scholarly journals Charged Dirac perturbations on Reissner-Nordström–anti–de Sitter spacetimes: Quasinormal modes with Robin boundary conditions

2019 ◽  
Vol 100 (12) ◽  
Author(s):  
Mengjie Wang ◽  
Carlos Herdeiro ◽  
Jiliang Jing
Keyword(s):  
Boundary Conditions ◽  
Quasinormal Modes ◽  
Robin Boundary Conditions ◽  
De Sitter ◽  
Robin Boundary

scholarly journals Maxwell perturbations in a cavity with Robin boundary conditions: two branches of modes with spectrum bifurcation on Schwarzschild black holes

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Yunhe Lei ◽  
Mengjie Wang ◽  
Jiliang Jing
Keyword(s):  
Black Holes ◽  
Boundary Conditions ◽  
Energy Flux ◽  
Maxwell Equations ◽  
Quasinormal Modes ◽  
De Sitter ◽  
Angular Momentum Quantum Number ◽  
Ads Black Holes ◽  
Maxwell Fields ◽  
Robin Boundary

AbstractWe perform a systematic study of the Maxwell quasinormal spectrum in a mirror-like cavity following the generic Robin type vanishing energy flux principle, by starting with the Schwarzschild black holes in this paper. It is shown that, for black holes in a cavity, the vanishing energy flux principle leads to two different sets of boundary conditions. By solving the Maxwell equations with these two boundary conditions both analytically and numerically, we observe two distinct sets of modes. This indicates that the vanishing energy flux principle may be applied not only to asymptotically anti-de Sitter (AdS) black holes but also to black holes in a cavity. In the analytic calculations, the imaginary part of the Maxwell quasinormal modes are derived analytically for both boundary conditions, which match well with the numeric results. While in the numeric calculations, we complete a thorough study on the two sets of the Maxwell spectrum by varying the mirror radius $$r_m$$ r m , the angular momentum quantum number $$\ell $$ ℓ , and the overtone number N. In particular, we proclaim that the Maxwell spectrum may bifurcate for both modes when the mirror is placed around the black hole event horizon, which is analogous to the spectrum bifurcation effects found for the Maxwell fields on asymptotically AdS black holes. This observation provides another example to exhibit the similarity between black holes in a cavity and the AdS black holes.

scholarly journals An efficient adaptive grid method for a system of singularly perturbed convection-diffusion problems with Robin boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Li-Bin Liu ◽  
Ying Liang ◽  
Xiaobing Bao ◽  
Honglin Fang
Keyword(s):  
Boundary Conditions ◽  
Grid Method ◽  
Posteriori Error ◽  
Adaptive Grid ◽  
Singularly Perturbed ◽  
Robin Boundary Conditions ◽  
Euler Formula ◽  
Convection Diffusion ◽  
Backward Euler ◽  
Robin Boundary

AbstractA system of singularly perturbed convection-diffusion equations with Robin boundary conditions is considered on the interval $[0,1]$ [ 0 , 1 ] . It is shown that any solution of such a problem can be expressed to a system of first-order singularly perturbed initial value problem, which is discretized by the backward Euler formula on an arbitrary nonuniform mesh. An a posteriori error estimation in maximum norm is derived to design an adaptive grid generation algorithm. Besides, in order to establish the initial values of the original problems, we construct a nonlinear optimization problem, which is solved by the Nelder–Mead simplex method. Numerical results are given to demonstrate the performance of the presented method.

Sign in / Sign up

Export Citation Format

Share Document