scholarly journals Lie point symmetries of near-horizon geometry equation

2020 ◽  
Vol 102 (12) ◽  
Author(s):  
E. Buk ◽  
J. Lewandowski ◽  
A. Szereszewski
Keyword(s):  
Lie Point Symmetries ◽  
Horizon Geometry

scholarly journals Uptunneling to de Sitter

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Mehrdad Mirbabayi
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
False Vacuum ◽  
De Sitter ◽  
Dimensional Theory ◽  
Hole Geometry ◽  
Horizon Geometry ◽  
Two Sides ◽  
Extremal Black Holes

Abstract We propose a Euclidean preparation of an asymptotically AdS2 spacetime that contains an inflating dS2 bubble. The setup can be embedded in a four dimensional theory with a Minkowski vacuum and a false vacuum. AdS2 approximates the near horizon geometry of a two-sided near-extremal Reissner-Nordström black hole, and the two sides can connect to the same Minkowski asymptotics to form a topologically nontrivial worm- hole geometry. Likewise, in the false vacuum the near-horizon geometry of near-extremal black holes is approximately dS2 times 2-sphere. We interpret the Euclidean solution as describing the decay of an excitation inside the wormhole to a false vacuum bubble. The result is an inflating region inside a non-traversable asymptotically Minkowski wormhole.

scholarly journals Projective Collineations of Decomposable Spacetimes Generated by the Lie Point Symmetries of Geodesic Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1018
Author(s):  
Andronikos Paliathanasis
Keyword(s):  
Differential Equations ◽  
Riemannian Space ◽  
Dimensional Subspace ◽  
Geometric Construction ◽  
Lie Point Symmetries ◽  
Geodesic Equations ◽  
Symmetries Of Differential Equations ◽  
Projective Collineations

We investigate the relation of the Lie point symmetries for the geodesic equations with the collineations of decomposable spacetimes. We review previous results in the literature on the Lie point symmetries of the geodesic equations and we follow a previous proposed geometric construction approach for the symmetries of differential equations. In this study, we prove that the projective collineations of a n+1-dimensional decomposable Riemannian space are the Lie point symmetries for geodesic equations of the n-dimensional subspace. We demonstrate the application of our results with the presentation of applications.

scholarly journals Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Tanki Motsepa ◽  
Chaudry Masood Khalique ◽  
Motlatsi Molati
Keyword(s):  
Option Pricing ◽  
Three Dimensional ◽  
Mathematical Finance ◽  
Group Classification ◽  
Lie Point Symmetries ◽  
Group Invariant ◽  
Black Scholes ◽  
Group Invariant Solutions ◽  
Bond Option

We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.

scholarly journals AdS3 GRAVITATIONAL INSTANTONS FROM CONFORMAL FIELD THEORY

1999 ◽  
Vol 14 (28) ◽  
pp. 1961-1981 ◽  
Author(s):  
SHUHEI MANO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Bound States ◽  
Three Dimensional ◽  
Partition Functions ◽  
De Sitter ◽  
Btz Black Hole ◽  
Gravitational Instantons ◽  
Conformal Field ◽  
Horizon Geometry

A conformal field theory on the boundary of three-dimensional asymptotic anti-de Sitter spaces which appear as near horizon geometry of D-brane bound states is discussed. It is shown that partition functions of gravitational instantons appear as high and low temperature limits of the partition function of the conformal field theory. The result reproduces phase transition between the anti-de Sitter space and the BTZ black hole in the bulk gravity.

scholarly journals How to construct the discrete symmetries of partial differential equations

2000 ◽  
Vol 11 (5) ◽  
pp. 515-527 ◽  
Author(s):  
P. E. HYDON
Keyword(s):  
Differential Equation ◽  
Discrete Symmetries ◽  
Gas Dynamics ◽  
Burgers Equation ◽  
Lie Point Symmetries ◽  
Discrete Point ◽  
Nonlocal Symmetry ◽  
Partial Differential ◽  
Nontrivial Group ◽  
Harry Dym Equation

This paper introduces an algorithm for calculating all discrete point symmetries of a given partial differential equation with a known nontrivial group of Lie point symmetries. The method enables the user to determine the discrete symmetries with little more effort than is used to find the Lie symmetries. It is used to obtain the discrete point symmetries of Burgers' equation, the spherical Burgers' equation, and the Harry–Dym equation. The method can be extended to some types of nonlocal symmetry; we derive the quasi-local discrete symmetries of a system of PDEs from gas dynamics.

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