacruz

Publications and source records attributed to Robert Santacruz.

5 recordsLinked to original sources

arXiv2023

Stationary cosmology in group field theory

Group field theory (GFT) models for quantum gravity coupled to a massless scalar field give rise to cosmological models that reproduce the (expanding or contracting) dynamics of homogeneous and isotropic spacetimes in general relativity at low energies, while including high-energy corrections that lead to singularity resolution by a "bounce." Here we investigate two possibilities for obtaining stationary solutions in GFT cosmology, which could be useful as an analogue of Minkowski spacetime. We first focus on a limit in which interactions are neglected and the effective Newton's constant in GFT cosmology is taken to zero. In this limit, we derive an effective Friedmann equation that shows no stationary solutions, but departures from the trivial classical dynamics falling off rapidly, similar to the usual correction terms responsible for the bounce. Since the effective Newton's constant needs to be exactly zero, the scenario is fine-tuned. A more satisfactory approach is obtained in a weakly interacting model: we find bound states with sharply peaked volume, representing a stationary semiclassical cosmology, and show that coherent states peaked around the minimum of the potential remain stable with small quantum fluctuations, and only small oscillations around a nearly constant volume. These coherent states realise the idea of a "quantum gravity condensate."

hep-th↗

arXiv2022

Black hole collapse and bounce in effective loop quantum gravity

We derive effective equations with loop quantum gravity corrections for the Lemaître-Tolman-Bondi family of space-times, and use these to study quantum gravity effects in the Oppenheimer-Snyder collapse model. For this model, after the formation of a black hole with an apparent horizon, quantum gravity effects become important in the space-time region where the energy density and space-time curvature scalars become comparable to the Planck scale. These quantum gravity effects first stop the collapse of the dust matter field when its energy density reaches the Planck scale, and then cause the dust field to begin slowly expanding. Due to this continued expansion, the matter field will eventually extend beyond the apparent horizon, at which point the horizon disappears and there is no longer a black hole. There are no singularities anywhere in this space-time. In addition, in the limit that edge effects are neglected, we show that the dynamics for the interior of the star of uniform energy density follow the loop quantum cosmology effective Friedman equation for the spatially flat Friedman-Lemaître-Robertson-Walker space-time. Finally, we estimate the lifetime of the black hole, as measured by a distant observer, to be $\sim (GM)^2/\ell_{\rm Pl}$.

gr-qc↗

arXiv2022

Effective loop quantum gravity framework for vacuum spherically symmetric space-times

We develop an effective framework for the $\barμ$ scheme of holonomy corrections motivated by loop quantum gravity for vacuum spherically symmetric space-times. This is done by imposing the areal gauge in the classical theory, and then expressing the remaining components of the Ashtekar-Barbero connection in the Hamiltonian constraint in terms of holonomies of physical length $\ell_{\rm Pl}$. The stationary solutions to the effective Hamiltonian constraint can be found exactly, and we give the explicit form of the effective metric in Painlevé-Gullstrand coordinates. This solution has the correct classical limit, the quantum gravity corrections decay rapidly at large distances, and curvature scalars are bounded by the Planck scale, independently of the black hole mass $M$. In addition, the solution is valid for radii $x \ge x_{\rm min} \sim (\ell_{\rm Pl}^2 M)^{1/3}$ indicating the need for a matter field, with an energy density bounded by the Planck scale, to provide a source for the curvature in the space-time. Finally, for $M \gg m_{\rm Pl}$, the space-time has an outer and also an inner horizon, within which the expansion for outgoing radial null geodesics becomes positive again. On the other hand, for sufficiently small $M \sim m_{\rm Pl}$, there are no horizons at all in the effective metric.

gr-qc↗

arXiv2022

On the fate of quantum black holes

We study the quantum dynamics of the Lemaître-Tolman-Bondi space-times using a polymer quantization prescription based on loop quantum cosmology that incorporates fundamental discreteness. By solving an effective equation derived from this quantization, we find analytical solutions for the Oppenheimer-Snyder and thin-shell collapse models, and numerical solutions for a variety of asymptotically flat collapsing dust profiles. Our study (i) tracks the formation, evolution and disappearance of dynamical horizons, (ii) shows that matter undergoes a non-singular bounce that results in an outgoing shock wave, (iii) determines black hole lifetime to be proportional to the square its mass, and (iv) provides a conformal diagram that substantially modifies the standard "information loss" picture by resolving the singularity and replacing the event horizon by transient apparent horizons.

gr-qc↗

arXiv2022

Quantum gravity of dust collapse: shock waves from black holes

We study the quantum gravitational collapse of spherically symmetric pressureless dust. Using an effective equation derived from a polymer quantization in the connection-triad phase space variables of general relativity, we find numerically, for a variety of initial dust configurations, that (i) trapped surfaces form and disappear as an initially collapsing density profile evolves into an outgoing shockwave; (ii) black hole lifetime is proportional to the square of its mass; and (iii) there is no mass inflation at inner apparent horizons. These results provide a substantially different view of black hole formation and subsequent evolution than found from semiclassical analyses.

gr-qc↗