Black Holes Astrophysics Lesson 14

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.

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

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

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

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…

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.

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.

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.

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

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

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

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

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.

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 )

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