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Q u a s i - n o r m a l m o d e s : w h a t c a n r i n g i n g b l a c k h o l e s Q Q u u a a s s i i - - n n o o r r m m a a l l m m o o d d e e s s : : w w h h a

  1. Q u a s i - n o r m a l m o d e s : w h a t c a n r i n g i n g b l a c k h o l e s Q Q u u a a s s i i - - n n o o r r m m a a l l m m o o d d e e s s : : w w h h a a t t c c a a n n r r i i n n g g i i n n g g b b l l a a c c k k h h o o l l e e s s t e l l u s a b o u t q u a n t u m g r a v i t y ? t t e e l l l l u u s s a a b b o o u u t t q q u u a a n n t t u u m m g g r r a a v v i i t t y y ? ? J e n s B o o s ( s u p e r v i s o r : P r o f . V a l e r i P . F r o l o v ) J J e e n n s s B B o o o o s s ( ( s s u u p p e e r r v v i i s s o o r r : : P P r r o o f f . . V V a a l l e e r r i i P P . . F F r r o o l l o o v v ) ) b o o s @ u a l b e r t a . c a b b o o o o s s @ @ u u a a l l b b e e r r t t a a . . c c a a U n i v e r s i t y o f A l b e r t a U U n n i i v v e e r r s s i i t t y y o o f f A A l l b b e e r r t t a a F r i d a y , S e p t 2 3 , 2 0 1 6 , 1 3 : 0 0 F r i d a y , S e p t 2 3 , 2 0 1 6 , 1 3 : 0 0 F r i d a y , S e p t 2 3 , 2 0 1 6 , 1 3 : 0 0 T h e S e v e n t h A n n u a l S y m p o s i u m f o r G r a d u a t e P h y s i c s T T h h e e S S e e v v e e n n t t h h A A n n n n u u a a l l S S y y m m p p o o s s i i u u m m f f o o r r G G r r a a d d u u a a t t e e P P h h y y s s i i c c s s R e s e a r c h , U n i v e r s i t y o f A l b e r t a R R e e s s e e a a r r c c h h , , U U n n i i v v e e r r s s i i t t y y o o f f A A l l b b e e r r t t a a

  2. I n t r o d u c i n g : g r a v i t a t i o n a l w a v e G W1 5 0 9 1 4 1 / 1 0

  3. G W1 5 0 9 1 4 = c o l l i d i n g b l a c k h o l e s ! 2 / 1 0

  4. H o w i s t h a t r e l a t e d t o q u a s i - n o r m a l m o d e s ? 3 / 1 0

  5. H o w i s t h a t r e l a t e d t o q u a s i - n o r m a l m o d e s ? 3 / 1 0

  6. H o w i s t h a t r e l a t e d t o q u a s i - n o r m a l m o d e s ? 3 / 1 0

  7. Wh a t a r e q u a s i - n o r m a l m o d e s ? ( 1 / 2 ) 4 / 1 0

  8. Wh a t a r e q u a s i - n o r m a l m o d e s ? ( 1 / 2 ) 4 / 1 0

  9. Wh a t a r e q u a s i - n o r m a l m o d e s ? ( 1 / 2 ) 4 / 1 0

  10. Wh a t a r e q u a s i - n o r m a l m o d e s ? ( 1 / 2 ) 4 / 1 0

  11. Wh a t a r e q u a s i - n o r m a l m o d e s ? ( 2 / 2 ) 5 / 1 0

  12. Wh a t a r e q u a s i - n o r m a l m o d e s ? ( 2 / 2 ) Q u a s i - n o r m a l m o d e s = s t a n d i n g w a v e s + d i s s i p a t i o n . 5 / 1 0

  13. H o w d o w e d e s c r i b e q u a s i - n o r m a l m o d e s m a t h e m a t i c a l l y ? ( 1 / 3 ) A p p r o x i m a t e a m p l i t u d e a s . → c o r r e s p o n d s t o w i t h . 6 / 1 0

  14. H o w d o w e d e s c r i b e q u a s i - n o r m a l m o d e s m a t h e m a t i c a l l y ? ( 1 / 3 ) A p p r o x i m a t e a m p l i t u d e a s . → c o r r e s p o n d s t o w i t h . Wh e r e d o e s t h e a m p l i t u d e c o m e f r o m ? → s o l u t i o n o f w a v e e q u a t i o n 6 / 1 0

  15. H o w d o w e d e s c r i b e q u a s i - n o r m a l m o d e s m a t h e m a t i c a l l y ? ( 1 / 3 ) A p p r o x i m a t e a m p l i t u d e a s . → c o r r e s p o n d s t o w i t h . Wh e r e d o e s t h e a m p l i t u d e c o m e f r o m ? → s o l u t i o n o f w a v e e q u a t i o n A p p l i c a t i o n t o b l a c k h o l e s ? → s o l v e w a v e e q u a t i o n “ i n b l a c k h o l e b a c k g r o u n d ” 6 / 1 0

