5.6) In its rest frame, quasar Q2203+29 produces a hydrogen emission line of wavelength 121.6 nm. Astronomers on Earth measure a wavelength of 656.8 nm for this line. Determine the redshift parameter and the apparent speed of recession for this quasar. (For more information about this quasar, see McCarthy et al. 1988.)

I understand that to an outside observer, the light from a star that is collapsing into a black hole will become more and more red-shifted as the surface of the star appears to approach the black hole event horizon. The outside observer will never actually see the surface of the star cross the black hole event horizon. This applies to all outside observers: at infinity, in orbit around the star/black hole or those using a rocket to hover above the black hole. Conversely, I know that for someone on the surface of the star that is collapsing to form a black hole it will appear quite different. The observer on the surface will not see anything unusual happen as they cross the event horizon and in a finite time they will reach the singularity at the center of the black hole where we do not know what will happen since general relativity breaks down in a singularity. So, now consider an observer that starts at a great distance from the star who is continually falling directly into the star…

The hydrogen Balmer line H, has a wavelength of 486.1 nm. It is shifted to 580.7 nm in a quasar's spectrum. What is the redshift of this quasar? (Hint: What is A2?)

Imagine you are in an indestructible spaceship orbiting a black hole and you decide to launch a probe into the black hole. Explain how time would pass differently for you and the probe as it is pulled into the black hole. Also, explain what the onboard camera would observe as it passed the photon sphere and the event horizon.

As a mass m of gas falls into a black hole, at most 0.1mc2 is likely to emerge as radiation; the rest is swallowed by the black hole. Show the Eddington luminosity for a black hole of mass M is equivalent to 2*10-9 Mc2yr-1. Explain why we expect the black hole's mass to grow by at least a factor of e every 5*107 years. Where Edding Luminicity is defined as LE=(4piGMmpc)/(sigmaT), where G is the gravitational constant, M is the mass of the black hole, mp is the mass of a proton, c is the speed of light, and sigmaT is Thomson scattering where sigmaT=6.653*10-25 cm2.

Which of the following statements best describes the behaviour of an object falling towards the Event Horizon of a Black Hole (according to an observer a long way from it)? As gravity increases the falling object will not suffer any change in appearence or the progression of time. As gravity increases the object's light will be compressed, leading to it looking bluer, with time appearing to passing more slowly for it. The falling object will appear to experience an increase in the rate of time, and it's colour will appear evermore red. As the falling object experiences ever stronger gravity, it will become redder and time will appear to pass more slowly for it.

The area of the event Horizon of a black hole is 4tRg². Use the Schwarzschild metric to verify this. (Please answer in detail or skip)

Suppose a quasar is shining with a luminosity L.  What is the approximate minimal mass of the black hole?  (If the black hole had a lower mass than this, the pressure in the material would overcome the gravity of the black hole and the material would be blown apart.) Give your answer in solar masses, in scientific notation to one significant figure (no decimal places). Value: L=1×10^12Lsun​ Suppose the quasar in the previous problem is 10% efficient at turning rest mass into energetic photons, according to Einstein's equation E=mc2.  What is the necessary rate of accretion of mass onto this black hole, to sustain its luminosity of 1* 1012 solar luminosities -- i.e. how much mass must be 'fed' to this black hole to keep the AGN shining so brightly?   Give your response in units of solar masses of material per year, with one decimal place.

Calculate the gravitational redshift of radiation of wavelength 550 nm (the middle of the visible range) that is emitted from a neutron star having a mass of 5.8 × 10³⁰ kg and a radius of 10 km. Assume that the radiation is being detected far from the neutron star.

Supermassive black holes are thought to exist in the centers of some galaxies. What would be the Schwarzschild radii of black holes of 1 million and 1 billion solar masses? How does the first black hole compare in size with the Sun? How does the second compare in size with the solar system?