arXiv subjects
Publications and source records attributed to Viqar Husain.
We present an asymptotically flat spherically symmetric non-singular metric that describes gravitational collapse and matter bounce with transient black hole and white hole regions. The metric provides a dynamical counterpart to proposed static non-singular black holes, and a phenomenological model for possible black hole to white hole transitions in quantum gravity.
During gravitational collapse of dust in spherical symmetry, matter particles may collide forming shell crossing surfaces (SCS) on which the Einstein equations become indeterministic. We show that there is a unique evolution beyond SCS such that a propagating shock wave forms, the metric remains continuous, and the stress-energy tensor dynamically becomes that of a thin shell. We give numerical simulations that exhibit this result.
We show that the canonical formulation of the semiclassical Einstein equation, where the matter terms in the constraints are replaced by expectation values of the corresponding operators in quantum states, is inconsistent due to the non-closure of the resulting constraint algebra.
We use a Hamiltonian version of the semiclassical Einstein equation to study classical gravity coupled to a quantum scalar field with potential in spherical symmetry. The system is defined by effective constraints where the matter terms are replaced by their expectation values in a quantum state. For the static case, we find numerically that the resulting equations admit asymptotically flat, de Sitter, and anti-de Sitter boson star and regular black hole solutions. We also show that the Bardeen and Hayward nonsingular black hole proposals (and some generalizations thereof) are not solutions to our equations.
We present a Group Field Theory (GFT) quantization of the Husain-Kuchař (HK) model formulated as a non-interacting GFT. We demonstrate that the path-integral formulation of this HK-GFT provides a complete spinfoam model and a unique Fock representation that describes the quantum three-geometries of the HK model. These results provide a link to the canonical quantization of the HK model and demonstrate how GFTs can bridge distinct quantization schemes.
We present a semiclassical study of the Mixmaster cosmology minimally coupled to a massive scalar field in the Hamiltonian formalism, with focus on three distinct scenarios: the classical cosmology coupled to the quantized scalar field, and "effective" cosmology, with spacetime discreteness corrections, coupled to the classical scalar field, and to the quantized scalar field. We find several results: (i) the effective cosmology undergoes several small bounces before expanding, with scalar field excitations rising through the bounce; (ii) anisotropies rise and fall as the universe undergoes a bounce, a feature that is enhanced with matter; (iii) Lyapunov exponents reveal that chaos is reduced in the effective systems compared to the classical case.
In quantum cosmology, it is expected that the Big Bang singularity is resolved and the universe undergoes a bounce. We find that for Gaussian initial states, matter-gravity entanglement entropy rises rapidly during the bounce, declines, and then approaches a steady-state value following the bounce. These observations suggest that matter-gravity entanglement is a feature of the macroscopic universe and that there is no Second Law of entanglement entropy.
We describe quantization schemes for scalar field cosmology in the metric variables with fundamental discreteness imposed with a lattice. The variables chosen for quantization determine the lattice, and each lattice produces distinct effective equations derived from semiclassical states. We show that requiring a bounce at the Planck density uniquely selects the volume lattice and gives the same effective Friedmann equation as that obtained in loop quantum cosmology. We also present conditions for the validity of the effective equations.
Global time is a gauge or relational choice of time variable in canonical gravity. Local time is the time used in a flat patch of spacetime. We compare the dynamics of a scalar field with respect to choices of global time and Minkowski patch time in an expanding cosmology. Our main results are that evolutions starting from the same initial conditions are similar on the time scales of terrestrial experiments, and that global time leads to a mechanism for evolving coupling constants.
Effective models of gravitational collapse in loop quantum gravity for the Lemaître-Tolman-Bondi spacetime predict that collapsing matter reaches a maximum finite density, bounces, and then expands outwards. We show that in the marginally bound case, shell-crossing singularities commonly occur for inhomogeneous initial profiles of the dust energy density; this is the case in particular for all profiles that are continuous and of compact support, including configurations arbitrarily close to the Oppenheimer-Snyder model. When a shell-crossing singularity occurs, it is necessary to seek weak solutions to the dynamics; we argue that weak solutions typically contain shock waves.
