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Falling into a black hole. by Alison Hammond and Jason Cheng. Background-Gravity. Gravity is one of the four fundamental interactions. General Relativity (GR) is the modern interpretation of gravity.

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Presentation Transcript
slide1

Falling into

a black hole

by Alison Hammond

and Jason Cheng

slide2

Background-Gravity

  • Gravity is one of the four

fundamental interactions.

  • General Relativity (GR)

is the modern interpretation of gravity.

  • GR says gravity is not a force! It is due to following paths of least resistance on a curved space-time.
slide3

What is a black hole?

  • Extremely massive astronomical object.
  • Extremely strong gravitational pull
  • Nothing can escape from below the event horizon.
slide4

How do we study black holes?

There are three ways we could study black holes.

1. We go to a black hole

  • Too far away, the closest black hole is some 1,600 light years away
  • Too dangerous, if anything goes wrong, one goes in, and will never come back out

2. We create a black hole

  • CERN is working on it, let’s do something else before they actually make one
slide5

How do we study black holes?

3. We simulate a black hole using GR equations

  • It would take more than 1000 years to do

this numerically by hand.

    • So we use our good

friend MATLAB

    • Modeling in 1 space and 1

time dimension

    • Use MATLAB to solve the

differential equations.

slide6

Aims of the Project

  • Using MATLAB:

-Explore motion near a black hole.

-Investigate objects falling into a black hole.

-Analyse the effect of radial acceleration.

-Model explorers approaching the black hole and then coming back out.

slide7

Method

  • GR equations in 2-D give 4 coupled differential equations.
  • Solve using Runge-Kutta 4th, 5th order method (ode45 in MATLAB).
  • Increasing complexity
slide8

Circular Motion

  • General relativity reduces to the classical picture in flat space time.
  • Solving equations

in the case of

circular motion.

slide9

Schwarzschild metric

  • Equations of GR near a black hole
  • Describes the space-time geometry near a non-rotating, non-charged black hole (Schwarzschild black hole)
  • In our project, we ignore angular terms
slide10

No Acceleration

  • Not surprisingly, our observer falls into the black hole.
  • Not so good for our observer.
slide11

Constant Acceleration

  • With constant acceleration, 3 things can happen:

1. Acceleration is too low:

  • Not so good for our observer.
slide12

Constant Acceleration

2. Acceleration is too high:

  • Not so good for science.
slide13

Constant Acceleration

Or if the acceleration is just right….

slide14

Hovering

  • The acceleration will just cancel out the gravitational pull.
slide15

Changing Acceleration

  • Now let’s look at when acceleration changes.
  • Introduce ‘k’ into equations. The acceleration can now take, for instance, a functional form over time.
  • N.B. ‘k’=1 is hovering acceleration
  • We want to get close to the black hole and investigate.
slide16

Physical Interpretation

  • Note about scaling factors – MATLAB solves the equations for the case m=1. Scaling factors were then calculated and used to give correct units for realistic masses.
  • This diagram models a super-massive black hole –it has a mass 1*109 greater than the sun. We start from 150 times away from the event horizon.
slide18

Physical Interpretation

  • So we have an approximately 2-month mission in the vicinity of a black hole.
  • The very sudden change brought about by our function, however, is quite physically unrealistic.
  • A smooth functional form gives a better picture.
slide19

Controlled Fall

and Escape

3

slide20

Physical Interpretation

  • This journey is more physically realistic.
  • We can also model the acceleration experienced during this journey.
  • This poses some problems.
slide21

Controlled Fall

and Escape

150

Total Acceleration

Acceleration Component at (blue)

Acceleration Component ar (red)

Acceleration measured in g

3

slide22

What are g-forces?

  • G-force is the acceleration experienced by an object relative to free-fall.
  • G-forces are measured in multiples of the acceleration we experience at the earth’s surface:

1g=9.8m/s2.

slide23

The problem of Survival

  • Humans cannot survive high g-force levels.
  • Our current model, with g-forces of 150g, is clearly going to kill whatever observers we send.
  • This is a problem.
slide24

How do you minimise g-forces?

  • Try to have change happen gradually.
  • In particular, a smooth transition from falling inwards to beginning to escape.
slide25

How do you minimise g-forces?

  • Though the path may look smooth, the rapid changes in g show it is not really.

3

3

slide26

What g-forces do we need?

  • Depends on who we want to send.

Scientists

Fighter Pilots

6-9g

1-2g

slide27

Results

  • An improvement, but it still kills them.

3

3

slide28

Results

  • But obviously we don’t get as close.

3

3

slide29

Discussion

  • Starting at 4.4*1013 m

corresponds to experiencing

around 1g when hovering.

  • It is impossible to go much
  • lower because hovering
  • acceleration alone would
  • be too many g.
slide30

Further Investigation

  • The next logical step would be to investigate the same problem in two spatial dimensions with time.
  • Another possibility is to

investigate smaller black holes.

  • The procedure is identical,

but the maths much

messier and more time

consuming.

slide31

Acknowledgments

  • We’d like to extend thanks to:
    • Our supervisor, Geraint Lewis.
    • TSP co-ordinator, Dick Hunstead.
slide32

References

  • Griffiths, David, Chapter 12: Electrodynamics and Relativity, Introduction to Electrodynamics, (San Francisco, USA, 2008: Pearson, Benjamin Cummings).
  • Hartle, James B., Gravity: An Introduction to Einstein's General Relativity (USA, 2003: Pearson, Addison Wesley).
  • Lewis, Geraint & Kwan, Juliana, ‘No Way Back: Maximising Survival Time Below the Schwarzschild Event Horizon’, Publications of the Astronomical Society of Australia, 2007, 24, p. 46-52.
  • Serway, Moses, Moyer, Modern Physics, (California, USA, 2005 (3rd Edition), Thomson, Brooks/Cole).
  • Wikipedia, G-forces, Black Holes, (2009, Wikipedia).
  • All graphs produced using MATLAB7. (2009, Mathworks Inc.).
  • Images from:
    • http://jcconwell.files.wordpress.com/2009/07/black_hole_milkyway.jpg
    • http://app.ucdavis.edu/algebra/blackhole3.jpg
    • http://lgo.mit.edu/blog/drewhill/files/blackhole.gif