How can a supermassive black hole be 13 billion years old? A supermassive black hole was discovered recently that is 13 billion years old. This blackhole is 1.6 billion times the mass of the sun. How can this blackhole have formed so quickly after the big bang? Do theories predict supermassive black holes forming so quickly?
The answer to this is unknown at the present time.
The issue is that an accreting &quot;seed black hole&quot; can only accrete at a limited rate. The limitation is provided by radiation pressure from the material it is accreting. This provides negative feedback and defines a maximum accretion rate for spherical accretion known as the Eddington limit, which defines a maximum luminosity and hence a maximum accretion rate (since accretion provides the luminosity).
The net result is that the black hole can grow exponentially, with a growth timescale of about 30-40 million years. That is, it can roughly double in mass in that timescale.
Now the first, primordial stars may have been much more massive than big stars in the universe today, as a result of their pure hydrogen/helium composition. Even if they were able to form up to a few hundred solar mass black holes, it would still take almost a billion years to build a $10^9 M_\odot$ black hole, even if it accreted at the maximum Eddington rate for all of that time.
This is a bit of a stretch so alternative solutions are being sought. These include

Maybe you can form even bigger black holes from early collapsing gas clouds. There are some ideas that if the primordial gas gets ionised by the very first massive stars then it doesn;t fragment into &quot;stellar&quot; objects. This can enable you to form very, very massive &quot;stars&quot; (sometimes called &quot;quasi-stars&quot;), which have black holes at their centres rather than nuclear-fusing cores. These might grow rapidly to be of order $10^5 M_{\odot}$ This can shave of many exponential growth timescales by starting off with a more massive seed.

Maybe you can merge black holes. We now know from gravitational wave detections that mergers can proceed between black holes with tens of solar masses to form $\sim 100M_\odot$ black holes. Perhaps in the early universe there may have been clusters of high-mass black holes that managed to merge with each other on short timescales. These would then form a massive seed black hole that could grow relatively quickly.

There are some ideas about how the Eddington limit can be circumvented and mass accretion can proceed at higher rates, perhaps by suppressing the radiative efficiency of the accreting black hole (e.g. Li et al. 2012).