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We analyze Planck scale induced modifications of the relativistic time dilation using data from the Muon Storage Ring experiment at CERN. By examining the lifetimes of muons, we establish, for the first time, a constraint on such quantum gravity-inspired deformations using this channel., Comment: 4 pages

There has been strong interest in the possibility that in the quantum-gravity realm momentum space might be curved, mainly focusing, especially for what concerns phenomenological implications, on the case of a de Sitter momentum space. We here take as starting point the known fact that quantum gravity coupled to matter in $2+1$ spacetime dimensions gives rise to an effective picture characterized by a momentum space with anti-de Sitter geometry, and we point out some key properties of $2+1$-dimensional anti-de Sitter momentum space. We observe that it is impossible to implement all of these properties in theories with a $3+1$-dimensional anti-de Sitter momentum space, and we then investigate, with the aim of providing guidance to the relevant phenomenology focusing on possible modified laws of conservation of momenta, the implications of giving up, in the $3+1$-dimensional case, some of the properties of the $2+1$-dimensional case., Comment: 19 pages. Matches published version in Classical and Quantum Gravity, "Special Issue: Focus on Quantum Gravity Phenomenology in the Multi-Messenger Era: Challenges and Perspectives"

We demonstrate a compatibility between the relativity principle and the clock postulate in deformed special relativity, by identifying the relevant deformed Lorentz transformations in position space between arbitrary frames. This result leads to a first-principles correction to the dilated lifetime of fundamental particles. It turns out that these modified time dilations offer a way to scrutinize Lorentz invariance (or deviations thereof) to high precision., Comment: 5 pages. Acknowledgments added. Matches published version

The last three decades have witnessed the surge of quantum gravity phenomenology in the ultraviolet regime as exemplified by the Planck-scale accuracy of time-delay measurements from highly energetic astrophysical events. Yet, recent advances in precision measurements and control over quantum phenomena may usher in a new era of low-energy quantum gravity phenomenology. In this study, we investigate relativistic modified dispersion relations (MDRs) in curved spacetime and derive the corresponding nonrelativistic Schr\"odinger equation using two complementary approaches. First, we take the nonrelativistic limit, and canonically quantise the result. Second, we apply a WKB-like expansion to an MDR-inspired deformed relativistic wave equation. Both approaches imply equivalent results for single-particle quantum mechanics. Based on a map between our approach and the generalized uncertainty principle (GUP), we recognise in the latter the MDR which is least amenable to low-energy experiments. Consequently, importing data from time-delay measurements, we constrain the linear GUP up to the Planck scale and improve on current bounds to the quadratic one by 17 orders of magnitude. MDRs with larger implications in the infrared, however, can be tightly constrained in the nonrelativistic regime, from which we use the ensuing deviation from the equivalence principle to bound some MDRs to up to one order of magnitude below the Planck scale, while constraining those customarily associated with the bicrossproduct basis of the $\kappa$-Poincar\'e algebra to energy scales beyond $10^{15}$GeV., Comment: 23 pages, one figure; v2 (published version) is significantly shortened with respect to v1; results unchanged

The last three decades have witnessed the surge of quantum gravity phenomenology in the ultraviolet regime as exemplified by the Planck-scale accuracy of time-delay measurements from highly energetic astrophysical events. Yet, recent advances in precision measurements and control over quantum phenomena may usher in a new era of low-energy quantum gravity phenomenology. In this study, we investigate relativistic modified dispersion relations (MDRs) in curved spacetime and derive the corresponding nonrelativistic Schr\"odinger equation using two complementary approaches. First, we take the nonrelativistic limit, and canonically quantise the result. Second, we apply a WKB-like expansion to an MDR-inspired deformed relativistic wave equation. Within the area of applicability of single-particle quantum mechanics, both approaches imply equivalent results. Surprisingly, we recognise in the generalized uncertainty principle (GUP), the prevailing approach in nonrelativistic quantum gravity phenomenology, the MDR which is least amenable to low-energy experiments. Consequently, importing data from the mentioned time-delay measurements, we constrain the linear GUP up to the Planck scale and improve on current bounds to the quadratic one by 17 orders of magnitude. MDRs with larger implications in the infrared, however, can be tightly constrained in the nonrelativistic regime. We use the ensuing deviation from the equivalence principle to bound some MDRs, for example the one customarily associated with the bicrossproduct basis of the $\kappa$-Poincar\'e algebra, to up to four orders of magnitude below the Planck scale., Comment: 34 pages, one figure

