Solution of the deformed Schwarzschild metric by the Yang-Baxter equation

This chapter discusses the Schwarzschild black hole. It demonstrates how, by a judicious change of coordinates, it is possible to eliminate the singularity of the Schwarzschild metric and reveal a spacetime that is much larger, like that of a black hole. At the end of its thermonuclear evolution, a star collapses and, if it is sufficiently massive, does not become stabilized in a new equilibrium configuration. The Schwarzschild geometry must therefore represent the gravitational field of such an object up to r = 0. This being said, the Schwarzschild metric in its original form is singular, not only at r = 0 where the curvature diverges, but also at r = 2m, a surface which is crossed by geodesics.

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Classification of Non-Degenerate Involutive Set-Theoretic Solutions to the Yang-Baxter Equation with Multipermutation Level Two

Algebras and Representation Theory ◽

10.1007/s10468-021-10067-5 ◽

2021 ◽

Author(s):

Wolfgang Rump

Keyword(s):

Baxter Equation

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Mapping TASEP back in time

Probability Theory and Related Fields ◽

10.1007/s00440-021-01074-0 ◽

2021 ◽

Author(s):

Leonid Petrov ◽

Axel Saenz

Keyword(s):

Markov Process ◽

Continuous Time ◽

Exclusion Process ◽

Discrete Space ◽

Baxter Equation ◽

Simple Exclusion Process ◽

Open Questions ◽

Asymmetric Simple Exclusion ◽

Simple Exclusion ◽

Hammersley Process

AbstractWe obtain a new relation between the distributions $$\upmu _t$$ μ t at different times $$t\ge 0$$ t ≥ 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions $$\upmu _t$$ μ t backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving $$\upmu _t$$ μ t which in turn brings new identities for expectations with respect to $$\upmu _t$$ μ t . The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang–Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.

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Maximal extension of the Schwarzschild metric: From Painlevé–Gullstrand to Kruskal–Szekeres

Annals of Physics ◽

10.1016/j.aop.2021.168497 ◽

2021 ◽

pp. 168497

Author(s):

José P.S. Lemos ◽

Diogo L.F.G. Silva

Keyword(s):

Maximal Extension ◽

Schwarzschild Metric

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The geometry of null-like disformal transformations

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887819501809 ◽

2019 ◽

Vol 16 (11) ◽

pp. 1950180 ◽

Cited By ~ 2

Author(s):

I. P. Lobo ◽

G. G. Carvalho

Keyword(s):

Vector Field ◽

Conformal Transformation ◽

Vector Fields ◽

Killing Vector ◽

Killing Vector Fields ◽

Spinor Structure ◽

Schwarzschild Metric ◽

Killing Vectors ◽

Symmetry Properties ◽

Geometric Objects

Motivated by the hindrance of defining metric tensors compatible with the underlying spinor structure, other than the ones obtained via a conformal transformation, we study how some geometric objects are affected by the action of a disformal transformation in the closest scenario possible: the disformal transformation in the direction of a null-like vector field. Subsequently, we analyze symmetry properties such as mutual geodesics and mutual Killing vectors, generalized Weyl transformations that leave the disformal relation invariant, and introduce the concept of disformal Killing vector fields. In most cases, we use the Schwarzschild metric, in the Kerr–Schild formulation, to verify our calculations and results. We also revisit the disformal operator using a Newman–Penrose basis to show that, in the null-like case, this operator is not diagonalizable.

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Trace and determinant in algebras associated with the yang-baxter equation

Functional Analysis and Its Applications ◽

10.1007/bf02577142 ◽

1987 ◽

Vol 21 (3) ◽

pp. 239-240

Author(s):

D. I. Gurevich

Keyword(s):

Baxter Equation

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Ore extensions of quasitriangular Hopf group coalgebras

Journal of Algebra and Its Applications ◽

10.1142/s0219498814500169 ◽

2014 ◽

Vol 13 (06) ◽

pp. 1450016 ◽

Cited By ~ 1

Author(s):

Daowei Lu ◽

Dingguo Wang

Keyword(s):

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Baxter Equation ◽

Ore Extension ◽

Ore Extensions ◽

Necessary And Sufficient

In this paper, we mainly consider some special Ore extension of quasitriangular Hopf group coalgebra, and give the necessary and sufficient conditions when the Ore extension of quasitriangular Hopf group coalgebras will preserve the same quasitriangular structure. Furthermore, in the two examples given at the end, we construct new solutions of Yang–Baxter equation of Hopf group coalgebras version.

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