Lecture 29 — General Relativityand Black Holes

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Einstein’s General Theory ofRelativity (1916) I

Special Relativity says nothing about forcesGeneral Theory: Theory of GravityGravity changes the geometry of spacetimeBodies follow straight lines in the curvedgeometryTheory gets orbit of Mercury Right

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Einstein’s General Theory ofRelativity (1916) II

Bending of starlightConfirmed by expedition led by Eddington toisland of Príncipe near Africa to watch thesolar eclipse of May 29, 1919.

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Einstein’s Idea

Person in Elevator can not tell whether they areaccelerated or in a gravitational field:Principle of Equivalence

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Acclerated Frame of Reference

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GR: Gravity warps spacetime

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GR: Light follows “straight line” incurved spacetime

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Straight Lines on the surface of earth

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Riemannian Geometry

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In Curved Space-Time Sum ofAngles 6= 180 degrees

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Square on a Sphere

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Energy = Mass warps space-time

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Gravitational Wave Effects

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How to measure graviational waves:Laser Interferometer

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Precesion of Perihelion of Mercury

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Recap

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Clicker Question

White dwarfs are supported by(a) Ordinary thermal pressure supplied by the energy

from nuclear reactions(b) Quantum mechanical pressure of relativistic

electrons(c) Quantum mechanical pressure of non-relativistic

neutrons(d) The nuclear force

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Clicker Question

Neutron stars are supported by(a) Ordinary thermal pressure supplied by the energy

from nuclear reactions(b) Quantum mechanical pressure of relativistic

electrons(c) Quantum mechanical pressure of non-relativistic

neutrons(d) The nuclear force

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Clicker Question

The maximum mass of a white dwarf is:(a) The Chandrasekhar mass(b) About 1.4 M�

(c) About 0.6 M�

(d) both (a) and (b)

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Clicker Question

The maximum mass of a neutron star is:(a) The Chandrasekhar mass(b) At least 2.2 M�

(c) Not completely certain, since we haven’t yetsolved nuclear physics

(d) both (b) and (c)

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