A prominent effective description of particles interacting with the quantum properties of gravity is through modifications of the general relativistic dispersion relation. Such modified dispersion relations lead to modifications in the relativistic time dilation. A perfect probe for this effect, which goes with the particle energy cubed $E^3$ over the quantum gravity scale $E_{\text{QG}}$ and the square of the particle mass $M^2$ would be a very light unstable particle for which one can detect the lifetime in the laboratory as a function of its energy to very high precision. In this article we conjecture that a muon collider or accelerator would be a perfect tool to investigate the existence of an anomalous time dilation, and with it the fundamental structure of spacetime at the Planck scale., Comment: 8 pages, 2 figures

In this work, we investigate the existence of neutron stars (NS) in the framework of $f$($\mathbb{T}$,$\mathcal{T}$) gravity, where $\mathbb{T}$ is the torsion tensor and $\mathcal{T}$ is the trace of the energy-momentum tensor. The hydrostatic equilibrium equations are obtained, however, with $p$ and $\rho$ quantities passed on by effective quantities $\bar{p}$ and $\bar{\rho}$, whose mass-radius diagrams are obtained using modern equations of state (EoS) of nuclear matter derived from relativistic mean field models and compared with the ones computed by the Tolman-Oppenheimer-Volkoff (TOV) equations. Substantial changes in the mass-radius profiles of NS are obtained even for small changes in the free parameter of this modified theory. The results indicate that the use of $f$($\mathbb{T}$,$\mathcal{T}$) gravity in the study of NS provides good results for the masses and radii of some important astrophysical objects, as for example, the low-mass X-ray binary (LMXB) NGC 6397 and the pulsar of millisecond PSR J0740+6620. In addition, radii results inferred from the Lead Radius EXperiment (PREX-2) can also be described for certain parameter values.

We propose a sequence of steps and a generic transformation for connecting common thermodynamic quantities considered in asymptotically anti-de Sitter black hole thermodynamics in the bulk and those that are appropriate for CFT thermodynamics in the boundary. We do this by constructing a "varying-$G$ map", where $G$ is the gravitational constant, and demonstrate its usefulness by considering various examples., Comment: 7 pages. Modification of the title; substitution from "holographic dictionary" to "varying-G map"; addition of two subsections on AdS Taub-NUT and Kerr-AdS5 black holes, with discussions about the role of the Casimir energy; addition of references. Matches version accepted for publication in PLB

Deformed relativistic kinematics is a framework which captures effects, that are expected from particles and fields propagating on a quantum spacetime, effectively. They are formulated in terms of a modified dispersion relation and a modified momentum conservation equation. In this work we use Finsler geometry to formulate deformed relativistic kinematics in terms of particle velocities. The relation between the Finsler geometric velocity dependent formulation and the original momentum dependent formulation allows us to construct deformed Lorentz transformations between arbitrary frames. Moreover, we find the corresponding compatible momentum conservation equation to first order in the Planck scale deformation of special relativity based on the $\kappa$-Poincar\'e algebra in the bicrossproduct basis. We find that the deformed Lorentz transformations, as well as the deformed time dilation factor, contain terms that scale with the energy of the particle under consideration to the fourth power. We derive how the distributions of decay products are affected when the deformed relativity principle is satisfied and find, for the case of a pion decaying into a neutrino and a muon, that the ratio of expected neutrinos to muons with a certain energy is just slightly modified when compared to the predictions based on special relativity. We also discuss the phenomenological consequences of this framework for cosmic-ray showers in the atmosphere., Comment: 27+4 pages, 1 figure. Title and abstract were modified. 3 new appendices. Important modifications in the second half of the paper: absence of strong threshold effects. Matches version published in JHEP

