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Entropy and temperature of black holes in a gravity's rainbow
General Relativity and Quantum Cosmology · Submitted 11 Aug 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that, for a family of doubly special relativity theories satisfying certain properties, the temperature can vanish in the limit of zero black hole mass.
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The abstract, sentence by sentence
The linear relation between the entropy and area of a black hole can be derived from the Heisenberg principle, the energy-momentum dispersion relation of special relativity, and general considerations about black holes. There exist results in quantum gravity and related contexts suggesting the modification of the usual dispersion relation and uncertainty principle. One of these contexts is the gravity's rainbow formalism. We analyze the consequences of such a modification for black hole thermodynamics from the perspective of two distinct rainbow realizations built from doubly special relativity. One is the proposal of Magueijo and Smolin and the other is based on a canonical implementation of doubly special relativity put forward recently by the authors. In these scenarios, we obtain modified expressions for the entropy and temperature of black holes. We show that, for a family of doubly special relativity theories satisfying certain properties, the temperature can vanish in the limit of zero black hole mass. For the Magueijo and Smolin proposal, this is only possible for some restricted class of models with bounded energy and unbounded momentum. With the proposal of a canonical implementation, on the other hand, the temperature may vanish for more general theories; in particular, the momentum may also be bounded, with bounded or unbounded energy. This opens new possibilities for the outcome of black hole evaporation in the framework of a gravity's rainbow.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The linear relation between the entropy and area of a black hole can be derived from the Heisenberg principle, the energy-momentum dispersion relation of special relativity, and general considerations about black holes. | background 1.00 | 0.12 | 0.03 | asserted 0.97 |
| s1 | There exist results in quantum gravity and related contexts suggesting the modification of the usual dispersion relation and uncertainty principle. | background 1.00 | 0.04 | 0.02 | hedged possibility 0.77 |
| s2 | One of these contexts is the gravity's rainbow formalism. | background 1.00 | 0.04 | 0.02 | asserted 0.98 |
| s3 | We analyze the consequences of such a modification for black hole thermodynamics from the perspective of two distinct rainbow realizations built from doubly special relativity. | contribution 0.95 | 0.85 | 0.06 | asserted 0.92 |
| s4 | One is the proposal of Magueijo and Smolin and the other is based on a canonical implementation of doubly special relativity put forward recently by the authors. | method 0.71 | 0.19 | 0.03 | asserted 0.99 |
| s5 | In these scenarios, we obtain modified expressions for the entropy and temperature of black holes. | result 0.86 | 0.94 | 0.23 | asserted 1.00 |
| s6 | We show that, for a family of doubly special relativity theories satisfying certain properties, the temperature can vanish in the limit of zero black hole mass. | result 1.00 | 0.93 | 0.39 | asserted 0.96 |
| s7 | For the Magueijo and Smolin proposal, this is only possible for some restricted class of models with bounded energy and unbounded momentum. | result 0.92 | 0.76 | 0.09 | hedged possibility 0.57 |
| s8 | With the proposal of a canonical implementation, on the other hand, the temperature may vanish for more general theories; in particular, the momentum may also be bounded, with bounded or unbounded energy. | result 0.99 | 0.84 | 0.20 | hedged possibility 0.99 |
| s9 | This opens new possibilities for the outcome of black hole evaporation in the framework of a gravity's rainbow. | interpretation 1.00 | 0.53 | 0.27 | hedged possibility 0.71 |
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The paper
Original abstract
The linear relation between the entropy and area of a black hole can be derived from the Heisenberg principle, the energy-momentum dispersion relation of special relativity, and general considerations about black holes. There exist results in quantum gravity and related contexts suggesting the modification of the usual dispersion relation and uncertainty principle. One of these contexts is the gravity's rainbow formalism. We analyze the consequences of such a modification for black hole thermodynamics from the perspective of two distinct rainbow realizations built from doubly special relativity. One is the proposal of Magueijo and Smolin and the other is based on a canonical implementation of doubly special relativity put forward recently by the authors. In these scenarios, we obtain modified expressions for the entropy and temperature of black holes. We show that, for a family of doubly special relativity theories satisfying certain properties, the temperature can vanish in the limit of zero black hole mass. For the Magueijo and Smolin proposal, this is only possible for some restricted class of models with bounded energy and unbounded momentum. With the proposal of a canonical implementation, on the other hand, the temperature may vanish for more general theories; in particular, the momentum may also be bounded, with bounded or unbounded energy. This opens new possibilities for the outcome of black hole evaporation in the framework of a gravity's rainbow.
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References
How the literature uses it
13 arXiv papers cite this in 17 sentences
Papers citing it · 8 sentences without a confident label
Uses its method or tool 1 paper
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Suppose we make the measurement with the use of radiation photons with average energy $E=<E>$, then we expect that the temperature of black holes can be identified with the energy of photons emitted from black hole [ref] , namely $T = E$.
Modified (A)dS Schwarzschild black holes in Rainbow spacetime · Thermodynamics with the modified (A)dS Schwarzschild black holes · 0.87
Cites it as background 7 papers
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Out of such theories, the Rastall [ref] and Rainbow [ref] and combined Rastall-Rainbow [ref] formalisms have attracted a lot of interest in the fields of astrophysics and cosmology in recent times [ref] .
Bose-Einstein condensate stars in combined Rastall-Rainbow gravity · Introduction · 0.96
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Rainbow black-hole thermodynamics was developed through energy-dependent temperature and entropy relations [ref] , while rainbow cosmology generalized the Friedmann description to energy-dependent geometries [ref] .
Rainbow McVittie Horizons in an Expanding Universe · Introduction · 0.97
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Rainbow gravity formalism has received a lot of attention recently and other stimulating work on this formalism can be found, for instance, in [ref] .
The Big Bounce in Rainbow Universe · Introduction · 1.00
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