Department of Physics Papers

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Journal Article

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Mach’s principle is the proposition that inertial frames are determined by matter. We put forth and implement a precise correspondence between matter and geometry that realizes Mach’s principle. Einstein’s equations are not modified and no selection principle is applied to their solutions; Mach’s principle is realized wholly within Einstein’s general theory of relativity. The key insight is the observation that, in addition to bulk matter, one can also add boundary matter. Given a space-time, and thus the inertial frames, we can read off both boundary and bulk stress tensors, thereby relating matter and geometry. We consider some global conditions that are necessary for the space-time to be reconstructible, in principle, from bulk and boundary matter. Our framework is similar to that of the black hole membrane paradigm and, in asymptotically anti-de Sitter space-times, is consistent with holographic duality.


Suggested Citation:
Khoury, J. and Parikh, M. (2009). "Mach's holographic principle." Physical Review D. 80, 084004.

© 2009 The American Physical Society

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Date Posted: 14 December 2010

This document has been peer reviewed.