5. Gravitational Collapse and Black Holes Flashcards
Describe the properties of the interior of a star
The stress energy momentum tensor is not 0 (like it is for a vacuum)
- Approximated as a perfect fluid
- Made of fermions (electrons, protons, neutrons)
What is hydrostatic equilibrium?
When the pressure gradient balances with the gravitational force of attraction
How do stars generate their massive pressure to support it against the gravitational force?
Burn nucler fuel
- Gives a high temperature and a corresponding high pressure
What state is an old star in at the end of its life?
In its quantum ground state
What provides the pressure against the gravitational forces for old stars in their quantum ground state?
The fermions form a degenerate Fermi gas
- Gives a degenerate pressure which opposes gravity
What defines a white dwarf?
When the degeneracy pressure is balanced against the gravitational pressure (equilibrium)
What is a consequence of the equation of state for a white dwarf in relation to the mass of the star?
That more massive stars are more dense
- Fermions are more tightly confined
- Momenta from the uncertainty principle puts them into a relativistic regime
What is the Chandrasekhar limit?
1.44 Mass of the sun
What is a consequence of the Chandrasekhar limit?
Stars more massive than the limit have no known mechanism for supporting themselves against the gravity
- Stars more massive than the limit cannot end up as white dwarfs
What is the mass limit for a neutron star?
2 -> 3 stellar masses
- Heavier stars than this collapse into a black hole
State the two extra parameters in the metric for the Kerr black hole
- mass m = GM/c^2
- spin a = J/Mc
State what happens to the Kerr metric if you set the values of a or m to 0
- a=0 you recover the Schwarz. solution
- m=0 you recover the Minkowski metric in bispherical coordinates
State the symmetry properties of the Kerr metric
- Axissymmetric meaning it is constant under translations of the phi angle
- Not spherically symmetric
- Also stationary (constant under time translations), but not static (not time reversal)
What are the necessary conditions for event horizon to exist, and when is there an extremal black hole?
Only exists when the spin a <= m
- Extremal when a=m
What is the consequence of the Penrose conjecture and the properties of a black hole?
Penrose conjected that all black holes must have event horizons
- This means the spin is always less than or equal to the mass of the black hole implying a limit on the angular momentum of a BH
Describe the structure of the ergosurface and ergosphere
Central blackhole enclosed in an oval like shape
- Oval is called the ergosurface
- Inside between the surface and BH is the ergosphere
Describe the motion when inside the ergosphere
All observers including light must corotate with the black hole
- Impossible to counter-rotate or stand still
Describe the areas of the masses of a black hole when there is no spin, and when the spin is at a maximum value
No spin: A = 16 pi m^2
a=n: A=8 pi m^2
- Faster spinning black holes are more compact objects
State Stephen Hawking’s Area Theorem:
The total area of the event horizon does not decrease. dA >= 0
What is the fundamental implication of the Area Theorem?
It is impossible to increase the spin of the black hole without adding mass
- Also places a limit on the amount of energy that can be radiated away from a BH in the accretion of mass/merger event
What is the fundamental upper limit on the mass radiated away in the black hole merger?
0.29
Describe the general process of accretion
Mass falls into the black hole
- Area increases and it spins faster
Describe the analogy of the process of accretion and black hole thermodynamics
- Small changes in mass are now changes in energy
- Increasing the spin of the BH is like the work done
- The area of the event horizon is the BH entropy
What is the second law of thermodynamic equivalent?
Area theorem is the second law
Describe the Hawking Temperature
Particle emission from the black hole radiate like a black body
What is the main problem with the observational evidence for black holes?
Receive no direct signals from the event horizon or within it
- Evidence is indirect
State the main sources of evidence for BHs
Compacy X ray binaries, gravitational waves, AGN
Describe the evidence of BHs from XRBs
Cosmic X-rays come from normal stars
- Spectra show periodic variation associated to orbital motion of a binary system
- If the mass is large enough, it is a BH
Describe the evidence of BHs from AGN
Highly luminous (outshine galaxies) and compact source
- Narrow jets extending 10s of 1000s of light years
- Only plausible explanation is accretion onto a SMBH
