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Summer School on Gravitational-Wave Astronomy
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Black Holes Lecture - 04
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Stability of Stars
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Stability of Matter
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OV: Oppenheimer - Volkoff Equation of State
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Stability of Stars in GTR
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General Relativistic Instability
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Laws of gravitation
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Newtonian Gravity
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Einstein's generalizations
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Einstein's Zeroth Law of Gravity
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In regions where no matter is present
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In regions where matter is present
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Conservation Laws
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Einstein's field equations
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Newtonian limit
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Schwarzschild metric
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The Schwarzschild Geometry
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The Schwarzschild Radius
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The surface of the black hole is known as the Event Horizon
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Approximate metric at large distances from the centre.
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Effective potential in Newtonian theory
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Effective potential in Einstein's theory
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ORBITS in Einstein's theory
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The last "unstable" circular orbit is at a radius of 1.5 Rg. The velocity of the particle will be 'c'
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Important new result
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Gravitational Capture
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Cross Section for Gravitational capture
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Radial Motion of Particles
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Falling towards a black hole
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Time to reach Rg from r = r1
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Falling into a black hole
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Radial motion of photons
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Inside the horizon
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The Lemaitre coordinates 1933
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Q&A
Description:
Explore the fascinating world of black holes in this comprehensive lecture from the Summer School on Gravitational-Wave Astronomy. Delve into topics such as the stability of stars and matter, Einstein's laws of gravitation, Schwarzschild geometry, and the behavior of particles and photons near black holes. Learn about the Oppenheimer-Volkoff equation of state, Einstein's field equations, and the concept of the event horizon. Examine the differences between Newtonian and Einstein's theories in terms of effective potentials and orbits. Investigate gravitational capture, radial motion of particles, and the journey of falling into a black hole. The lecture concludes with a discussion on the Lemaitre coordinates and a Q&A session, providing a thorough understanding of black hole physics and its implications in gravitational-wave astronomy.

Black Holes - Lecture 4

International Centre for Theoretical Sciences
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