By Elcio Abdalla; et al

ISBN-10: 0387578056

ISBN-13: 9780387578057

ISBN-10: 3540578056

ISBN-13: 9783540578055

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**Extra resources for 2D-gravity in non-critical strings : discrete and continuum approaches**

**Sample text**

In 1998 Silk & Rees [66] proposed that it was the phenomenal energy output in the quasar phase, as the black hole grew in mass by accretion, which was responsible. Both grow from gas in the galaxy – the galaxy forming stars from the gas, the black hole accreting the gas. Eventually the black hole is so big and powerful that it blasts all the gas from the galaxy so both stop growing and we are left with the observed relation. There is clear evidence that massive black holes have grown by accretion from the Soltan relation [67]: η (60) where z is the mean redshift at which the accretion occurs.

Of the equation: (52) where A = 3(GM)3/c2h4 is very small. I. can be found to be: (53) Now, in this expression, the first and third terms are tiny, since A is. However, the second term, Aeφ sin φ, might be tiny at first, but will gradually grow with time, since the φ part (without a cos or sin enclosing it) means it is cumulative. We must therefore retain it, and our second approximation is (54) where (55) Using (56) we can therefore write (57) u is therefore periodic, but with period . 2 and we know M⊙ = 2 × 1030 kg.

The electron and proton, although assumed free, are bound together by electrostatic attraction. (46) where the radiative force term is the flux of photons (of typical energy hν) times the cross-section times the momentum of a photon. This gives (47) which is about 1031 W per Solar mass. Since the Eddington limit is proportional to the mass of the black hole the black hole mass can grow exponentially, if sufficient fuel is available. If growth is at the Eddington limit, the e-folding time of the black hole mass is about 4 × 107 yr.

### 2D-gravity in non-critical strings : discrete and continuum approaches by Elcio Abdalla; et al

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