We study the classical-quantum (CQ) hybrid dynamics of homogeneous cosmology from a Hamiltonian perspective where the classical gravitational phase space variables and matter state evolve self-consistently with full backreaction. We compare numerically the classical and CQ dynamics for isotropic and anisotropic models, including quantum scalar-field induced corrections to the Kasner exponents. Our results indicate that full backreaction effects leave traces at late times in cosmological evolution; in particular, the scalar energy density at late times provides a potential contribution to dark energy. We also show that the CQ equations admit exact static solutions for the isotropic, and the anisotropic Bianchi IX universes with the scalar field in a stationary state.
We present a 4-dimensional generally covariant gauge theory which leads to the Gauss constraint but lacks both the Hamiltonian and spatial diffeomorphism constraints. The canonical theory therefore resembles Yang-Mills theory without the Hamiltonian. We describe its observables, quantization, and some generalizations.
We study spin models on Euclidean black hole backgrounds. These resemble the Ising model, but are inhomogeneous with two parameters, the black hole mass and the cosmological constant. We use Monte-Carlo methods to study macroscopic properties of these systems for Schwarzschild and anti-deSitter black holes in four and five dimensions for spin-1/2 and spin-1. We find in every case that increasing the black hole mass causes the spins to undergo a second order phase transition from disorder to order and that the phase transition occurs at sub-Planckian black hole mass.
We derive a "classical-quantum" approximation scheme for a broad class of bipartite quantum systems from fully quantum dynamics. In this approximation, one subsystem evolves via classical equations of motion with quantum corrections, and the other subsystem evolves quantum mechanically with equations of motion informed by the evolving classical degrees of freedom. Using perturbation theory, we derive an estimate for the growth rate of entanglement of the subsystems and deduce a "scrambling time" - the time required for the subsystems to become significantly entangled from an initial product state. We argue that a necessary condition for the validity of the classical-quantum approximation is consistency of initial data with the generalized Bohr correspondence principle. We illustrate the general formalism by numerically studying the fully quantum, fully classical, and classical-quantum dynamics of a system of two oscillators with nonlinear coupling. This system exhibits parametric resonance, and we show that quantum effects quench parametric resonance at late times. Lastly, we present a curious late-time scaling relation between the average value of the von Neumann entanglement of the interacting oscillator system and its total energy: $S\sim 2/3 \ln E$.
We describe a case of indeterminacy in general relativity for homogeneous and isotropic cosmologies for a class of dark energy fluids. The cosmologies are parametrized by an equation of state variable, with one instance giving the same solution as Norton's mechanical dome. Our example goes beyond previously studied cases in that indeterminacy lies in the evolution of spacetime itself: the onset of the Big Bang is indeterminate. We show further that the indeterminacy is resolved if the dynamics is viewed relationally.
It is widely accepted that curvature singularity resolution should be a feature of quantum gravity. We present a class of time-dependent asymptotically flat spherically symmetric metrics that model gravitational collapse in quantum gravity. The metrics capture intuitions associated with the dynamics of singularity resolution, and horizon formation and evaporation following a matter bounce. A parameter in the metric associated with the speed of the bounce determines black hole lifetime as a power of its mass; this includes the Hawking evaporation time $M^{3}$.
Motivated by quantum gravity, semi-classical theory, and quantum theory on curved spacetimes, we study the system of an oscillator coupled to two spin-1/2 particles. This model provides a prototype for comparing three types of dynamics: the full quantum theory, the classical oscillator with spin backreaction, and spins propagating on a fixed oscillator background. From nonperturbative calculations of oscillator and entanglement entropy dynamics, we find that entangled tripartite states produce novel oscillator trajectories, and that the three systems give equivalent dynamics for sufficiently weak oscillator-spin couplings, but deviate significantly for intermediate couplings. These results suggest that semiclassical dynamics with back reaction does not provide a suitable intermediate regime between quantum gravity and quantum theory on curved spacetime.
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.