The propagation of nonrelativistic excitations in material media with topological defects can be modeled in terms of an external torsion field modifying the Schroedinger equation. Through a perturbative approach, we find a solution for the wave function which gives corrections in the interference patterns of the order of 0.1 Angstrom, for a possible experimental setup at atomic scales. Finally, we demonstrate how this geometric, but effective, approach can indeed accommodate a probabilistic interpretation of the wave function although the perturbative theory is nonunitary., Comment: 7 pages, 2 figures. Replaced to match the published version

In this work we study the inversion temperature associated with the Joule-Thomson expansion from the thermodynamics of AdS-Reissner-N\"ordstrom black holes. We include quantum corrections in a cosmological fluid that can describe phantom dark matter or quintessence, both in a Kiselev scenario. The description of such physical systems involves numerical solutions and the results are presented as temperature-pressure plots for various values of the parameters of our model. We find non-zero minimum inversion temperatures as well as non-zero minimum pressures depending on the values of those parameters. Completing our study, we also find isenthalpic curves associated with black hole fixed mass processes., Comment: V2: 18 pages, 7 figures. In this version, we included a discussion of the First Law and a deduction of equations with a non-zero pressure even at zero inversion temperature that explain our (unchanged) numerical results. This version matches the published one in PRD

Deformed relativistic kinematics are a framework which captures effect that are expected from particles and fields propagating on a quantum spacetime effectively. They are formulated in terms of a modified dispersion relation and a modified momentum conservation equation. In this work we use Finsler geometry to formulate deformed relativistic kinematics in terms of particle velocities. The relation between the Finsler geometric velocity dependent formulation and the original momentum dependent formulation allows us to construct deformed Lorentz transformations between arbitrary frames and the corresponding compatible momentum conservation equation, to first order in the Planck scale deformation of special relativity based on the $\kappa$-Poincar\'e algebra in the bicrossproduct basis. The deformed Lorentz transformations, as well as the deformed time dilation factor, contain terms that scale with the energy of the particle under consideration to the fourth power. This feature is an amplifier which opens access to observables that are close to the Planck scale with present technological capabilities. We derive how the distribution of particles in decays is affected and find, in the example of a pion decaying into a neutrino and a muon, how the ratio of expected neutrinos to muons with a certain energy, changes compared to the predictions based on special relativity. We also discuss the phenomenological consequences of this framework for cosmic-ray showers in the atmosphere., Comment: 16 pages, 2 figures

Deformed relativistic kinematics is a framework which captures effects, that are expected from particles and fields propagating on a quantum spacetime, effectively. They are formulated in terms of a modified dispersion relation and a modified momentum conservation equation. In this work we use Finsler geometry to formulate deformed relativistic kinematics in terms of particle velocities. The relation between the Finsler geometric velocity dependent formulation and the original momentum dependent formulation allows us to construct deformed Lorentz transformations between arbitrary frames. Moreover, we find the corresponding compatible momentum conservation equation to first order in the Planck scale deformation of special relativity based on the $\kappa$-Poincar\'e algebra in the bicrossproduct basis. We find that the deformed Lorentz transformations, as well as the deformed time dilation factor, contain terms that scale with the energy of the particle under consideration to the fourth power. We derive how the distributions of decay products are affected when the deformed relativity principle is satisfied and find, for the case of a pion decaying into a neutrino and a muon, that the ratio of expected neutrinos to muons with a certain energy is just slightly modified when compared to the predictions based on special relativity. We also discuss the phenomenological consequences of this framework for cosmic-ray showers in the atmosphere., Comment: 27+4 pages, 1 figure. Title and abstract were modified. 3 new appendices. Important modifications in the second half of the paper: absence of strong threshold effects. Matches version published in JHEP

