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Lecture07_GR1 - 1 The Principle of Equivalence Flat and...

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2 The Principle of Equivalence Flat and Curved Space The Schwarzschild Geometry Summary
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3 All objects fall with the same acceleration G. Galileo 1564–1642
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4 A person falling off a building experiences no gravity! “The happiest thought of my life” Albert Einstein (1907)
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5 free space The Principle of Equivalence free fall inside view free fall outside view free fall outside view
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6 Bending of light Sir Arthur Eddington Eclipse Expeditions 1919 Gravity is curved spacetime 1915
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7
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8 P O B A dl dx dy In 3-D, this becomes dl 2 = dx 2 + dy 2 + dz 2
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9 Q O P Hermann Minkowski 1864 -1909 ds dl dt Unfortunately, this does not work!
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10
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11 O C x` ct` x ct D A B E spacelike F
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12 A B D C X X’
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13 φ θ z y x r d φ C B A O P
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14 Consider the interval for flat spacetime in the plane θ = 90 o ds 2 = c 2 dt 2 dl 2 Spatial part AC = rd φ CB = dr (radial) AB = dl dl 2 = dr 2 + r 2 d φ 2
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