?e?a??? ?p??

1
?e?a??? ?p??

• Seµ?????? f?s????
  2007
• ?pe???? ????

2
?e??e??µe?a

• ?? e??a? ? µe?a?? ?p?
• ??? d?µ?????e?ta?
• ??d? µe?a??? ?p??
• ?et???? t?? Schwarzschild
• ??????ta? ?e????t??(Newton vs Einstein)
• ?aµp???t?ta ??????????-?a???????? ep?t????s?
• ?a?aµ??f?s? t?? ?????
• ?etat?p?s? p??? t? e?????
• ??µ?? t?? f?t??
• ?a??de???ta? p??? t? µe?a?? ?p?
• ??t???ß???a Hawkin
• ?a?at???s? µe?a??? ?p??

3
?? e??a? ? µa??? t??pa

• ?p???- d?a?s??t???? ???sµ??
• ? µe?a?? ?p? e??a? ??a a?t??e?µe?? p??a p???
  p???? ?ste t? ßa??t??? ped?? e??a? t?s? ?s????
  p?? de? µp??e? ?a d?af??e? ??te t? f??.
• F?s???? ???sµ??
• ? µe?a?? ?p? e??a? µ?a pe????? t?? ?????????? µe
  t?s? µe???? ?aµp???t?ta p?? de? µp??e? ?a
  d?af??e? ??te t? f??.
• ?a??µat???? ???sµ??
• ? µe?a?? ?p? e??a? µ?a s?µe?a?? a??µa??a st?
  ??????????? s??e??? ? ?p??a pe??ß???eta? ap?
  ??????ta ?e????t??.

4
??? d?µ?????e?ta? µ?a µa??? t??pa

• ?? µet? t?? ?????? ?pe??a???fa???? ? µ??a p??
  ap?µe??e? e??a? µe????, ? ßa??t?ta ep???ate? ?a?
  t? ?st?? ?ata???e? se µe?a?? ?p?.

5
??d? µe?a??? ?p??

• ????S ?a?a?t???st???? ?d??t?te?
• ???a, st??f??µ? ?a? ??e?t???? f??t??.
• ( no hair theorem )

6
?????te?a e?d? (1)

• ?e?a?? ?p? Schwarzschild(1916)
• -sfa????? s?µµet??a
• -??? ??. f??t??
• -??? st??f??µ?
• -µ??? µ??a
• ??µ?
• ??????ta? ?e????t??, RSch
• S?µe?a?? a??µa??a

7
?????te?a e?d? (2)

• ?e?a?? ?p? Kerr(1963)
• -??e? st??f??µ?
• -??? f??t??
• ??µ?
• Stat??? ????
• ????sfa??a
• ??????ta? ?e????t??,RSch
• ???µa??a da?t?????

8
???a e?d?

• 1.Reissner Nordstorm
• -sfa????? s?µµet??a
• -??e?t???? f??t??
• 2.Kerr Newman
• -st??f??µ?
• - ??e?t???? f??t??

9
?aµp???t?ta ??????????-?a???????? ep?t????s?

• ???t? st?? ep?f??e?a t?? ??? ?e????µe t??
  pa????????? ep?ta???se?? aµe??t?e?.
• ? ?????????? e??a? ep?ped???e?d??? ?e???a t??
  s?et???t?ta?.
• ?a???? ap? t?? ep?f??e?a t?? ??? ? se p??? ?s????
  ßa??t??? ped?? ?? pa????????? ep?ta???se?? de?
  µp????? ?a a????????.
• ? ?????????? e??a? ?aµp???µ??????e???? ?e???a t??
  s?et???t?ta?.
• ? ?aµp???t?ta t?? ?????????? ?a? ?? pa????????
  ep?t????s? e??a? t? ?d?? p???µa se d?af??et????
  ???sse?!

10
(No Transcript)
11
? µet???? t?? Schwarzschild

• ? ??s? t?? Schwarzschild st?? e??s?se??
  ?e????? s?et???t?ta? t?? Einstein.
• dt2(1-2M/r)dt2- dr2/(1-2M/r)-r2df2
  (timelike form)
• ?p?? ? GMkg/c2
• t?????? st? ped?? t?? µa???? t??pa?(proper time)
• t?????? ap?µa???sµ???? pa?at???t?(far away time)

12
? µet???? t?? Schwarzschild (2)

• ? µet???? pe?????fe? t? ?e?µet??a t??
  ?aµp???µ???? ?????????? st? e??te???? ???e
  sfa????? s?µµet????? s?µat?? st? s?µpa?
• rSch 2? ??????ta? ?e????t??
• ?p?f??e?a ap? t?? ?p??a ?t?d?p?te pe???e? p??? ta
  µ?sa ?a? t?p?ta p??? ta ???.

