THE BLACK HOLE WAR BY Leonard Susskind is a non mathematical discussion of black holes.
BLACK HOLES AND TIME WARPS BY Kip Thorne is a bit more technical, traditional and comprehensive...very detailed; very little math. It's 99% black holes and 1% time warps...
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There is a law which is violated in a semi-classical calculation by Hawking describing black hole evaporation. The law is the unitary evolution of the quantum wave function.
I thought Hawking conceded to Susskind that Susskind was correct. Is there a source you can recommend so I can read more??
The major 'conservation law' that was thought to be violated was the 'conservation of information' or the 'Information Loss Paradox' of black Holes. It turns out that most of the information of the universe resides in BH!...like the supermassive BH at the heart of virtually all galaxies...
What happens to information that 'disappears' into a black hole [BH]? Is it 'lost'?
Susskind's work...
Briefly, Unruh showed that thermal and quantum jitters get mixed up in an odd way. Susskind following d'Hooft's early work showed the information is encoded in subsequent Hawking radiation.
Bits [information] is displayed on the stretched horizon, and later recovered even though a ‘copy’ is headed toward the singularity…Could someone grab the bit, jump in the BH and duplicate the information. No: the infalling bit arrives at the singularity in a finite, relatively short time. To recover even a single bit from the horizon, from outside, would supposedly take 10
68 Years..a vastly longer period than the current age of the universe…to be recovered. [Don Page did this work.] [pg 264]
An interesting view Susskind offers from string theory: long strings on the stretched horizon are subject to quantum jitters...and as a segment of string is bumped off, it is emitted as Hawking radiation... in which BH information is scrambled/encoded.
You can read summaries and other 'solutions' of the 'paradox' here:
http://en.wikipedia.org/wiki/Information_loss_paradox
http://en.wikipedia.org/wiki/Holographic_principle