A proof of the uniqueness theorem for axionic black holes

1991 ◽  
Vol 8 (4) ◽  
pp. 779-785 ◽  
Author(s):  
Rue-Ron Hsu
Keyword(s):  
Black Holes ◽  
Uniqueness Theorem ◽  
The Uniqueness Theorem

scholarly journals HORIZON MASS THEOREM

2005 ◽  
Vol 14 (12) ◽  
pp. 2219-2225 ◽  
Author(s):  
YUAN K. HA
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Uniqueness Theorem ◽  
Hawking Radiation ◽  
General Theorem ◽  
Positive Energy ◽  
Singularity Theorem ◽  
Area Theorem ◽  
Classical Black Holes ◽  
The Uniqueness Theorem

A new theorem for black holes is found. It is called the horizon mass theorem. The horizon mass is the mass which cannot escape from the horizon of a black hole. For all black holes, neutral, charged or rotating, the horizon mass is always twice the irreducible mass observed at infinity. Previous theorems on black holes are: (i) the singularity theorem, (ii) the area theorem, (iii) the uniqueness theorem, (iv) the positive energy theorem. The horizon mass theorem is possibly the last general theorem for classical black holes. It is crucial for understanding Hawking radiation and for investigating processes occurring near the horizon.

scholarly journals Distorted vacuum black holes in the canonical ensemble

2019 ◽  
Vol 34 (07n08) ◽  
pp. 1950060
Author(s):  
O. B. Zaslavskii
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Coordinate System ◽  
Uniqueness Theorem ◽  
Canonical Ensemble ◽  
Finite Size ◽  
Horizon Area ◽  
Spatial Symmetry ◽  
Flat Spacetime ◽  
The Uniqueness Theorem

We consider a vacuum static spacetime in a finite size cavity. On the boundary, we specify a metric and a finite constant local temperature [Formula: see text]. No spherical or any other spatial symmetry is assumed. We show that (i) inside a cavity, only a black hole or flat spacetime are possible, whereas a curved horizonless regular spacetime is excluded, (ii) in the limit when the horizon area shrinks, the Hawking temperature diverges, (iii) for the existence of a black hole, [Formula: see text] should be high enough. When [Formula: see text], a black hole phase is favorable thermodynamically. Our consideration essentially uses the coordinate system introduced by Israel in his famous proof of the uniqueness theorem.

scholarly journals The uniqueness theorem for entanglement measures

2002 ◽  
Vol 43 (9) ◽  
pp. 4252-4272 ◽  
Author(s):  
Matthew J. Donald ◽  
Michał Horodecki ◽  
Oliver Rudolph
Keyword(s):  
Uniqueness Theorem ◽  
Entanglement Measures ◽  
The Uniqueness Theorem

scholarly journals On the uniqueness theorem

1970 ◽  
Vol 14 (3) ◽  
pp. 376-384 ◽  
Author(s):  
Helmut Bender
Keyword(s):  
Uniqueness Theorem ◽  
The Uniqueness Theorem

scholarly journals Link theorem and distributions of solutions to uncertain Liouville-Caputo difference equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hari Mohan Srivastava ◽  
Pshtiwan Othman Mohammed ◽  
Juan L. G. Guirao ◽  
Y. S. Hamed
Keyword(s):  
Uniqueness Theorem ◽  
Difference Equations ◽  
Special Linear ◽  
Uncertain Variables ◽  
Important Theorem ◽  
Special Case ◽  
The Uniqueness Theorem

<p style='text-indent:20px;'>We consider a class of initial fractional Liouville-Caputo difference equations (IFLCDEs) and its corresponding initial uncertain fractional Liouville-Caputo difference equations (IUFLCDEs). Next, we make comparisons between two unique solutions of the IFLCDEs by deriving an important theorem, namely the main theorem. Besides, we make comparisons between IUFLCDEs and their <inline-formula><tex-math id="M1">\begin{document}$ \varrho $\end{document}</tex-math></inline-formula>-paths by deriving another important theorem, namely the link theorem, which is obtained by the help of the main theorem. We consider a special case of the IUFLCDEs and its solution involving the discrete Mittag-Leffler. Also, we present the solution of its <inline-formula><tex-math id="M2">\begin{document}$ \varrho $\end{document}</tex-math></inline-formula>-paths via the solution of the special linear IUFLCDE. Furthermore, we derive the uniqueness of IUFLCDEs. Finally, we present some test examples of IUFLCDEs by using the uniqueness theorem and the link theorem to find a relation between the solutions for the IUFLCDEs of symmetrical uncertain variables and their <inline-formula><tex-math id="M3">\begin{document}$ \varrho $\end{document}</tex-math></inline-formula>-paths.</p>

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