Black Holes

Eternal? Or just long lived?

by Patrick Murphy

A Brief History Of Black Holes.

• First proposed in thought experiment by John Mitchell in 1783

• 1916: Karl Schwarzschild solves Einstein’s field equation for spacetime around a spherical body.

• A little more on Einstein….

General Relativity

• Published in 1915• Describes the

relationship between mass and spacetime.

• Spacetime tells mass how to move and mass tells spacetime how to curve.

• Confirmed in 1919 by Arthur Eddington

Spacetime:

• Apparent vs. real trajectory of a light beam

Karl Schwarzschild

• Solved metric for spacetime surrounding a spherical mass.

• Schwarzschild metric :

• Schwarzschild radius :

2 2 2 2 2ds = 1/(1-2M/r)dr + r d - 1/(1-2M/r)dt

2R = 2GM/c

Classic Black Holes

• 1939 : Oppenheimer shows massive stars collapse to a singular point.

• Multiple solutions involving small perturbations confirm results.

• Singularity surrounded by event horizon, point of no return.

• Three parameters : Mass, Charge and Spin

Roger Penrose• 1969: Proved all

full gravitational collapses result in a singularity

• Postulated Cosmic Censorship Law

Classic Black Holes

2 main types

Schwarzschild• Static, no rotation• Point-like singularity• Event Horizon

Kerr• Rotates• Ring shaped

singularity• Inner Horizon• Outer Horizon• Ergosphere

2 main types

Schwarzschild Kerr

So nothing can escape the gravitational attraction of the black hole once past the event horizon?

Classically, yes

Problems with classical theory

• Assumed TBH = 0 K, despite mathematical evidence to the contrary .

• No thermal spectrum• Singularity too small for Relativity

Can Black Holes Radiate?

Maybe so…• 1970 : Jacob Berkenstein suggests area

of event horizon is a measurement of black holes entropy.

• 1970 : Stephen Hawking shows that area of event horizon always increases.

• 1971 : Borisovitch Zel’dovitch claims rotating black holes radiate until they stop spinning .

1974: Hawking Radiation

• Hawking repeats Zel’dovitch’s calculatons.

• Agrees except….• Finds they continue to

radiate!• There’s more…• His solution predicted the

emission spectrum to be exactly that of a hot body.

• That means temperature and entropy

How can it radiate?

• Various mechanisms are possible, depending on your frame of reference.

• They all acknowledge quantum vacuum fluctuations as source.

• Quantum vacuum fluctuations are unavoidable due to Heisenberg’s Uncertainty Principle

And…?

• Say you’re safely at rest, watching vacuum fluctuations.

• You see a virtual pair of photons created just outside the event horizon.

• Tidal gravity pulls them apart, they become real.

• One gets sucked in, the other escapes forever.

So What’s Left?

• Resolution of the “Information paradox”

• Development of an adequate quantum theory of gravity, Relativity is no longer a valid approximation on scales smaller than the Planck length, lp = (hG/2πc3)1/2 .

Information loss?

• In technical jargon, the black hole has performed a non-unitary transformation on the state of the system.  As you may recall, non-unitary evolution is not allowed to occur naturally in a quantum theory because it fails to preserve probability.

• Hawking suggests that black hole radiation contains information about what went in, albeit in a mangled form.

Branes?

• P brane: length in p dimensions

• P = 1 : String

• P = 2 : Membrane

• Etc…

• Information stored

Quantum Gravity?

• Singularities are tiny• Quantum foam• No time, how space

manifests itself is probabilistic

• Many candidates, include : M-theory, Supergravity, AdS/CFT , holography …

So Why study Black holes?

• Black holes push the limits of physical theories

• Among the most extreme phenomena in the universe

• I think they’re cool.• That’s it• Thanks for listening• The End• (applause…. please?)

References :• Kip Thorne, Black Holes And Timewarps (Norton, 1994)

• Eric Poisson, A Relativist's Toolkit, The mathematics of black hole mechanics (Cambridge University Press, 2004).

• Alessandro Fabbri and Jos\'{e} Navarro-Salas,Modeling Black Hole Evaporation (Imperial College Press, 2005)

• John A. Wheeler, E.F. Taylor, Exploring Black Holes, Introduction to General Relativity (Addison Wesley, 2000)

• Stephen Hawking, The Universe In A Nutshell (Bantam, 2001)

Images :• http://chandra.harvard.edu/resources• http://www.belmontnc.4dw.net/DWFNEU5.gif• www.tqnyc.org/NYC040808/ neutron_star.jpg• http://en.wikipedia.org• www.scienceweek.at