Descriptions of highly relativistic fermions in a gravitational field in the classical (nonquantum) and quantum approaches are discussed. The results following from the Mathisson-Papapetrou equations for a fast spinning particle in Schwarzschild's and Kerr's background are considered. Numerical estimates for electron, proton and neutrino in the gravitational field of black holes are presented.The general relativistic Dirac equation is analyzed from the point of view it is using for the adequate description of highly relativistic fermions in a gravitational field, in the linear and nonlinear spin approximation. It is necessary to have some corrected Dirac equation for a highly relativistic fermion with strong spin-gravity coupling.
We present a method of contraction that can be applied to re-construct the recent extended non-relativistic and ultra-relativistic algebras as well as corresponding action principles. The methodology involves the use of multiple copies of Poincaré algebra. Consequently, the contraction defines non-relativistic or ultra-relativistic limits of multimetric theories of gravity. In particular, we show that the non-relativistic scaling limit of bi-metric gravity corresponds to the recent formulation of an action principle for Newtonian gravity with a constant background mass density.
We show that Schwarzschild black hole solutions in asymptotically Anti-de Sitter (AdS) and de Sitter (dS) spaces may, up to a conformal factor, be reproduced in the framework of analogue gravity. The aforementioned derivation is performed using relativistic and non-relativistic Bose-Einstein condensates. In addition, we demonstrate that the (2+1) planar AdS black hole can be mapped into the non-relativistic acoustic metric. Given that AdS black holes are extensively employed in the gauge/gravity duality, we then comment on the possibility to study the AdS/CFT correspondence and gravity/fluid d…
Fermions in (anti) de Sitter gravity theory in four dimensions are considered. Especially we propose new fermion actions to derive a Weyl or Majorana fermion action if we break the AdS (dS) group to the Lorentz group in curved spacetime.
We derive the dynamics of the gravitational collapse of a homogeneous and spherically symmetric cloud in a classical set-up endowed with a topological sector of gravity and a non-minimal coupling to fermions. The effective theory consists of the Einstein-Hilbert action plus Dirac fermions interacting through a four-fermion vertex. At the classical level, we obtain the same picture that has been recently studied by some of us within a wide range of effective theories inspired by a super-renormalizable and asymptotically free theory of gravity. The classical singularity is replaced by a bounce, …
In this work we present a non-relativistic gravity theory defined in four spacetime dimensions using the MacDowell-Mansouri geometrical formulation. We obtain a Newtonian gravity action which is constructed from the curvature of a Newton-Hooke version of the so-called Newtonian algebra. We show that the non-relativistic gravity theory presented here contains the Poisson equation in presence of a cosmological constant. Moreover we make contact with the Modified Newtonian Dynamics (MOND) approach for gravity by considering a particular ansatz for a given gauge field. We extend our results to a g…
We study the impact of quantum gravity on a system of chiral fermions that are charged under an Abelian gauge group. Under the impact of quantum gravity, a finite value of the gauge coupling could be generated and in turn drive four-fermion interactions to criticality. We find indications that the gravity-gauge-fermion interplay protects the lightness of fermions for a large enough number of fermions. On the other hand, for a smaller number of fermions, chiral symmetry may be broken, which would be in tension with the observation of light fermions.
I review recent work on nonperturbative path integral quantization of two-dimensional dilaton gravity coupled to Dirac fermions, employing the "Vienna school" approach.
Canonical gravity in real Ashtekar-Barbero variables is generalized to allow for fermionic matter. The resulting torsion changes several expressions in Holst's original vacuum analysis, which are summarized here. This in turn requires adaptations to the known loop quantization of gravity coupled to fermions, which is discussed on the basis of the classical analysis. As a result, parity invariance is not manifestly realized in loop quantum gravity.
We argue that generic non-relativistic quantum field theories have a holographic description in terms of Horava gravity. We construct explicit examples of this duality embedded in string theory by starting with relativistic dual pairs and taking a non-relativistic scaling limit.
