Relativity and Black Holes: The Physics of...

Relativity andBlack Holes:The Physicsof Interstellar

T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

Relativity and Black Holes:The Physics of Interstellar

T. Daniel Brennan

December 12, 2014


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

1 Special Relativity

2 General Relativity

3 Black Holes

4 Energy Extraction

5 Summary


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

Special RelativityProblem with Electricity and Magnetism

In the late 1800’s physicists realized there was a problem withelectromagnetism: the speed of light was given in terms offundamental constants which describe materials.

c =1√εµ


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

Special RelativityGalilean Transforms

How do we add velocities of objects?


T. DanielBrennan

SpecialRelativity

GeneralRelativity

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EnergyExtraction

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Special RelativityThought Experiment

What happens when you do it with light?


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

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Special RelativityLorentz and his Transformations

In the early-mid 1890’s famous physicist Lorentz figured outthat you can add velocities u and v

u + v√1 + uv

c2(1)

This reduces to the usual addition of velocities for slow speeds.

uv

c2≈ 0


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

Special RelativityTime Dilation


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

Special RelativityEinstein’s Idea

Einstein figured out that Lorentz’s addition of velocity could bederived from the principle of relativity and assuming that thespeed of light is constant in all reference frames. In order toincorporate time dilation, there must also be lengthcontraction.

For two observers at same location moving at differentspeeds, there is time dilation, ∆t ′ = γ∆t

For two observers at same time moving at differentspeeds, there is length contraction ∆x = 1

γ ∆x ′.

γ =1√

1−(vc

)2


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

Special RelativityTime Dilation and Length Contraction


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

Special RelativityTwin Paradox


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

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Special RelativityProblem with Special Relativity

Einstein realized that there was something special aboutgravity...


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

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General RelativitySpacetime

These ideas lead Einstein to propose ideas that drasticallychange the way we look at the universe:

Time is not a parameter but another dimension like space- “Spacetime”

Spacetime is dynamical - it is not flat, but is like a sheetof rubber that we live on

Spacetime is curved by energy and mass:

Rµν −1

2Rgµν =

8πG

c4Tµν


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

General RelativityGeodesics

Relativity also tells us that particles will move in “straight”lines called Geodesics. That is relative to the surface.


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

General RelativityMore Geodesics


T. DanielBrennan

SpecialRelativity

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General RelativityEven More Geodesics!

The geodesics of this surface give the planet’s orbits andgravitational lensing.


T. DanielBrennan

SpecialRelativity

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General RelativityEffects of Curving Spacetime

Time is slowed where spacetime is curved more

Space is stretched causing paths to bend


T. DanielBrennan

SpecialRelativity

GeneralRelativity

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EnergyExtraction

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Black HolesSolution for the Sun

Look for a spherically symmetric solution to Einstein’s fieldequations to find solution for the sun. If you let the size of thesun be small enough, you get solution for the SchwarzchildBlack hole.


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

Black HolesSchwarzchild Black Hole

If a star’s radius becomes smaller than the Schwarzchildradius distance Rs = 2Gm

c2, then it forms a black hole.

Inside Rs nothing can escape the gravitational pullbecause the curvature becomes too great.

There is a singularity of infinite mass density at r=0.


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

Black HolesOther Types of Black Holes

There are 3 parameters which describe every type of black hole:M,Q,J

Non-Rotating (J=0) Rotating (J 6=0)

Un-Charged (Q=0) Schwarzchild Kerr

Charged (Q 6=0) Reissner-Nordstrom Kerr-Newman


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

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Black HolesKerr Black Holes

Rotating black holes have many interesting properties

Cause spacetime (ergosphere) nearby to corotate

Often have accretion disks: a disk of superheated plamsaaround its equator like Saturn’s rings

Are at the center of galaxies


T. DanielBrennan

SpecialRelativity

GeneralRelativity

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EnergyExtraction

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Black HolesErgosphere

Rotating faster than the speed of light causes space and timecoordinates to mix allowing for negative energy.


T. DanielBrennan

SpecialRelativity

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Black HolesInterstellar Black Hole: Gargantua


T. DanielBrennan

SpecialRelativity

GeneralRelativity

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EnergyExtraction

Summary

Black HolesFalling In

What would happen as you fell into a black hole? Not sure...

Time slows infinitely - See the universe age (potentiallyend)

Can be pulled apart by gravity: FG ∼ 1MBH

Could blow up

Can have a lot of light orbiting Black HoleCan have particle-anti particle creationCan have Black Hole evaporate


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

Energy ExtractionSummary

3 Main ways to extract energy from Black Holes

Hawking Radiation - Quantum effect

Blandford-Znajek Effect - Magnetohydrodynamic Effect

Penrose Process - Exploitation of properties of Ergosphere


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

Energy ExtractionHawking Radiation

Strong curvature of spacetime causes spontaneousparticles-antiparticle pair creation. There is a net flux ofanti-particles into the event horizon which “evaporates” theblack hole.


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

Energy ExtractionBlandford-Znajek Effect

Rotating black hole with an accretion disk causes plasma torotate, powering magnetic fields which swirl outwards, carryingangular momentum, particles, and energy.


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

Energy ExtractionPenrose Process

A particle goes into the ergosphere of a rotating black hole andbreaks into two pieces, one of which has negative energy. Thisfalls into the black hole and the remaining leaves with a netgain in energy.


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

Summary

Summary

Energy radiates from black holes naturally in two processesHawking radiation- due to the quantum effects of intensecurvatureBlandford Znajek effect - due to the corotation poweringintense magnetic fields

Energy can be actively extracted by using Penrose ProcessImpractical


T. DanielBrennan

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Conclusion

Questions?


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Supplemental MaterialWorm Holes


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Applying to College


T. DanielBrennan

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Applying to College

...actually you do...


T. DanielBrennan

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Applying for CollegeWhat they want

Want people who will make the school look good

Leaders in the worldWant to have good statistics

This produces wealthy donors and funding


T. DanielBrennan

SpecialRelativity

GeneralRelativity

Black Holes

EnergyExtraction

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Applying for College


T. DanielBrennan

SpecialRelativity

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EnergyExtraction

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College AdmissionsAcademics

Want to know you will be successful academically in College

Successful in High SchoolClasses

DifficultyGrades

SATsRecommendationsAcademic Extra CurricularsEssay


T. DanielBrennan

SpecialRelativity

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College Admissions

See that you can contribute to the College culture

Extra-curricular activitiesCommunity serviceLeadership opportunities

Want people to stand out among the hundreds ofthousands of applicants


T. DanielBrennan

SpecialRelativity

GeneralRelativity

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Applying for CollegeAdvice

Name recognition is not always most important

Apply to many schools

Make people think of you as a college student

Keep your eyes on the goal

Remember, a college education is invaluable.

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Relativity and Black Holes: The Physics of...

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