Black Hole Surface Gravity in Doubly Special Relativity Geometries

Relancio, J. J.; Liberati, Stefano

doi:10.3390/universe8020136

Cited by 7 publications

(7 citation statements)

References 94 publications

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“…As we saw in [40], the surface gravity obtained from the inaffinity of null geodesics is the same of the one of GR for a generic metric of the form of (17), i.e., independently of the choice of f 1 and f 2 . Here we show that, for any choice of these functions, the surface gravity is a constant, as in GR, when considering massless particles.…”

Section: Zero Lawmentioning

confidence: 69%

“…In [40] it was found that only for the basis leading to Eq. ( 18) the diverse possible notions of surface gravity coincide.…”

Section: B Deformed Relativistic Kinematics In Curves Spacetimesmentioning

confidence: 99%

“…It was shown in [40] that the surface gravity, defined as the inaffinity of the generators of the horizon, is the same as in GR for a black hole metric of the from ( 17), i.e.…”

Section: B Generator Surface Gravitymentioning

confidence: 99%

“…In [36][37][38][39][40] the proposal of [33] was generalized so allowing the metric to describe a curved spacetime, so leading to a geometry in the cotangent bundle depending on all the phase-space variables. This scheme is a generalization of the aforementioned Hamilton structures, the so-called generalized Hamilton spaces [21].…”

Section: Introductionmentioning

confidence: 99%

“…In this case, a first remarkable result is that, in spite of the particle-dependent modified dispersion relations, there is still a common horizon for all particles, independently of their energy [36]. However, the usual alternative and equivalent definitions of surface gravity [59] adopted in GR turn out to not coincide anymore, albeit they can do so in a very particular momentum basis [40]. This opens the question if the laws of black hole mechanics/thermodynamics can be generically extended in this context and in which way.…”

Section: Introductionmentioning

confidence: 99%

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Exploring black hole mechanics in cotangent bundle geometries

Relancio,

Liberati

2022

Preprint

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The classical and continuum limit of a quantum gravitational setting could lead, at mesoscopic regimes, to a very different notion of geometry w.r.t. the pseudo-Riemannian one of special and general relativity. A possible way to characterize this modified space-time notion is by a momentum dependent metric, in such a way that particles with different energies could probe different spacetimes. Indeed, doubly special relativity theories, deforming the special relativistic kinematics while maintaining a relativity principle, have been understood within a geometrical context, by considering a curved momentum space. The extension of these momentum spaces to curved spacetimes and its possible phenomenological implications have been recently investigated. Following this line of research, we address here the first two laws of black holes thermodynamics in the context of a cotangent bundle metric, depending on both momentum and space-time coordinates, compatible with the relativistic deformed kinematics of doubly special relativity.

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Section: Zero Lawmentioning

confidence: 69%

“…In [40] it was found that only for the basis leading to Eq. ( 18) the diverse possible notions of surface gravity coincide.…”

Section: B Deformed Relativistic Kinematics In Curves Spacetimesmentioning

confidence: 99%

“…It was shown in [40] that the surface gravity, defined as the inaffinity of the generators of the horizon, is the same as in GR for a black hole metric of the from ( 17), i.e.…”

Section: B Generator Surface Gravitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exploring black hole mechanics in cotangent bundle geometries

Relancio,

Liberati

2022

Preprint

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Spacetime thermodynamics in momentum-dependent geometries

2022

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Reinterpreting deformed Heisenberg algebras

Wagner

2023

Eur. Phys. J. C

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Minimal and maximal uncertainties of position measurements are widely considered possible hallmarks of low-energy quantum as well as classical gravity. While General Relativity describes interactions in terms of spatial curvature, its quantum analogue may also extend to the realm of curved momentum space as suggested, e.g. in the context of Relative Locality in Deformed Special Relativity. Drawing on earlier work, we show in an entirely Born reciprocal, i.e. position and momentum space covariant, way that the quadratic Generalized Extended Uncertainty principle can alternatively be described in terms of quantum dynamics on a general curved cotangent manifold. In the case of the Extended Uncertainty Principle the curvature tensor in position space is proportional to the noncommutativity of the momenta, while an analogous relation applies to the curvature tensor in momentum space and the noncommutativity of the coordinates for the Generalized Uncertainty Principle. In the process of deriving this map, the covariance of the approach constrains the admissible models to an interesting subclass of noncommutative geometries which has not been studied before. Furthermore, we reverse the approach to derive general anisotropically deformed uncertainty relations from general background geometries. As an example, this formalism is applied to (anti)-de Sitter spacetime.

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Black Hole Surface Gravity in Doubly Special Relativity Geometries

Cited by 7 publications

References 94 publications

Exploring black hole mechanics in cotangent bundle geometries

Exploring black hole mechanics in cotangent bundle geometries

Spacetime thermodynamics in momentum-dependent geometries

Reinterpreting deformed Heisenberg algebras

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