We study the consistency of dynamical fermionic matter with the asymptotic safety scenario of quantum gravity using the functional renormalisation group. Since this scenario suggests strongly coupled quantum gravity in the UV, one expects gravity-induced fermion self-interactions at energies of the Planck-scale. These could lead to chiral symmetry breaking at very high energies and thus to large fermion masses in the IR. The present analysis which is based on the previous works \cite{Christiansen:2015rva, Meibohm:2015twa}, concludes that gravity-induced chiral symmetry breaking at the Planck s…
We define a procedure that, starting from a relativistic theory of supergravity, leads to a consistent, non-relativistic version thereof. As a first application we use this limiting procedure to show how the Newton-Cartan formulation of non-relativistic gravity can be obtained from general relativity. Then we apply it in a supersymmetric case and derive a novel, non-relativistic, off-shell formulation of three-dimensional Newton-Cartan supergravity.
In this paper, we present novel and known non-relativistic and ultra-relativistic spin-3 algebras, by considering the Lie algebra expansion method. We start by applying the expansion procedure using different semigroups to the spin-3 extension of the AdS algebra, leading to spin-3 extensions of known non-relativistic and ultra-relativistic algebras. We then generalize the procedure considering an infinite-dimensional semigroup, which allows to obtain a spin-3 extension of two new infinite families of the Newton-Hooke type and AdS-Carroll type. We also present the construction of the gravity th…
In this paper, we investigate the fermions Hawking radiation and quasinormal modes in infra-red modified Ho$\check{r}$ava-Lifshitz gravity under tunneling and perturbation perspectives.Firstly, through the fermions tunneling in IR modified Ho$\check{r}$ava-Lifshitz gravity,we obtain the Hawking radiation emission rate, tunneling temperature and entropy for the Kehagias-Sfetsos black hole. It is found that the results of fermions tunneling are in consistence with the thermodynamics results obtained by calculating surface gravity.Secondly, we numerically calculate the lowing quasinormal modes fr…
Fermions coupled to Yang-Mills matrix models are studied from the point of view of emergent gravity. We show that the simple matrix model action provides an appropriate coupling for fermions to gravity, albeit with a non-standard spin connection. Integrating out the fermions in a nontrivial geometrical background induces indeed the Einstein-Hilbert action and a dilaton-like term, at least for on-shell geometries. This explains and precisely reproduces the UV/IR mixing for fermions in noncommutative gauge theory, extending recent results for scalar fields. It also explains why some UV/IR mixing…
In the model of a fermion field coupled to loop quantum gravity, we consider the Gauss and the Hamiltonian constraints. According to the explicit solutions to the Gauss constraint, the fermion spins and the gravitational spin networks intertwine with each other so that the fermion spins contribute to the volume of the spin network vertices. For the Hamiltonian constraint, the regularization and quantization procedures are presented in detail. By introducing an adapted vertex Hilbert space to remove the regulator, we propose a diffeomorphism covariant graph-changing Hamiltonian constraint opera…
The existence of intrinsic spin of matter requires the metric-affine formulation of gravity, in which the affine connection is not constrained to be symmetric and its antisymmetric part (torsion tensor) is a dynamical variable. We show that the cyclic identity for the curvature tensor in the metric-affine formulation forbids fermions represented by Dirac spinors to form point or string configurations. Consequently, fermionic strings contradict the gravitational field equations in the presence of spin. Superstring theory is therefore incorrect.
Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2) times SU(2). Relativistic quantum spins are related to the geometry of the 2-dimensional faces of a 4-simplex. This extends the idea of Ponzano and Regge that SU(2) spins are related to the geometry of the edges of a 3-simplex. This leads us to suggest that there may be a 4-dimensional state sum model for quantum gravity based on relativistic spin networks which parallels the construction of 3-dimensional quantum gravity from ordinary spin networks.
