The purpose of the studies presented in this paper is to point out the need for further work towards a definitive answer to the following question: How do perturbations of a rotating black hole get radiated away? Using the Teukolsky formalism [1], we can search for an answer to that question by studying the evolution of a complex spin-weighted wavefunction that is defined in terms of curvature ...

I summarize the basic ideas and formalism of loop quantum gravity. I illustrate the results on the discrete aspects of quantum geometry and two applications of these results to black hole physics. In particular, I discuss in detail the derivation of the Bekenstein-Hawking formula for the entropy of a black hole from rst principles.

We present a numerical study of the effects of carrier diffusion and spatial hole-burning in vertical-cavity surfaceemitting lasers under gain switching. Our model includes spatial and temporal dependences of both the optical field and the carrier density. Results show that spatial hole burning places a limit on the minimum achievable pulse width. We demonstrate that spatial hole-burning can be...

We investigate giant and dual giant type BPS configurations in the nearhorizon geometry of a certain 1 16 -BPS AdS5 black hole. By quantising the space of solutions we count the dual giant configurations and compare with the black hole entropy. This suggests a missing degeneracy factor which we argue comes from an angular momentum quantum number. From the D-brane world volume this arises from B...

The purpose of this paper is to present a generalized hole argument for gauge field theories and their geometrical setting in terms of fiber bundles. The generalized hole argument is motivated and extended from the spacetime hole arguments which appear in spacetime theories based on differentiable manifolds such as general relativity. Analogously, the generalized hole argument rules out fiber b...

We investigate giant and dual giant type BPS configurations in the nearhorizon geometry of a certain 1 16 -BPS AdS5 black hole. By quantising the space of solutions we count the dual giant configurations and compare with the black hole entropy. This suggests a missing degeneracy factor which we argue comes from an angular momentum quantum number. From the D-brane world volume this arises from B...

A paradigm describing black hole evaporation in non-perturbative quantum gravity is developed by combining two sets of detailed results: i) resolution of the Schwarzschild singularity in loop quantum gravity [1]; and ii) time-evolution of black holes in the dynamical horizon framework [2, 3, 4]. Quantum geometry effects introduce a major modification in the traditional space-time diagram of bla...

We review the way the BTZ black hole relaxes back to thermal equilibrium after a small perturbation and how it is seen in the boundary (finite volume) CFT. The unitarity requires the relaxation to be quasi-periodic. It is preserved in the CFT but is not obvious in the case of the semiclassical black hole the relaxation of which is driven by complex quasi-normal modes. We discuss two ways of mod...

We present an in-depth examination of the effectiveness of radial basis function kernel (beyond Gaussian) estimators based on orthogonal random feature maps. We show that orthogonal estimators outperform state-of-the-art mechanisms that use iid sampling under weak conditions for tails of the associated Fourier distributions. We prove that for the case of many dimensions, the superiority of the ...

We derive simple bootstrap bounds on correlation functions of the BFSS matrix theory/D0-brane quantum mechanics. The result strengthens and extends Polchinski's virial theorem bound to finite energies gives first non-trivial $\langle{\text{Tr}\, X^2\rangle}$. Despite their simplicity, hint at some features dual black hole geometry. Our best lower are already a factor $\sim 2$ from existing Mont...