For a remote observer, a black hole with mass $M$ has a temperature $T=1/M$. Now I am confused with the problem:

  • A larger black hole can achieve a task faster or slower if it's regarded as a kind of information processor.

(1)For example, for the task to 'swallow information', if we send a bit of information to a black hole, it will be swallowed by the black hole in a 'scrambling' time $t_w=M \log(M)$ by 'scrambling' the bit. Since from a quantum circuit point of view, a single bit will be scrambled(correlated / mixed) to all the other DOF in this scrambling time, i.e., it need $\log(M^2)$ steps and each step takes a time interval of $1/T=M$.

(2)Similarly, when the black hole evaporates, it 'spit out' a bit in a time interval of $t_r=1/T=M$ since $\mathrm{d}M/\mathrm{d}t=-1/M^2\implies (1/T)\cdot \mathrm{d}S/\mathrm{d}t=\textrm{constant}$ with $S$ the entropy. So every time step $1/T=M$, a constant number of bits are spitted out or evaporated.

So we have: It seems a larger black hole processes information slower (with a time step $1/T=M$) and this is consistent with its lower temperature.

But a larger black hole has a larger mass $M$, it should 'evolve' faster with a larger $H$ so that it can accomplish a single operation faster by the uncertainty relationship so that the time step is $\hbar/M$ . But why it accomplish a unit task (swallow or spit out a bit) slower?

Is this a contradiction? Or there is a misunderstanding here? If a black hole is regarded as an information processor, what should be its CPU clock rate? $M$ or $1/M\,?$

Please correct me if I am wrong.

  • $\begingroup$ Let us know when you have found a black hole that can give you the answer to which countries border Afghanistan. $\endgroup$ – CuriousOne Feb 1 '16 at 9:04
  • 2
    $\begingroup$ can you explain the motivation behind regarding a black hole as a kind of information processor along with exact details of its working? This way the question seems vague... $\endgroup$ – Bruce Lee Feb 1 '16 at 10:11
  • $\begingroup$ @Bruce Lee I am trying to understand the black hole from the quantum information point of view, then I have to problem if the black hole is regarded as an information processor, what should be its CPU clock rate? M or 1/M? $\endgroup$ – XXDD Feb 1 '16 at 10:42
  • $\begingroup$ Are you sure you understand the working principle of CPUs? $\endgroup$ – CuriousOne Feb 1 '16 at 16:08

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