We discover that chiral symmetry does not act as an infrared attractor of the renormalization group flow under the impact of quantum gravity fluctuations. Thus, observationally viable quantum gravity models must respect chiral symmetry. In our truncation, asymptotically safe gravity does, as a chiral fixed point exists. A second non-chiral fixed point with massive fermions provides a template for models with dark matter. This fixed point disappears for more than 10 fermions, suggesting that an asymptotically safe ultraviolet completion for the standard model plus gravity enforces chiral symmet…
We compute the lowest order gravitational UV divergent radiative corrections to the S matrix element of the $fermion + fermion\rightarrow fermion + fermion$ scattering process in the massive Yukawa theory, coupled either to Unimodular Gravity or to General Relativity. We show that both Unimodular Gravity and General Relativity give rise to the same UV divergent contribution in Dimensional Regularization. This is a nontrivial result, since in the classical action of Unimodular Gravity coupled to the Yukawa theory, the graviton field does not couple neither to the mass operator nor to the Yukawa…
Any theory of quantum gravity must ultimately be connected to observations. This demand is difficult to be met due to the high energies at which we expect the quantum nature of gravity to become manifest. Here we study, how viable quantum gravity proposals can be restricted by investigating the interplay of gravitational and matter degrees of freedom. Specifically we demand that a valid quantum theory of gravity must allow for the existence of light (compared to the Planck scale) fermions, since we observe these in our universe. Within the effective theory framework, we can thus show that UV c…
We derive the relativistic transformation laws for the annihilation operators of the scalar field, the massive spin-1 vector field, the electromagnetic field and the spinor field. The technique developed here involves straightforward mathematical techniques based on fundamental quantum field theory, and is applicable to the study of entanglement in arbitrary coordinate transformations. In particular, it predicts particle creation for non-inertial motion. Furthermore, we present a unified description of relativistic transformations and multi-particle interferometry with bosons and fermions, whi…
We define and study kinematical observables involving fermion spin, such as the total spin of a collection of particles, in loop quantum gravity. Due to the requirement of gauge invariance, the relevant quantum states contain strong entanglement between gravity and fermionic degrees of freedom. Interestingly we find that properties and spectra of the observables are nevertheless similar to their counterparts from quantum mechanics. However, there are also new effects. Due to the entanglement between gravity and fermionic degrees of freedom, alignment of quantum spins has consequences for quant…
In this paper, by presenting the potentials of Kaluza-Klein (KK) modes in the corresponding Schrödinger equations, we investigate the localization and resonances of gravity and fermion on the symmetric and asymmetric Bloch {branes}. We find that the localization properties of zero modes for gravity and fermion in the symmetric brane case are the same, whereas, for the asymmetric brane case, the fermion zero mode is localized on one of the sub-branes, while the gravity zero mode is localized on another sub-brane. The spectra of the gravity and the left- or right-handed fermion are composed of a…
We zoom in on the microscopic dynamics for fermions and quantum gravity within the asymptotic-safety paradigm. A key finding of our study is the unavoidable presence of a nonminimal derivative coupling between the curvature and fermion fields in the ultraviolet. Its backreaction on the properties of the Reuter fixed point remains small for finite fermion numbers within a bounded range. This constitutes a nontrivial test of the asymptotic-safety scenario for gravity and fermionic matter, additionally supplemented by our studies of the momentum-dependent vertex flow which indicate the subleading…
The effects of highly relativistic spin-gravity coupling in the Schwarzschild-de Sitter background which follow from the Mathisson-Papapetrou equations are investigated. The dependence of gravitoelectric and gravitomagnetic components of gravitational field on the velocity of an observer which is moving in Schwarzschild-de Sitter's background is estimated. The action of gravitomagnetic components on a fast moving spinning particle is considered. Different cases of the highly relativistic circular orbits of a spinning particle which essentially differ from the corresponding geodesic orbits are …
Fermions constitute an important component of matter and their quantization in presence of dynamical gravity is essential for any theory of quantum gravity. We revisit the classical formulation adapted for a background free quantization. The analysis is carried out with the Hilbert-Palatini form for gravity together with the Nieh-Yan topological term which keeps the nature of Barbero-Immirzi parameter independent of inclusion of arbitrary matter with arbitrary couplings. With dynamical gravity, a priori, there are two distinct notions of `parity' - orientation reversing diffeomorphisms and imp…
We investigate some cosmological models arising from a non-minimal coupling of a fermionic field to gravity in the geometrical setting of Einstein-Cartan-Sciama-Kibble gravity. The role played by the non-minimal coupling together with torsion in facing problems such as cosmological singularity, inflation and dark energy is discussed.