  16. H o w d o w e d e s c r i b e q u a s i - n o r m a l m o d e s m a t h e m a t i c a l l y ? ( 1 / 3 ) A p p r o x i m a t e a m p l i t u d e a s . → c o r r e s p o n d s t o w i t h . Wh e r e d o e s t h e a m p l i t u d e c o m e f r o m ? → s o l u t i o n o f w a v e e q u a t i o n A p p l i c a t i o n t o b l a c k h o l e s ? → s o l v e w a v e e q u a t i o n “ i n b l a c k h o l e b a c k g r o u n d ” Q u e s t i o n ( u s e d t o b e ) : I s t h e b l a c k h o l e s t a b l e ? 6 / 1 0

  17. H o w d o w e d e s c r i b e q u a s i - n o r m a l m o d e s m a t h e m a t i c a l l y ? ( 1 / 3 ) A p p r o x i m a t e a m p l i t u d e a s . → c o r r e s p o n d s t o w i t h . Wh e r e d o e s t h e a m p l i t u d e c o m e f r o m ? → s o l u t i o n o f w a v e e q u a t i o n A p p l i c a t i o n t o b l a c k h o l e s ? → s o l v e w a v e e q u a t i o n “ i n b l a c k h o l e b a c k g r o u n d ” Q u e s t i o n ( n o w ) : Wh a t c a n w e l e a r n a b o u t q u a n t u m g r a v i t y ? 6 / 1 0

  18. H o w d o w e d e s c r i b e q u a s i - n o r m a l m o d e s m a t h e m a t i c a l l y ? ( 2 / 3 ) z y x E u c l i d e a n s p a c e t h e 2 - s p h e r e 7 / 1 0

  19. H o w d o w e d e s c r i b e q u a s i - n o r m a l m o d e s m a t h e m a t i c a l l y ? ( 2 / 3 ) z y x E u c l i d e a n s p a c e t h e 2 - s p h e r e 7 / 1 0

  20. H o w d o w e d e s c r i b e q u a s i - n o r m a l m o d e s m a t h e m a t i c a l l y ? ( 2 / 3 ) z y x E u c l i d e a n s p a c e t h e 2 - s p h e r e → t h e w a v e o p e r a t o r s k n o w a b o u t t h e g e o m e t r y o f s p a c e t i m e 7 / 1 0

  21. H o w d o w e d e s c r i b e q u a s i - n o r m a l m o d e s m a t h e m a t i c a l l y ? ( 2 / 3 ) z y x E u c l i d e a n s p a c e t h e 2 - s p h e r e → t h e w a v e o p e r a t o r s k n o w a b o u t t h e g e o m e t r y o f s p a c e t i m e → q u a s i - n o r m a l m o d e s e n c o d e g e o m e t r i c p r o p e r t i e s o f s p a c e t i m e 7 / 1 0

  22. H o w d o w e d e s c r i b e q u a s i - n o r m a l m o d e s m a t h e m a t i c a l l y ? ( 3 / 3 ) r o t a t i n g b l a c k h o l e ( m a s s M, a n g u l a r m o m e n t u m Ma ) w h e r e t h e b l a c k h o l e p a r a m e t e r s M a n d a h i d e i n . 8 / 1 0

  23. T h e r e s u l t : b l a c k h o l e q u a s i - n o r m a l m o d e s a r e d i s c r e t e ! 9 / 1 0

  24. 1 0 / 1 0

  25. U s e f u l a n a l o g y : q u a n t u m b e h a v i o r o f h y d r o g e n 1 0 / 1 0

  26. U s e f u l a n a l o g y : q u a n t u m b e h a v i o r o f h y d r o g e n 1 0 / 1 0

  27. U s e f u l a n a l o g y : q u a n t u m b e h a v i o r o f h y d r o g e n → C a n w e t h i n k o f b l a c k h o l e s a s t h e “ a t o m s o f q u a n t u m g r a v i t y ” ? 1 0 / 1 0

  28. U s e f u l a n a l o g y : q u a n t u m b e h a v i o r o f h y d r o g e n → C a n w e t h i n k o f b l a c k h o l e s a s t h e “ a t o m s o f q u a n t u m g r a v i t y ” ? → Wi l l t h e i r d i s c r e t e “ s p e c t r u m ” h e l p u s t o f i n d c l u e s a b o u t q u a n t u m g r a v i t y ? 1 0 / 1 0

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