The propagation of nonrelativistic excitations in material media with topological defects can be modeled in terms of an external torsion field modifying the Schroedinger equation. Through a perturbative approach, we find a solution for the wave function which gives corrections in the interference patterns of the order of 0.1 Angstrom, for a possible experimental setup at atomic scales. Finally, we demonstrate how this geometric, but effective, approach can indeed accommodate a probabilistic interpretation of the wave function although the perturbative theory is nonunitary., Comment: 7 pages, 2 figures. Replaced to match the published version

We constructed thin-shell wormholes using the well-known "cut and paste" technique for static black holes sourced by an anisotropic fluid within the context of the Rastall gravity. Using the generalized Lanczos equations we explored the energy conditions at the wormhole's throat along with the traversability condition. We determined the stability regions when the wormhole configurations are surrounded by different bulk sources and obtained that the stability regions are considerably modified due to the non-trivial dependence of the Rastall parameter in the effective potential energy., Comment: 26 pages, 7 figures, and 4 tables

Planck scale modified dispersion relations are one way how to capture the influence of quantum gravity on the propagation of fundamental point particles effectively. We derive the time dilation between an observer's or particle's proper time, given by a Finslerian length measure induced from a modified dispersion relation, and a reference laboratory time. To do so, the Finsler length measure for general first order perturbations of the general relativistic dispersion relation is constructed explicitly. From this we then derive the time dilation formula for the $\kappa$-Poincar\'e dispersion relation in several momentum space bases, as well as for modified dispersion relations considered in the context of string theory and loop quantum gravity. Most interestingly we find that the momentum Lorentz factor in the present and future colliders can, in principle, become large enough to constrain the Finsler realization of the $\kappa$-Poincar\'e dispersion relation in the bicrossproduct basis as well as a string theory inspired modified dispersion relation, at Planck scale sensitivity with the help of the muon's lifetime., Comment: 9 pages, 1 table

We present a generalization of Rastall's gravity in which the conservation law of the energy-momentum tensor is altered, and as a result, the trace of the energy-momentum tensor is taken into account together with the Ricci scalar in the expression for the covariant derivative. Afterwards, we obtain the field equations in this theory and solve them by considering a spherically symmetric space-time. We show that the external solution has two possible classes of solutions with spherical symmetry in the vacuum in generalized Rastall's gravity, and we analyse one of them explicitly. The generalization, in contrast to constant value $k=8\pi G$ in general relativity, has a gravitational parameter $k$ that depends on the Rastall constant $\alpha$. As an application, we perform a careful analysis of the effects of the theory on neutron stars using realistic equations of state (EoS) as input. Our results show that important differences on the profile of neutron stars are obtained within two representatives EoS.

Planck scale modified dispersion relations are one way how to capture the influence of quantum gravity on the propagation of fundamental point particles effectively. We derive the time dilation between an observer's or particle's proper time, given by a Finslerian length measure induced from a modified dispersion relation, and a reference laboratory time. To do so, the Finsler length measure for general first order perturbations of the general relativistic dispersion relation is constructed explicitly. From this we then derive the time dilation formula for the $\kappa$-Poincar\'e dispersion relation in several momentum space bases, as well as for modified dispersion relations considered in the context of string theory and loop quantum gravity. Most interestingly we find that the momentum Lorentz factor in the present and future colliders can, in principle, become large enough to constrain the Finsler realization of the $\kappa$-Poincar\'e dispersion relation in the bicrossproduct basis as well as a string theory inspired modified dispersion relation, at Planck scale sensitivity with the help of the muon's lifetime., Comment: 9 pages, 1 table

We present a generalization of Rastall's gravity in which the conservation law of the energy-momentum tensor is altered, and as a result, the trace of the energy-momentum tensor is taken into account together with the Ricci scalar in the expression for the covariant derivative. Afterwards, we obtain the field equations in this theory and solve them by considering a spherically symmetric space-time. We show that the external solution has two possible classes of solutions with spherical symmetry in the vacuum in generalized Rastall's gravity, and we analyse one of them explicitly. The generalization, in contrast to constant value $k=8\pi G$ in general relativity, has a gravitational parameter $k$ that depends on the Rastall constant $\alpha$. As an application, we perform a careful analysis of the effects of the theory on neutron stars using realistic equations of state (EoS) as input. Our results show that important differences on the profile of neutron stars are obtained within two representatives EoS.

