New coordinates for de Sitter space and de Sitter radiation

Mach's principle is the concept that inertial frames are determined by matter. We propose and implement a precise formulation of Mach's principle in which matter and geometry are in one-to-one correspondence. 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. Specification of both boundary and bulk stress tensors uniquely specifies the geometry and thereby the inertial frames. Our framework is similar to that of the black hole membrane paradigm and, in asymptotically AdS space-times, is consistent with holographic duality. I. MACH'S PRINCIPLEAcceleration appears absolute. A snapshot of a rotating bucket of water reveals, through the gentle curve in the water's surface, that the bucket was rotating. Two rocks tied with a rope and set spinning about an axis perpendicular to the rope are measurably distinct from the same two rocks undergoing linear motion: the rope becomes tense. A passenger in an elevator or a windowless spaceship is aware of starts and stops even though the vehicle is a closed system.With his principle of equivalence, Einstein recognized that gravity was simply acceleration in disguise. Moreover, Einstein's equations, like Newton's law of gravitation, indicate that matter is the source for gravity. But if acceleration and gravity are linked, and if gravity

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“…1, as seen from (32). From the Brown-York perspective, these can be canceled with appropriate G 3 and to yield a finite T BY-out .…”

Section: A Minkowski Spacementioning

confidence: 98%

Mach’s holographic principle

Khoury

Parikh

2009

Phys. Rev. D

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“…Inserting (38) into the (chargeless) Dirac equation (5) and following the same procedure as before results in the same expression (27) for the temperature. This is not surprising since all we have done is applied a similarity transformation to the Dirac equation, and we shall not repeat the (somewhat more tedious) calculations here.…”

Section: Technical Issuesmentioning

confidence: 99%

Charged fermions tunnelling from Kerr–Newman black holes

2008

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“…where f is required to be a function of r alone to ensure that the metric remains stationary [6,7]. The form of f (r) can be obtained by imposing the condition that the resulting metric be regular at the horizon.…”

Section: Painlevé Coordinatementioning

confidence: 99%

“…[The authors in Refs. [6,7] extended the method introduced in Ref. [11] to the Painlevé coordinates of (Schwarzschild)dS.]…”

Section: Introductionmentioning

confidence: 99%

Temperature and entropy of Schwarzschild–de Sitter space-time

2003

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In the light of recent interest in quantum gravity in de Sitter space, we investigate semi-classical aspects of 4-dimensional Schwarzschild-de Sitter space-time using the method of complex paths. The standard semi-classical techniques (such as Bogoliubov coefficients and Euclidean field theory) have been useful to study quantum effects in space-times with single horizons; however, none of these approaches seem to work for Schwarzschild-de Sitter or, in general, for space-times with multiple horizons. We extend the method of complex paths to space-times with multiple horizons and obtain the spectrum of particles produced in these space-times. We show that the temperature of radiation in these space-times is proportional to the effective surface gravity -inverse harmonic sum of surface gravity of each horizon. For the Schwarzschild-de Sitter, we apply the method of complex paths to three different coordinate systems -spherically symmetric, Painleve and Lemaitre. We show that the equilibrium temperature in Schwarzschild-de Sitter is the harmonic mean of cosmological and event horizon temperatures. We obtain Bogoliubov coefficients for space-times with multiple horizons by analyzing the mode functions of the quantum fields near the horizons. We propose a new definition of entropy for space-times with multiple horizons analogous to the entropic definition for space-times with a single horizon. We define entropy for these space-times to be inversely proportional to the square of the effective surface gravity. We show that this definition of entropy for Schwarzschild-de Sitter satisfies the D-bound conjecture.

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New coordinates for de Sitter space and de Sitter radiation

Cited by 286 publications

References 9 publications

Mach’s holographic principle

Mach’s holographic principle

Charged fermions tunnelling from Kerr–Newman black holes

Temperature and entropy of Schwarzschild–de Sitter space-time

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