Mach’s holographic principle

Justin Khoury and Maulik Parikh
Phys. Rev. D 80, 084004 – Published 6 October 2009

Abstract

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.

  • Figure
  • Received 16 February 2007

DOI:https://doi.org/10.1103/PhysRevD.80.084004

©2009 American Physical Society

Authors & Affiliations

Justin Khoury1,2 and Maulik Parikh3,4

  • 1Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, Ontario, Canada N2L 2Y5
  • 2Center for Particle Cosmology, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
  • 3Institute for Strings, Cosmology, and Astroparticle Physics, Columbia University, New York, New York 10027, USA
  • 4Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Pune 411007, India

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Issue

Vol. 80, Iss. 8 — 15 October 2009

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