Black Holes - Lecture 4

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.

Summer School on Gravitational-Wave Astronomy
Black Holes Lecture - 04
Stability of Stars
Stability of Matter
OV: Oppenheimer - Volkoff Equation of State
Stability of Stars in GTR
General Relativistic Instability
Laws of gravitation
Newtonian Gravity
Einstein's generalizations
Einstein's Zeroth Law of Gravity
In regions where no matter is present
In regions where matter is present
Conservation Laws
Einstein's field equations
Newtonian limit
Schwarzschild metric
The Schwarzschild Geometry
The Schwarzschild Radius
The surface of the black hole is known as the Event Horizon
Approximate metric at large distances from the centre.
Effective potential in Newtonian theory
Effective potential in Einstein's theory
ORBITS in Einstein's theory
The last "unstable" circular orbit is at a radius of 1.5 Rg. The velocity of the particle will be 'c'
Important new result
Gravitational Capture
Cross Section for Gravitational capture
Radial Motion of Particles
Falling towards a black hole
Time to reach Rg from r = r1
Falling into a black hole
Radial motion of photons
Inside the horizon
The Lemaitre coordinates 1933
Q&A