An essential step towards the identification of a fermion mass generation mechanism at Planck scale is to analyse massive fermions in a given quantum gravity framework. In this letter the two mass terms entering the Hamiltonian constraint for the Einstein-Majorana system are studied in the loop representation of quantum gravity and fermions. One resembles a bare mass gap because it is not zero for states with zero (fermion) kinetic energy as opposite to the other that is interpreted as `dressing' the mass. The former contribution originates from (at least) triple intersections of the loop stat…
In this note, we examine the scattering of two identical fermions in theories where fermionic fields minimally coupled to higher derivative gravity. In particular, we consider the extension of general relativity with $R^2$ corrections or non-local terms. We expand the action of fermions around the flat space background and obtain two fermion-one graviton vertex. Then, by considering the scattering amplitude of two fermions, we calculate the non-relativistic limit and that obtain the potential for two fermion-fermion interaction which would be the usual Newtonian potential corrected with a Yuka…
It has recently been pointed out that under certain circumstances the back-reaction of charged, massive Dirac fermions causes important modifications to AdS_2 spacetimes arising as the near horizon geometry of extremal black holes. In a WKB approximation, the modified geometry becomes a non-relativistic Lifshitz spacetime. In three dimensions, it is known that integrating out charged, massive fermions gives rise to gravitational and Maxwell Chern-Simons terms. We show that Schrodinger (warped AdS_3) spacetimes exist as solutions to a gravitational and Maxwell Chern-Simons theory with a cosmolo…
Leinweber Institute for Theoretical Physics and Department of Physics, University of California, Berkeley（加州大学伯克利分校莱因韦伯理论物理研究所和物理系）；Leinweber Institute for Theoretical Physics, Stanford University（斯坦福大学莱因韦伯理论物理研究所）；Physics Department, University of Washington（华盛顿大学物理系）
We consider the N-body problem in (1+1) dimensional lineal gravity. For 2 point masses (N=2) we obtain an exact solution for the relativistic motion. In the equal mass case we obtain an explicit expression for their proper separation as a function of their mutual proper time. Our solution gives the exact Hamiltonian to infinite order in the gravitational coupling constant.
In this paper we carry out a quantization of gravity coupled to massless spin 1/2 fermions through the instanton representation of Plebanski gravity. We have constructed a Hilbert space of states for this model, and we have computed the Hamilton's equations of motion. The classical equations appear, at a superficial level, to be consistent with the quantum dynamics of the theory.
In this paper, we study thermodynamical contributions to the theory of gravity under the $q$-deformed boson and fermion gas models. According to the Verlinde's proposal, the law of gravity is not based on a fundamental interaction but it emerges as an entropic force from the changes of entropy associated with the information on the holographic screen. In addition, Strominger shows that the extremal quantum black holes obey neither boson nor fermion statistics, but they obey deformed statistic. Using these notions, we find $q$-deformed entropy and temperature functions. We also present the cont…
We have studied holographic superconductors with spherical symmetry in the Ho$\check{\textbf{r}}$ava-Lifshitz gravity by using a semi analytical method, and also we have calculated the critical temperature and shown when the condensation will appear in a similar pattern as in the Einstein-Gauss- Bonnet gravity. We have computed the dependency of the conductivity as a function of frequency in this new non-relativistic model of quantum gravity.
Many non-relativistic Quantum Field Theories with conserved particle number share a common set of symmetries: time dependent spatial diffeomorphisms acting on the background metric and U(1) invariance acting on the background fields which couple to particle number. Here we use these symmetries to deduce a gravity dual for any such theory in terms of a non-relativistic theory of gravity, a variant of Horava gravity. This duality allows the extension of holography to generic non-relativistic field theories. As Horava gravity is presumed to be a consistent quantum theory, this duality also allows…
We show that the recently constructed holographic duals of conformal non-relativistic theories behave hydrodynamically at long distances, and construct the gravitational dual of fluid flows in a long-wavelength approximation. We compute the thermal conductivity of the holographic conformal non-relativistic fluid. The corresponding Prandtl number is equal to one.
In view of growing interest in long range scalar forces in the early universe to generate primordial black holes, we study in detail the general relativistic formulation of a Fermi gas interacting with a scalar field in cosmology. Our main finding is that the Yukawa interaction leads to a solution where the scalar field oscillates around zero fermion mass and all energy densities decay as radiation. On one hand, we show that if the Fermi gas starts relativistic, it could stay relativistic. On the other hand, if the fermions are initially non-relativistic, they remain non-relativistic for all p…
In this paper, we study the effects of a modified theory of gravity - the rainbow gravity - on the relativistic Bose-Einstein condensate (BEC). We initially discuss some formal aspects of the model in order to compute the corrections to the relevant quantities of the condensate. Following, we evaluate the generating functional from which obtain some thermodynamic parameters. Then we calculate the corrected critical temperature $T_c$ that sets the relativistic Bose-Einstein condensate considering the three principal rainbow functions, finding, in addition, a phenomenological upper bound for the…
We present a metric-independent, diffeomorphism-invariant model with interacting fermions that contains a massless composite graviton in its spectrum. The model is motivated by the supersymmetric D-brane action, modulated by a fermion potential. The gravitational coupling is related to new physics at the cutoff scale that regularizes UV divergences. We also speculate on possible extensions of the model.
