1. Black Holes Astrophysics Lesson 14

2. Learning Objectives To know:-  How to define the event horizon for a black hole.  How to calculate the Schwarzschild radius, R S, for the event horizon of a black hole.  To discuss the evidence for and the density of the super massive black hole at the centre of the Galaxy.

3. Homework  Collecting - the mock EMPA.  Reminder another mock EMPA on Monday.  Homework – Q6-8, p180-181  Read p173-180 if you have the time – it’s interesting stuff!

4. Recap What determines whether a black hole will form in the first place? What is the defining feature of a:- Supernova Neutron Stars Black Holes

5. How can they be observed? Either from material falling into the black hole:- Gravitational potential energy  electromagnetic radiation.

6. How can they be observed?  Stars orbiting an invisible centre of mass.  This is what we observe at the centre of the Milky Way galaxy.  Video clip…

7. Some definitions The Event Horizon:- This is defined as the boundary at which the escape velocity is equal to the speed of light. The Schwarzschild Radius, R S :- This is defined as the radius of the event horizon. Anything that is within the Event Horizon of the black hole cannot escape – not even light.

8. Energy Equations Supposed we have an object of mass, m on the surface of a more massive object of mass M. How do we calculate the kinetic energy and gravitational potential energy of mass m.

9. Energy Equations The kinetic energy of an object of mass, m:- It’s gravitational potential energy on the surface of a more massive object M is given by:- Think force x distance, where the force is Newton’s law of gravity. At inifinity GPE = 0.

10. The Escape Velocity This is the velocity required for a less massive object of mass, m, to completely escape the gravitational field (to infinity) of a more massive object of mass M. If m is taken to infinity, the difference in GPE is:- So the initial kinetic energy of m must be equal to:-  make v the subject

11. The Escape Velocity So the escape velocity is given by:- At the boundary of the event horizon of a black hole, R=R S, the Schwarzschild radius, and v = c, the speed of light:-  Rearrange this for R s

12. The Escape Velocity So the escape velocity is given by:- At the boundary of the event horizon of a black hole, R=R S, the Schwarzschild radius, and v = c, the speed of light:-  Rearrange this for R s

13. Schwarzschild Radius This is defined as the radius of the event horizon of a black hole.

14. Density of a Black Hole Recall the equation for density:- If we substitute our equation for R S into the equation:- We can derive an equation for the density of a black hole.

15. Density of a Black Hole I get:- Evaluate ρfor M= 10 solar masses. What value of M would give a density equal to that of water? (1,000 kg m -3 )

16. Density of a Black Hole Density is not constant, it is infinite at the centre.