A Weyl structure is usually defined by an equivalence class of pairs $({\bf g}, \boldsymbol{\omega})$ related by Weyl transformations, which preserve the relation $\nabla {\bf g}=\boldsymbol{\omega}\otimes{\bf g}$, where ${\bf g}$ and $\boldsymbol{\omega}$ denote the metric tensor and a 1-form field. An equivalent way of defining such a structure is as an equivalence class of conformally related metrics with a unique affine connection $\Gamma_{\boldsymbol{\omega}}$, which is invariant under Weyl transformations. In a standard Weyl structure, this unique connection is assumed to be torsion-free and have vectorial non-metricity. This second view allows us to present two different generalizations of standard Weyl structures. The first one relies on conformal symmetry while allowing for a general non-metricity tensor, and the other comes from extending the symmetry to arbitrary (disformal) transformations of the metric., Comment: 9 pages, updated to match published version, some discussions extended

A Weyl structure is usually defined by an equivalence class of pairs $({\bf g}, \boldsymbol{\omega})$ related by Weyl transformations, which preserve the relation $\nabla {\bf g}=\boldsymbol{\omega}\otimes{\bf g}$, where ${\bf g}$ and $\boldsymbol{\omega}$ denote the metric tensor and a 1-form field. An equivalent way of defining such a structure is as an equivalence class of conformally related metrics with a unique affine connection $\Gamma_{\boldsymbol{\omega}}$, which is invariant under Weyl transformations. In a standard Weyl structure, this unique connection is assumed to be torsion-free and have vectorial non-metricity. This second view allows us to present two different generalizations of standard Weyl structures. The first one relies on conformal symmetry while allowing for a general non-metricity tensor, and the other comes from extending the symmetry to arbitrary (disformal) transformations of the metric., Comment: 9 pages, updated to match published version, some discussions extended

The hypersurface deformation algebra consists in a fruitful approach to derive deformed solutions of general relativity based on symmetry considerations with quantum gravity effects, whose linearization has been recently demonstrated to be connected to the DSR program by the $\kappa$-Poincar\'e symmetry. Based on this approach, we analyzed the solution derived for the interior of a black hole and we found similarities with the, so called, rainbow metrics, like a momentum-dependence of the metric functions. Moreover, we derived an effective, time-dependent Planck length and compared different regularization schemes., Comment: 29 pages

The hypersurface deformation algebra consists in a fruitful approach to derive deformed solutions of general relativity based on symmetry considerations with quantum gravity effects, whose linearization has been recently demonstrated to be connected to the DSR program by the $\kappa$-Poincar\'e symmetry. Based on this approach, we analyzed the solution derived for the interior of a black hole and we found similarities with the, so called, rainbow metrics, like a momentum-dependence of the metric functions. Moreover, we derived an effective, time-dependent Planck length and compared different regularization schemes., Comment: 29 pages

For theories formulated with a maximally symmetric momentum space we propose a general characterization for the description of interactions in terms of the isometry group of the momentum space. The well known cases of $\kappa$-Poincar\'e-inspired and (2+1)-dimensional gravity-inspired composition laws both satisfy our condition. Future applications might include the proposal of a class of models based on momenta spaces with anti-de Sitter geometry., Comment: 9 pages, Contribution to the proceedings of the 9th Alexander Friedmann International Seminar, St. Petersburg, Russia, June 21-27, 2015

Rainbow metrics are a widely used approach to metric formalism for theories with Modified Dispersion Relations. They have had a huge success in the Quantum Gravity Phenomenology literature, since they allow to introduce momentum-dependent spacetime metrics into the description of systems with Modified Dispersion Relation. In this paper, we introduce the reader to some realizations of this general idea: the original Rainbow metrics proposal, the momentum-space-inspired metric, the standard Finsler geometry approach and our alternative definition of a four-velocity-dependent metric with a massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations., Comment: 10 pages. Discussion on the role of connections was added. Matches published version

