Can Information Escape for a Black Hole?
The Black Hole Information Paradox suggests information can’t escape a black hole intact. While new theories show information may be able to escape, it hasn’t been proven as of 2016. This means despite new theories like Stephen Hawking’s Soft Hair theorem, there is still a chance that calculations suggest that physical information could permanently disappear in a black hole could be correct.
Stephen Hawking: Black Hole Paradox Explained By ‘Soft Hairs’. This video is a simple introduction to the sometimes difficult concept of black holes, soft hair, and the information paradox.
An Introduction to Soft Hair on Black Holes – Stephen Hawking, black holes, and the Information Paradox
Stephen Hawking’s most recent work, Soft Hair on Black Holes, provides a compelling theory showing that soft gravitons and photons trapped on the event horizon of a black hole could record information previously thought to be lost (as the photon for example would distort, along with the area around it, as new information passed into the hole; essentially holding all information about what has passed into the hole on the event horizon and allowing that information to escape later). 
Do Black Holes Have No Hair? Stephen Hawking
Why is it called “soft hair”? The idea is that electromagnetic and gravitational radiation gets stuck trying to escape the blackhole at the speed of light creating a sort of fuzz or “soft hair” around the event horizon of the blackhole. This hair can record information by distorting the radiation and spacetime around the radiation. Imagine light trying to escape an event horizon, not going fast enough to escape and not going slow enough to fall in the blackhole, it might look like little hairs sticking up out of the event horizon. This is a soft hair, like light speed peach fuzz on the black hole of a cheek, a very simple term for a complex concept. See another soft hair explainer here.
Why does it matter if black holes destroy information? Black holes destroying information means that the world is not deterministic. That the present doesn’t predict the future perfectly, and it also can’t be used to reconstruct the past. This would flip physics on its head by showing limits to the causal nature of the universe.
TIP: All the information contained in three dimensions can be recorded on a two dimensional surface. This helps explain both soft hair on black holes and the holographic universe theory.
What is a Black Hole? Mysteries of Astronomy
The History of Hawking Radiation and the Black Hole Information Paradox – In Simple Terms
To understand the black hole debate and “soft hair” we need to go back to 1975 when Stephen Hawking and Jacob Bekenstein showed that black holes should slowly radiate away energy to let information escape, albeit not intact via aptly named “Hawking radiation”.
What Stephen Hawking Really Said About Black Holes
In simple terms, scientists expected that Hawking radiation should be independent of the information going into a black hole. All information about the matter going in to the black hole should disappear and be permanently inaccessible, and the only thing that should be observable is mass, electric charge, and angular momentum (no-hair theorem).
Hawking remained convinced that quantum information may be destroyed, but others tried to prove him wrong, saying that information could be retained.
From No-Hair to Soft Hair – Information Stored on the Event Horizon
In 2004, Stephen Hawking published a paper presenting the theory that quantum perturbations of the event horizon could allow information to escape from a black hole, which would resolve the information paradox. This led to the idea that information could be stored not inside the black hole, where he still thought it would be lost, but on its boundary, the event horizon (which leads to a holographic universe theory and Hawking’s own Soft Hair theory in 2016).
Hawking presents new idea on how information could escape black holes – KTH Royal Institute of Technology
LIGO, Soft Hair, and Beyond: the Future of Black Hole Science
Now, with new science like LIGO, which detected gravitational waves (ripples in spacetime), Hawking has presented his solution to the information paradox, the aforementioned “Soft Hair on Black Holes.”
Moving beyond Hawking’s own work, a new paper, published in Physical Review Letters (which describes a computer simulation confirming Hawking’s theory), written about in March of 2016, seems to hint that Hawking’s revised views are right, and that information can be preserved.
An article with an interview of the paper’s authors says, “The issue was never laid to rest because Hawking’s calculation was not able to capture the effect that the radiation, called Hawking radiation, has on the black hole itself,” Adami said. “Physicists assumed that the black hole would shrink in time as the Hawking radiation carries away the black hole’s mass, but no one could verify this through mathematical calculations.” A calculation of the black hole’s evaporation seemed impossible unless a full theory of quantum gravity that unites Einstein’s general relativity with the framework of quantum field theory could be found.
The paper explains how the team created a mathematical model that shows that information can leak back out of a Black hole as it evaporates, and that information can stay in the black hole as it shrinks. When they ran their computer-based model, it showed that information could be found outside the black hole after a long enough time.
None of the above proves for sure that information can escape black holes, but the new findings from LIGO and generally advances in computing, science, and other technology mean that we could have a definitive answer soon. For now we can be pretty sure Hawking is on the right track, but as we know from Hawking’s own no-hair theorem and the history of science in general, we have been wrong before.
Black Holes: Crash Course Astronomy #33