If there was a black hole on earth, what would it look like?
An interesting and horrifying possibility for your book could be that of a tiny black hole with negligible mass relative to the mass of the Earth. It would silently sink into the ground, completely unnoticed. It would make damped oscillations around the center of the Earth until eventually staying within the nucleus. There it would stay unnoticed, slowly growing like a parasite. The Earth radius would start to diminish, and thus the crust would have to adapt by means of earthquakes - very weak at first, but of increasing frequency and strength. Eventually, chains of volcanoes would appear along giant fault lines, heating and poisoning the atmosphere, bringing total obliteration. After that, the Earth would continue shrinking until all that was left would be a tiny black hole with little more than one Earth mass in the place where our planet was. And the Moon would stay there as a horrified witness of the catastrophe.
Nothing on Earth would be able to stop the process and save us. Nothing except Chuck Norris.
Note: Classical GR black holes are fully determined with just three values: mass, electric charge and angular momentum (No-hair theorem). If the charge is large enough in the black hole of your novel, then the hero might be able to confine it by using strong magnetic fields.
There are some visualizations of what it would look like to travel past the event horizon, assuming you survive the process of course.
This video gives you an idea of what the black hole looks like. What you see is a distortion of everything around you, as bit like looking through curved glass.
Unfortunately these videos aren't set on Earth; I'm sure the hole chewing up Earth would look spectacular, but I don't know how long this might last. I suspect things would get pretty hot as matter is compressed on its way towards the hole.
In this, I have taken the assumption that the singularity is created within the atmosphere, perhaps by an experiment or some such, rather than a wandering black hole, and therefore starts life with much less mass than the earth. A naturally created black hole travelling in space would generally be far more massive, having been created from a collapsing star. in the latter case, the planet would simply be shredded as it nears the event horizon, killing everyone on the planet, or possibly just swallowing the earth in seconds, dependent on the relative motions and trajectories of the two
The thing about a singularity is that any matter which falls within its event horizon is consumed, and from an external frame of reference instantly becomes part of the mass of the singularity. Any mass which exists within the atmosphere of earth will move towards the earth at an acceleration of 10 m/s/s. A singularity would not be slowed by air resistance, as it would draw in any air molecules that contacted the event horizon, rather than displace them.
Also, due to the curvature of the Earth, nothing within the atmosphere near the philipines would ever be visible from 90 or 180 degrees away in any direction.
Therefore this singularity would fall rapidly to earth, where it would proceed through the crust experiencing drag equivalent to the ability of whatever matter it contacts to resist, albeit briefly, being torn apart by the singularity pulling in any matter contacting the event hozizon. once through the crust to the liquid part of the core, it would accelerate again, initially passing directly through the gravitational centre of the earth repeatedly back and forth, until it consumes enough matter to shift the centre of gravity of the earth, at which point, the singularity and the earth would begin to orbit their common centre of gravity. This would result in erratic changes as the singularity consumes matter in intermittent pulses, as it passes in and out of voids created by it previous motions.
as the singularity consumes more and more of the planet, the earth would break up under the vibrations caused by the wobbling motion within, speeding the growth of the singularity, as the remains of the crust fall inwards to the common centre of gravity, where they will be consumed by the ever growing black hole. when the earth is fully consumed, the black hole would continue to orbit the sun in its place, until it consumes enough orbiting debris to begin a spiral orbit towards the sun, likely collecting venus and mercury on the way. when it eventually hits the sun, it will repeat the process on a much larger scale, either consuming the star entirely, leaving a black hole in its place, or potentially destabilising the sun enough that it goes supernova before the black hole can consume it.
If the singularity had enough mass to survive longer than a few seconds after creation, without evaporating, I would expect it to destroy the earth completely in just a few hours, with all life being wiped out quite early on due to the cataclysmic disruption to the crust.
If a living person were to enter the event horizon, they would die, torn apart by the forces inside. However, they would feel nothing as the electrical nerve impulses from the affected nerves would never reach the brain, themselves being pulled into the centre of the singularity.