In recent years, Planck-scale modifications to particles' dispersion relation have been deeply studied for the possibility to formulate some phenomenology of Planckian effects in astrophysical and cosmological frameworks. There are some indications [arXiv:gr-qc/0611024] that Finsler geometry can provide some generalization of Riemannian geometry which may allow to account for non-trivial (Planckian) structure of relativistic particles' configuration space. We investigate the possibility to formalize Planck-scale deformations to relativistic models in curved spacetime, within the framework of Finsler geometry. We take into account the general strategy of analysis of modifications of dispersion relations in curved spacetimes proposed in [arXiv:1507.02056], generalizing to the de Sitter case the results obtained in [arXiv:1407.8143], for deformed relativistic particle kinematics in flat spacetime using Finsler formalism., Comment: 21 pages, 2 figures. Matches version published in PRD

For theories formulated with a maximally symmetric momentum space we propose a general characterization for the description of interactions in terms of the isometry group of the momentum space. The well known cases of $\kappa$-Poincar\'e-inspired and (2+1)-dimensional gravity-inspired composition laws both satisfy our condition. Future applications might include the proposal of a class of models based on momenta spaces with anti-de Sitter geometry., Comment: 9 pages, Contribution to the proceedings of the 9th Alexander Friedmann International Seminar, St. Petersburg, Russia, June 21-27, 2015

Rainbow metrics are a widely used approach to metric formalism for theories with Modified Dispersion Relations. They have had a huge success in the Quantum Gravity Phenomenology literature, since they allow to introduce momentum-dependent spacetime metrics into the description of systems with Modified Dispersion Relation. In this paper, we introduce the reader to some realizations of this general idea: the original Rainbow metrics proposal, the momentum-space-inspired metric, the standard Finsler geometry approach and our alternative definition of a four-velocity-dependent metric with a massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations., Comment: 10 pages. Discussion on the role of connections was added. Matches published version

In recent years, Planck-scale modifications to particles' dispersion relation have been deeply studied for the possibility to formulate some phenomenology of Planckian effects in astrophysical and cosmological frameworks. There are some indications [arXiv:gr-qc/0611024] that Finsler geometry can provide some generalization of Riemannian geometry which may allow to account for non-trivial (Planckian) structure of relativistic particles' configuration space. We investigate the possibility to formalize Planck-scale deformations to relativistic models in curved spacetime, within the framework of Finsler geometry. We take into account the general strategy of analysis of modifications of dispersion relations in curved spacetimes proposed in [arXiv:1507.02056], generalizing to the de Sitter case the results obtained in [arXiv:1407.8143], for deformed relativistic particle kinematics in flat spacetime using Finsler formalism., Comment: 21 pages, 2 figures. Matches version published in PRD

In this paper we analyze the invariance of the Dirac equation under disformal transformations depending on the propagating spinor field. Using the Weyl-Cartan formalism, we construct a large class of disformal maps between different metric tensors, respecting the order of differentiability of the Dirac operator and satisfying the Clifford algebra in both metrics. Then, we have shown that there is a subclass of solutions of the Dirac equation, provided by Inomata's condition, which keeps the Dirac operator invariant under the action of the disformal group., Comment: 12 pages; This matches the version to be published in CQG

In this paper we analyze the invariance of the Dirac equation under disformal transformations depending on the propagating spinor field. Using the Weyl-Cartan formalism, we construct a large class of disformal maps between different metric tensors, respecting the order of differentiability of the Dirac operator and satisfying the Clifford algebra in both metrics. Then, we have shown that there is a subclass of solutions of the Dirac equation, provided by Inomata's condition, which keeps the Dirac operator invariant under the action of the disformal group., Comment: 12 pages; This matches the version to be published in CQG