Related papers: Garrett approximation revisited
Many systems of interest in general relativistic astrophysics, including neutron stars, accreting compact objects in X-ray binaries and active galactic nuclei, core collapse, and collapsars, are assumed to be approximately spherically…
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…
A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…
Gravitational-wave observations of quasicircular compact binary mergers imply complicated posterior measurements of their parameters. Though Gaussian approximations to the pertinent likelihoods have decades of history in the field, the…
Certain quantum topological invariants of three manifolds can be written in the form of the Gaussian sum. It is shown that such topological invariants can be approximated efficiently by a quantum computer. The invariants discussed here are…
Gauss quadrature integral approximation is extended to include integrals with a measure consisting of continuous as well as discrete components. That is, we give an approximation for the integral of a function plus its sum over a discrete…
We analyze the convergence of quasi-Newton methods in exact and finite precision arithmetic. In particular, we derive an upper bound for the stagnation level and we show that any sufficiently exact quasi-Newton method will converge…
In the first part of this thesis, Kerr-Schild metrics and extended Kerr-Schild metrics are analyzed in the context of higher dimensional general relativity. Employing the higher dimensional generalizations of the Newman-Penrose formalism…
In this work, we obtain the analytically approximation of static, spherically symmetric black hole solutions to Einstein$-$Weyl squared gravity by using the continued fraction expansion method. The black hole solutions are found for various…
Exact stationary axially symmetric solutions of the 4D Einstein equations with corotating pressureless perfect fluid sources are studied. A particular solution with approximately flat rotation curve is discussed in some detail. We find that…
I discuss gauge and global symmetries in particle physics, condensed matter physics, and quantum gravity. In a modern understanding, global symmetries are approximate and gauge symmetries may be emergent. (Based on a lecture at the April,…
This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…
This paper presents the classification of a general quadric into an axisymmetric quadric (AQ) and the solution to the problem of the proximity of a given point to an AQ. The problem of proximity in $R^3$ is reduced to the same in $R^2$,…
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…
Detailed observations of phenomena involving black holes, be it via gravitational waves or more traditional electromagnetic means, can probe the strong field regime of the gravitational interaction. The prediction of features in such…
We give a novel procedure for approximating general single-qubit unitaries from a finite universal gate set by reducing the problem to a novel magnitude approximation problem, achieving an immediate improvement in sequence length by a…
We do not yet know how to quantize gravity in 3+1 dimensions, but in lower dimensions we face the opposite problem: many of the approaches originally developed for (3+1)-dimensional gravity can be successfully implemented in 2+1 dimensions,…
There are strong reasons to believe that global symmetries of quantum theories cannot be exact in the presence of gravity. While this has been argued at the qualitative level, establishing a quantitative statement is more challenging. In…
In this comment we show that the approach presented by Foj\'on et al~\cite{Fojon10} is not as accurate as they claim. A straightforward calculation using the models considered buy those authors clearly shows that the spectral method, which…
This note includes results of a study of stationary spherically symmetric ``dark holes'', objects merging central black holes and peripheral scalar graviton dark haloes arising in the framework of the modified gravity -- the quartet-metric,…