13
??????ta? ?e????t?? (Newton vs Einstein)

• ?????e?a s?µat?d??? m ?????µ???? se ped??
  ßa??t?ta?
• ?m?2/2- GMm/r
• St?? ???a?? pe??pt?s?
• E0 ? ?(2GM/r)1/2
• G?a f?t???? ?c ? c(2GM/r)1/2
• r2GM/c2rSch ???
• ??as??? ???a???? t? f?? pe??? ap? t?? ??????ta
  ?e????t?? a??? de? d?afe??e?.
• Ge???? ?e???a t?? s?et???t?ta? t?p?ta de?
  pe???e? p??? ta ??? t?? ??????ta ?e????t??.

14
?aµp???t?ta ?????

• ?e??aµa 1
• ?st? 2pR1 µ?a t?????
• ?st? ?a?2pR2 µe R1gtR2
• ?? µet??s??µe ape??e?a?
• ? ap?stas? r a??µesa st?? t?????? e??a?
• rgtR1-R2 !!!

15
?etat?p?s? p??? t? e?????

• ?e??aµa 2
• ??a ????? e?p?µpe? f?? se ???e ?t?p? ?a?
  ???e?ta? p??? µ?a µe?a?? ?p?.
• ???t? st? µe?a?? ?p? ? pa?at???t?? ß??pe? s??????
  pa?µ???(t) ?a? f?? µe µ???? pe???d?.
• ? ap?µa???sµ???? pa?at???t?? ß??pe? pa?µ??? a??
  µe?a??te?a d?ast?µata(t) ?a? f?? µe µe?a??te??
  pe???d?.
• ?e?a??te?? pe???d?? ?p?? ??????? f??.
• ?s? p?? ???t? st?? ??????ta t?s? µe?a??te?? t.
• St?? ??????ta ?e????t?? t?8!!!

16
??µ?? f?t??

• St?? ?aµp???µ??? ????????? t? f?? de?
  d?ad?deta? e?????aµµa.
• ??ast?eß??µ??? ?pt??? e????a.
• Fa???µe?a p???ap??? e?d????
• Gravity lensing

17

18
?a??d? p??? t? µe?a?? ?p?

• ?????? ? ast???a?t?? pa?at??e? ?t? ? e????a t??
  aste??sµ?? ?p?? t??? ??e?e pa?aµ??f??eta?.
• ??? ???t? st?? ??????ta ???t??ta? e??e?a µp??e?
  ?a de? t? p?s? µ???? t?? ?efa???? t??!
• Ft????ta? st?? ??????ta ?e????t?? ???e
  ep????????a µe t?? ta??de?t? ???eta?. ?a???a s?µa
  ? f?te???? pa?µ?? de? µp??e? ?a d?af??e? ap? t??
  ??????ta ?e????t??.
• ??? ??a e?e???? ? ?????? ???? ?a??????, ??p????
  p?? t?? pa?a??????e? ap? µa???? ß??pe? p??
  ??e???eta? ?pe??? ????? ?a ft?se? st?? ??????ta.
• ??a ta pa?ap??? a? ?e??s??µe t?? pa?????????
  ep?ta???se?? p?? te????? ?a t?? ?atast??????.

19
??t???ß???a Hawking

• St? ?e?? ????µe s??e?? d?µ??????a ?a? e?a???s?
  s?µat?d??? a?t?s?µat?d???.
• ???t? st? ??????ta t? ??a pa?as??eta? st?? µe?a??
  ?p? e?? t? ???? d?afe??e?(fa???µe?? s??a????).
• ???tµ?s? t?? µe?a??? ?p?? .

20
?a?at???s? µe?a??? ?p??

• ?-rays ?a s?µat?d?a p?? ?????ta? ap? t? µe?a??
  ?p? ep?ta????µe?a e?p?µp??? a?t??e? ?.
• ?e??st?ef?µe?? s?µa ??a s?µa pe??st??feta? ????
  ap? ??t? ????st?. ?p? t?? ????s? t?? µp??e? ?a
  s?µpe???e? ?a?e?? a? t? ????st? e??a? µe?a?? ?p?
  .
• Gravity lensing ?? f?? ??µpteta? ?a? est???eta?.
  

21
??a?µat??? st???e?a

• ?? Hubble space telescope t?? ?ASA µa? ??e? d?se?
  ta s?µa?t???te?a st???e?a ??a t?? ?pa??? t??
  µe?a??? ?p??.
• (?a?a??a? NG4438)

22
(M87)
(NGC4261)
23
(No Transcript)
24
??ß?????af?a

• Exploring Black Holes-E.F.Taylor,J.Wheeler.
• ?st??f?s??? ,??µ? ?a? e?????? t?? s?µpa?t??-F.H
  Shu.
• www.hubblesite.org
• www.eftaylor.com
• www.damtp.cam.ac.uk/user/gr/public/bh_home.html
• ? ??sµ?????a t?? ???s?? ,e?sa???? st??
  ??sµ?????a-?.?a?????,S.Te?d?s???