Gaurav Khanna

Lattice refining loop quantum cosmology, anisotropic models and stability

A general class of loop quantizations for anisotropic models is introduced and discussed, which enhances loop quantum cosmology by relevant features seen in inhomogeneous situations. The main new effect is an underlying lattice which is being refined during dynamical changes of the volume. In general, this leads to a new feature of dynamical difference equations which may not have constant step-size, posing new mathematical problems. It is discussed how such models can be evaluated and what lattice refinements imply for semiclassical behavior. Two detailed examples illustrate that stability conditions can put strong constraints on suitable refinement models, even in the absence of a fundamental Hamiltonian which defines changes of the underlying lattice. Thus, a large class of consistency tests of loop quantum gravity becomes available. In this context, it will also be seen that quantum corrections due to inverse powers of metric components in a constraint are much larger than they appeared recently in more special treatments of isotropic, free scalar models where they were artificially suppressed.

Massive scalar field instability in Kerr spacetime

We study the Klein-Gordon equation for a massive scalar field in Kerr spacetime in the time-domain. We demonstrate that under conditions of super-radiance, the scalar field becomes unstable and its amplitude grows without bound. We also estimate the growth rate of this instability.

Universality of massive scalar field late-time tails in black-hole spacetimes

The late-time tails of a massive scalar field in the spacetime of black holes are studied numerically. Previous analytical results for a Schwarzschild black hole are confirmed: The late-time behavior of the field as recorded by a static observer is given by

Generating function techniques for loop quantum cosmology

\ensuremath{\psi}(t)\ensuremath{\sim}{t}^{\ensuremath{-}5/6}\mathrm{sin}[\ensuremath{\omega}(t)\ifmmode\times\else\texttimes\fi{}t],

Wave functions for the Schwarzschild black hole interior

where

Numerical solutions to lattice-refined models in loop quantum cosmology

\ensuremath{\omega}(t)

A SPECTRAL COLLOCATION APPROXIMATION FOR THE RADIAL-INFALL OF A COMPACT OBJECT INTO A SCHWARZSCHILD BLACK HOLE

depends weakly on time. This result is carried over to the case of a Kerr black hole. In particular, it is found that the power-law index of

Computational Efficiency of Frequency- and Time-Domain Calculations of Extreme Mass-Ratio Binaries: Equatorial Orbits

\ensuremath{-}5/6

Instabilities in numerical loop quantum cosmology

depends on neither the multipole mode

Intermediate behavior of Kerr tails

\mathcal{l}