Class notes
ASTRO 101: Black Holes Module 6
- Course
- ASTRO 101
- Institution
- University Of Alberta (UofA)
Notes for ASTRO 101 based on the official Coursera videos for the class. Covers Module 6.
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Module 6Definitions:
● Event Horizon: A boundary that separates the insideof a black hole from the
outside, marking the point of no return for any material or light that crosses it.
● Comparison to Sun's Surface: Stars, like the Sun,don't have a defined surface,
but the outermost layer is called the photosphere, which we see in visible light.
Beyond this, there are faint layers like the chromosphere and corona.
● Black Hole Surface: Black holes don’t have a traditionalsurface but have an event
horizon, which is the defined boundary.
● Hydrostatic Equilibrium: The balance between gravitationalforce and gas
pressure in stars. Inside a black hole’s event horizon, gravity overwhelms gas
pressure, leading to a collapse.
● Gravitational Effects: Light is bent by the mass ofa black hole, similar to how a
ball’s path curves on a stretched sheet. The closer the light gets to the black hole,
the more it curves.
● Schwarzschild Radius: The radius of a non-rotatingblack hole’s event horizon,
which depends on the mass of the black hole. For the Sun, it’s 3 km, and it scales
linearly with the black hole’s mass.
● Black Hole Size and Mass: Larger black holes havelarger event horizons. The
event horizon of a black hole 15 times the mass of the Sun would be 45 km, while a
supermassive black hole’s event horizon could be millions of kilometers.
● Tidal Forces: For supermassive black holes, tidalforces are weaker, making them
safer for exploration. A black hole must be at least 1,000 times the Sun’s mass for a
safe visit.
● Photon Sphere: A region around a black hole wherelight can travel in unstable
circular orbits. This sphere is 1.5 times the size of the event horizon.
● Ring of Fire: The bright ring formed by photons trappedin circular orbits around a
black hole, seen by observers as light escapes the photon sphere.
● Black Hole Shadow: The dark region outside the eventhorizon, where no light
escapes, forming a shadow around the black hole.
● Gravitational Time Dilation: An astronaut fallinginto a black hole would
experience time normally, but an outside observer would see their time stretch
infinitely as they approach the event horizon.
● One-Way Nature of Event Horizon: The event horizonis a "one-way street" where
light can enter but cannot escape, making it difficult to observe what happens
inside.
, ● Danger of Crossing the Event Horizon: There's no visible marker for the event
horizon, making it easy to cross accidentally, but it's extremely dangerous due to
extreme tidal forces.
● Black Hole Interior: No information can escape frominside the event horizon, so
the interior remains a mystery. The singularity at the center is theorized to have
extreme physical properties.
● Cosmic Censorship Hypothesis: A theory that suggeststhe event horizon shields
us from seeing the singularity, a concept still under investigation in theoretical
physics.
The Singularity:
● Traveling Past the Event Horizon of a Black Hole:
○ Choose a supermassive black hole to avoid tidal forces.
○ Once past the event horizon, we enter the strange interior of a black hole.
○ Although we can't send information back to the universe, observers inside
can make scientific discoveries.
● Light and Space-Time Inside the Event Horizon:
○ Inside a black hole, it's not dark; light emitted from outside is still visible.
○ Any light inside the event horizon always points inward, towards the black
hole's singularity.
○ Radial distance and time dimensions switch roles inside the event horizon:
moving towards smaller radius values is akin to moving forward in time.
○ Escaping the black hole is impossible as this would require moving
backwards in time.
● Black Hole Interior and Space-Time Diagrams:
○ A collapsing star forms a black hole, represented by a time-space diagram.
○ The event horizon forms as the star collapses to the Schwarzschild radius.
○ Penrose diagrams help visualize the interior of black holes, highlighting
time and space dimensions.
● Time and Gravity Inside a Black Hole:
○ Once inside, objects inevitably move towards the singularity at r=0.
○ The time to fall from the event horizon to the singularity varies with black
hole mass.
○ For supermassive black holes, one could have hours to fall, while for
smaller ones, it’s just milliseconds.
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