By Peter G. Bergmann
The writer shows that the ebook is written for "the layman." i believe he is a section faraway from the historical past of the common individual. even supposing he has skillfully got rid of the mathematics from a few very complex topics, the subjects are only too advanced to simplify for Joe common. That having been stated, it he bargains factors that I want I had heard whilst i used to be an undergraduate.
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Extra info for The Riddle of Gravitation: Revised and Updated Edition
11) at P . Let ra be the spacelike unit normal to the stretched horizon , pointing in the direction of increasing N. We know that as N → 0, the stretched horizon approaches the local horizon and Nr i approaches ξ i . With this background, we compute J a for the ξ a introduced above in the neighbourhood of P . Since it is an approximate Killing vector, satisfying Eq. 11), it follows that δξ v = 0 giving the current to be J a = 2E ab ξb + Lξ a . The product ra J a for the vector r a , which satisfies ξ a ra = 0 on the stretched horizon, becomes quite simple: ra J a = 2E ab ra ξb .
Different theories of gravity are characterized by different forms of entropy density just as different physical systems are characterized by different forms of entropy functionals. I think this is completely in harmony with the thermodynamic spirit. Thermodynamics applies to any system; if you want to describe a particular system, you need to specify its entropy functional or some other thermodynamic potential. So what the development so far is telling us is that we need to put in some more extra physical input into the theory to find the field equations describing the theory.
When equations of motion hold, the bulk also gets a contribution from matter which cancels it out, leaving the entropy of a region V to reside in its boundary ∂ V . Me: Yes. I need to think more about this. Harold: Also, arising out of your letting me into the trick, I realize that I can now find an S for any theory, even if Eq. 25) does not hold. You just have to reverseengineer it starting from (2Eab − Tab )na nb as the entropy density and using the expression in Eq. 2) for Eab , right? So why do you insist on Eq.