On Gravity and the Uncertainty Principle

Adler, Ronald J.; Santiago, David I.

doi:10.1142/s0217732399001462

Cited by 471 publications

(480 citation statements)

References 7 publications

(2 reference statements)

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“…As a result of string theory [16], or noncommutative spacetime algebra [17,19], or general considerations of quantum mechanics and gravity [15,18], the standard uncertainty principle must be modified when the gravity effect is included. A heuristic derivation may be made on dimensional grounds.…”

Section: Generalized Uncertainty Principle and Black Hole Remnantmentioning

confidence: 99%

Inflation induced Planck-size black hole remnants as dark matter

Chen

2005

New Astronomy Reviews

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While there exist various candidates, the identification of dark matter remains unresolved. Recently it was argued that the generalized uncertainty principle (GUP) may prevent a black hole from evaporating completely, and as a result there should exist a Planck-size BHR at the end of its evaporation. We speculate that the stability of BHR may be further protected by supersymmetry in the form of extremal black hole. If this is indeed the case and if a sufficient amount of small black holes can be produced in the early universe, then the resultant BHRs can be an interesting candidate for DM. We demonstrate that this is the case in the hybrid inflation model. By assuming BHR as DM, our notion imposes a constraint on the hybrid inflation potential. We show that such a constraint is not fine-tuned. Possible observational signatures are briefly discussed.

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Section: Generalized Uncertainty Principle and Black Hole Remnantmentioning

confidence: 99%

Inflation induced Planck-size black hole remnants as dark matter

Chen

2005

New Astronomy Reviews

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“…As a result of string theory [6] or more general considerations of quantum mechanics and gravity [7,8], the GUP gives the position uncertainty as…”

Section: Generalized Uncertainty Principlementioning

confidence: 99%

“…In a recent paper [5], we invoked the generalized uncertainty principle (GUP) [6][7][8] and argued the contrary, that the total collapse of a black hole may be prevented by dynamics and not by symmetry, just like the prevention of hydrogen atom from collapse by the uncertainty principle [9]. Our arguments then lead to a modified black hole entropy and temperature, and as a consequence the existence of a BHR at around the Planck mass.…”

Section: Introductionmentioning

confidence: 99%

Black hole remnants and dark matter

Chen

Adler

2003

Nuclear Physics B - Proceedings Supplements

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We argue that, when the gravity effect is included, the generalized uncertainty principle (GUP) may prevent black holes from total evaporation in a similar way that the standard uncertainty principle prevents the hydrogen atom from total collapse. Specifically we invoke the GUP to obtain a modified Hawking temperature, which indicates that there should exist non-radiating remnants (BHR) of about Planck mass. BHRs are an attractive candidate for cold dark matter. We investigate an alternative cosmology in which primordial BHRs are the primary source of dark matter.

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“…The rod's center of mass will also have an uncertainty in its position, given by equation (3). Both this and ∆x will contribute to the uncertainty of any distance we measure by sending a burst of light from the clock and measuring the time it takes for the light to return.…”

Section: A Modified Thought Experimentsmentioning

confidence: 99%

Uncertainty in measurements of distance

Baez

Olson

2002

Class. Quantum Grav.

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Ng and van Dam have argued that quantum theory and general relativity give a lower bound ∆ℓ ℓ 1/3 ℓ 2/3 P on the uncertainty of any distance, where ℓ is the distance to be measured and ℓP is the Planck length. Their idea is roughly that to minimize the position uncertainty of a freely falling measuring device one must increase its mass, but if its mass becomes too large it will collapse to form a black hole. Here we show that one can go below the Ng-van Dam bound by attaching the measuring device to a massive elastic rod. Relativistic limitations on the rod's rigidity, together with the constraint that its length exceeds its Schwarzschild radius, imply that zero-point fluctuations of the rod give an uncertainty ∆ℓ ℓP .

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On Gravity and the Uncertainty Principle

Cited by 471 publications

References 7 publications

Inflation induced Planck-size black hole remnants as dark matter

Inflation induced Planck-size black hole remnants as dark matter

Black hole remnants and dark matter

Uncertainty in measurements of distance

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