Physics 616

  • Prof. Andrew W. Steiner
    (or Andrew or "Dr. Steiner")
  • Office hour: 103 South College, Thursday 11am
  • Email:
  • Homework: Electronically as .pdf
  • You may work with each other on the homework, but you must write the solution in your own words
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Black Holes and Effacement

No-Hair Theorem

Other Metrics

No-Hair and Neutron Stars

  • However, no-hair theorem doesn't tell us what's going on inside the event horizon
  • It is expected that GR breaks down before density becomes infinite in the center
  • Neutron stars are more complicated
  • Recently, several have suggested that there are no-hair like results which simply neutron star structure
  • Tidal deformability is called "Love number"
Yagi and Yunes (2013)


Black Hole Properties, Etc.

Black Holes in X-ray Binaries

Black Hole Mass Distribution

Milky Way BH

Guidry ch. 18

Hawking Radiation II

Hawking Radiation III

  • What is the energy of the outgoing photon? Now consider an observer freely falling in to $r=2M$ from a finite radius $R=2M+\varepsilon$
  • The observer has $$ \tilde{E} = \left(2 - \frac{2 M}{2 M + \varepsilon}\right)^{1/2} \approx(\varepsilon/2M)^{1/2} $$
  • Remember that $$ d \tau = - \frac{dr}{\left(\tilde{E}^2-1+2 M/r\right)^{1/2}} $$
  • Integrate this $$ \Delta \tau = - \int^{2M}_{2 M+\varepsilon} \left(\frac{2 M}{r} - \frac{2 M}{2 M + \varepsilon}\right)^{-1/2} dr $$ which to lowest order in $\varepsilon$ gives $$ \Delta \tau = 2 \left(2 M \varepsilon\right)^{1/2} $$

Hawking Radiation IV

Hawking Radiation V

Area theorem and Entropy

Information Paradox

Group Work