Topic
Coordinate singularity
About: Coordinate singularity is a research topic. Over the lifetime, 121 publications have been published within this topic receiving 2612 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, a simple semiclassical method based on the method of complex paths was used to obtain particle production in Schwarzschild-like spacetimes with a horizon. But this method was not suitable for the case of a purely time-dependent gauge.
Abstract: This paper discusses particle production in Schwarzschild-like spacetimes and in a uniform electric field. Both problems are approached using the method of complex path analysis which is used to describe tunnelling processes in semiclassical quantum mechanics. Particle production in Schwarzschild-like spacetimes with a horizon is obtained here by a new and simple semiclassical method based on the method of complex paths. Hawking radiation is obtained in the $(t,r)$ coordinate system of the standard Schwarzschild metric without requiring the Kruskal extension. The coordinate singularity present at the horizon manifests itself as a singularity in the expression for the semiclassical propagator for a scalar field. We give a prescription whereby this singularity is regularized with Hawking's result being recovered. The equation satisfied by a scalar field is also reduced to solving a one-dimensional effective Schr\"odinger equation with a potential $(\ensuremath{-}{1/x}^{2})$ near the horizon. Constructing the action for a fictitious nonrelativistic particle moving in this potential and applying the above mentioned prescription, one again recovers Hawking radiation. In the case of the electric field, standard quantum field theoretic methods can be used to obtain particle production in a purely time-dependent gauge. In a purely space-dependent gauge, however, the tunnelling interpretation has to be resorted to in order to recover the previous result. We attempt, in this paper, to provide a tunnelling description using the formal method of complex paths for both the time and space dependent gauges. The usefulness of such a common description becomes evident when ``mixed'' gauges, which are functions of both space and time variables, are analyzed. We report, in this paper, certain mixed gauges which have the interesting property that mode functions in these gauges are found to be a combination of elementary functions unlike the standard modes which are transcendental parabolic cylinder functions. Finally, we present an attempt to interpret particle production by the electric field as a tunnelling process between the two sectors of the Rindler spacetime.
815 citations
TL;DR: In this paper, a method for treating the coordinate singularity whereby singular coordinates are redefined so that data are differentiated smoothly through the pole, and avoiding placing a grid point directly at the pole is proposed.
343 citations
TL;DR: In this paper, the early-proper-time boundary dynamics of strongly coupled conformal plasma were studied in the regime of early proper-time using the AdS/CFT correspondence.
Abstract: Boost-invariant dynamics of a strongly-coupled conformal plasma is studied in the regime of early proper-time using the AdS/CFT correspondence. It is shown, in contrast with the late-time expansion, that a scaling solution does not exist. The boundary dynamics in this regime depends on initial conditions encoded in the bulk behavior of a Fefferman-Graham metric coefficient at initial proper-time. The relation between the early-time expansion of the energy density and initial conditions in the bulk of AdS is provided. As a general result it is proven that a singularity of some metric coefficient in Fefferman-Graham frame exists at all times. Requiring that this singularity at tau = 0 is a mere coordinate singularity without the curvature blow-up gives constraints on the possible boundary dynamics. Using a simple Pade resummation for solutions satisfying the regularity constraint, the features of a transition to local equilibrium, and thus to the hydrodynamical late-time regime, have been observed. The impact of this study on the problem of thermalization is discussed.
113 citations
TL;DR: In this article, the early-proper-time boundary dynamics of strongly coupled conformal plasma were studied in the regime of early proper-time using the AdS/CFT correspondence.
Abstract: Boost-invariant dynamics of a strongly-coupled conformal plasma is studied in the regime of early proper-time using the AdS/CFT correspondence. It is shown, in contrast with the late-time expansion, that a scaling solution does not exist. The boundary dynamics in this regime depends on initial conditions encoded in the bulk behavior of a Fefferman-Graham metric coefficient at initial proper-time. The relation between the early-time expansion of the energy density and initial conditions in the bulk of AdS is provided. As a general result it is proven that a singularity of some metric coefficient in Fefferman-Graham frame exists at all times. Requiring that this singularity at ? = 0 is a mere coordinate singularity without the curvature blow-up gives constraints on the possible boundary dynamics. Using a simple Pade resummation for solutions satisfying the regularity constraint, the features of a transition to local equilibrium, and thus to the hydrodynamical late-time regime, have been observed. The impact of this study on the problem of thermalization is discussed.
93 citations
TL;DR: In this paper, a finite-difference time-domain (FDTD) algorithm for the solution of electromagnetic scattering problems is formulated in numerically defined generalized coordinates in three dimensions and implemented in a code with the lowest order Bayliss-Turkel radiation boundary condition expressed in spherical coordinates.
Abstract: The finite-difference time-domain (FDTD) algorithm for the solution of electromagnetic scattering problems is formulated in numerically defined generalized coordinates in three dimensions and implemented in a code with the lowest order Bayliss-Turkel radiation boundary condition expressed in spherical coordinates. It is shown that the algorithm is capable of accurately tracking the progress of a pulse of electromagnetic radiation through the curvilinear mesh generated by a body of revolution, the only problems occurring in the vicinity of the rotation axis, which represents a coordinate singularity. A simple method to deal with this singular line is presented and discussed, and its is shown that, at least for the test problem, this approximation is sufficient. The algorithm discussed is useful for the solution of the exterior problem in the presence of conductors and dielectrics with complicated shapes and electrical compositions, and for near-field problems such as cavity penetration problems. The far fields are obtained by replacing the scatterer with a virtual surface enclosing all sources. >
84 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 4 |
| 2020 | 6 |
| 2019 | 3 |
| 2018 | 6 |
| 2017 | 4 |
| 2016 | 8 |