Universal horizons and Hawking radiation in nonprojectable 2d Hořava gravity coupled to a nonrelativistic scalar field

Li, Bao-Fei; Bhattacharjee, Madhurima; Wang, Anzhong

doi:10.1103/physrevd.96.084006

“…For an asymptotically flat Schwarzschild black hole, the corresponding "universal horizon" is the hypersurface r = 3M/2, instead of the event horizon r = 2M [35]. The universal horizons exhibit thermodynamical properties [37][38][39], and should be thought as being associated with the Hawking temperature in HL gravity and Lorentz-violating theories in general [40][41][42], much like the event horizon is associated with Hawking radiation in general relativity. Nevertheless, in the geometric optics limit, the effective emission surface is not the event horizon even in general relativity.…”

Section: Introductionmentioning

confidence: 99%

Black hole evaporation in Hořava–Lifshitz gravity

Xu

¹

,

Ong

²

2020

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Hořava–Lifshitz (HL) gravity was formulated in hope of solving the non-renormalization problem in Einstein gravity and the ghost problem in higher derivative gravity theories by violating Lorentz invariance. In this work we consider the spherically symmetric neutral AdS black hole evaporation process in HL gravity in various spacetime dimensions d, and with detailed balance violation parameter $$0\leqslant \epsilon ^2\leqslant 1$$ 0 ⩽ ϵ 2 ⩽ 1 . We find that the lifetime of the black holes under Hawking evaporation is dimensional dependent, with $$d=4,5$$ d = 4 , 5 behave differently from $$d\geqslant 6$$ d ⩾ 6 . For the case of $$\epsilon =0$$ ϵ = 0 , in $$d=4,5$$ d = 4 , 5 , the black hole admits zero temperature state, and the lifetime of the black hole is always infinite. This phenomenon obeys the third law of black hole thermodynamics, and implies that the black holes become an effective remnant towards the end of the evaporation. As $$d\geqslant 6$$ d ⩾ 6 , however, the lifetime of black hole does not diverge with any initial black hole mass, and it is bounded by a time of the order of $$\ell ^{d-1}$$ ℓ d - 1 , similar to the case of Schwarzschild-AdS in Einstein gravity (which corresponds to $$\epsilon ^2=1$$ ϵ 2 = 1 ), though for the latter this holds for all $$d\geqslant 4$$ d ⩾ 4 . The case of $$0<\epsilon ^2<1$$ 0 < ϵ 2 < 1 is also qualitatively similar with $$\epsilon =0$$ ϵ = 0 .

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“…For example, a recent model in 1+1 dimensions of the Hořava theory coupled to a nonrelativistic scalar field has been studied in Ref. [29], finding black holes with universal horizons. This paper is organized as follows: to illustrate on simple grounds how in some systems there can be differences on the space of solutions of the Hamiltonian and the Lagrangian, we discuss in section 2 a simple toy model that mimics the gravitational theory and that exhibits this behavior.…”

Section: Introductionmentioning

confidence: 99%

On the space of solutions of the Hořava theory at the kinetic-conformal point

Bellorín

¹

,

Restuccia

²

2017

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The nonprojectable Hořava theory at the kinetic-conformal point is defined by setting a specific value of the coupling constant of the kinetic term of the Lagrangian. This formulation has two additional second class-constraints that eliminate the extra mode. We show that the space of solutions of this theory in the Hamiltonian formalism is bigger than the space of solutions in the original Lagrangian formalism. In the Hamiltonian formalism there are certain configurations for the Lagrange multupliers that lead to solutions that cannot be found in the original Lagrangian formulation. We show specific examples in vacuum and with a source. The solution with the source has homogeneous and isotropic spatial hypersurfaces. The enhancement of the space of solutions leaves the possibility that new solutions applicable to cosmology, or to other physical systems, can be found in the Hamiltonian formalism.

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“…For an asymptotically flat Schwarzschild black hole, the corresponding "universal horizon" is the hypersurface r = 3M/2, instead of the event horizon r = 2M [35]. The universal horizons exhibit thermodynamical properties [37][38][39], and should be thought as being associated with the Hawking temperature in HL gravity and Lorentz-violating theories in general [40][41][42], much like the event horizon is associated with Hawking radiation in general relativity. Nevertheless, in the geometric optics limit, the effective emission surface is not the event horizon even in general relativity.…”

mentioning

confidence: 99%

Black Hole Evaporation in Hořava-Lifshitz Gravity

Xu,

Ong

2020

Preprint

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Hořava-Lifshitz (HL) gravity was formulated in hope of solving the nonrenormalization problem in Einstein gravity and the ghost problem in higher derivative gravity theories by violating Lorentz invariance. In this work we consider the black hole evaporation process in HL gravity in various spacetime dimensions d, and with detailed balance violation parameter 0 2 1. We find that the lifetime of the black holes under Hawking evaporation is dimensional dependent, with d = 4, 5 behave differently from d 6. For the case of = 0, in d = 4, 5, the black hole admits zero temperature state, and the lifetime of the black hole is always infinite. This phenomenon obeys the third law of black hole thermodynamics, and implies that the black holes become an effective remnant towards the end of the evaporation. As d 6, however, the lifetime of black hole does not diverge with any initial black hole mass, and it is bounded by a time of the order of d−1 , similar to the case of Schwarzschild-AdS in Einstein gravity (which corresponds to 2 = 1), though for the latter this holds for all d 4. The case of 0 < 2 < 1 is also qualitatively similar with = 0.

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Universal horizons and Hawking radiation in nonprojectable 2d Hořava gravity coupled to a nonrelativistic scalar field

Cited by 3 publications

References 88 publications

Black hole evaporation in Hořava–Lifshitz gravity

Black hole evaporation in Hořava–Lifshitz gravity

On the space of solutions of the Hořava theory at the kinetic-conformal point

Black Hole Evaporation in Hořava-Lifshitz Gravity

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