Several f(R) modified gravity models have been proposed which realize the correct cosmological evolution and satisfy solar system and laboratory tests. Although nonrelativistic stellar configurations can be constructed, we argue that relativistic stars cannot be present in such f(R) theories. This problem appears due to the dynamics of the effective scalar degree of freedom in the strong gravity regime. Our claim thus raises doubts on the viability of f(R) models.
We provide a simple argument showing that, in the limit of infinite acceleration, the entanglement in a fermionic field bipartite system must be independent of the choice of Unruh modes. This implies that most tensor product structures used previously to compute field entanglement in relativistic quantum information cannot give rise to physical results.
We study the impact of quantum gravity, formulated as a quantum field theory of the metric, on chiral symmetry in a fermionic matter sector. We specifically address the question as to whether metric fluctuations can induce chiral symmetry breaking and bound state formation. Our results based on the functional Renormalization Group indicate that chiral symmetry is left intact even at strong gravitational coupling. In particular, we find that asymptotically safe quantum gravity where the gravitational couplings approach a non-Gaussian fixed point generically admits universes with light fermions.…
We study expectation values of observables in three-dimensional spinfoam quantum gravity coupled to Dirac fermions. We revisit the model introduced by one of the authors and extend it to the case of massless fermionic fields. We introduce observables, analyse their symmetries and the corresponding proper gauge fixing. The Berezin integral over the fermionic fields is performed and the fermionic observables are expanded in open paths and closed loops associated to pure quantum gravity observables. We obtain the vertex amplitudes for gauge-invariant observables, while the expectation values of g…
Using the non-relativistic hydrodynamic expansion, we solve equations of motion for Einstein gravity and Gauss-Bonnet gravity with a negative cosmological constant within the region between a finite cutoff surface and a black brane horizon, up to the second order of the expansion parameter. Through the Brown-York tensor, we calculate the stress energy tensor of dual fluids living on the cutoff surface. With the black brane solutions, we show that for both Einstein gravity and Gauss-Bonnet gravity, the ratio of shear viscosity to entropy ensity of dual fluid does not run with the cutoff surface…
We study static, spherically symmetric equilibrium configurations in extended theories of gravity (ETG) following the notation introduced by Capozziello et {\it al}. We calculate the differential equations for the stellar structure in such theories in a very generic form i.e., the Tolman-Oppenheimer-Volkoff generalization for any ETG is introduced. Stability analysis is also investigated with special focus on the particular example of scalar-tensor gravity.
We investigate superfluidity of the relativistic fermi-gas with gravitational interaction. The excitation spectrum is obtained within the linearized theory. While superfluidity may take place at a definite ratio of the Fermi momentum, rest mass and coupling constant, the metric coefficients play predominant role forming the gap of excitation spectrum.
We provide a set of exact spherically symmetric solutions describing the interior of a relativistic star under f(T) modified gravity. To tackle the problem with lucidity we also assume the existence of a conformal Killing vector field within this f(T) gravity. We study several cases of interest to explore physically valid features of the solutions.
We investigate detection of Dirac quanta in a uniformly eccentric rotating frame both with canonical and detector approaches by employing relativistic rotational transformations. First we consider a relativistic uniformly eccentric rotating detector that is coupled to the scalar density of a massless Dirac field, and show that this detector has a nonzero response function and observes a Planckian energy spectrum. Then using relativistic rotational transformations, we investigate the canonical quantization of Dirac field in relativistic eccentric rotating frame. We show that it's not possible t…
We analyse the non-relativistic approximation of the Dirac equation for slow fermions moving in spacetimes with a static metric, caused by the weak gravitational field of the Earth and a chameleon field, and derive the most general effective gravitational potential, induced by a static metric of spacetime. The derivation of the non-relativistic Hamilton operator of the Dirac equation is carried out by using a standard Foldy-Wouthuysen (SFW) transformation. We discuss the chameleon field as source of a torsion field and torsion-matter interactions.
Working with a magnetic field periodic along $Oz$ and decaying in time, we deal with the Dirac-type equation characterizing the fermions evolving in magnetar's crust. For ultra-relativistic particles, one can employ the perturbative approach, to compute the conserved current density components. If the magnetic field is frozen and the magnetar is treated as a stationary object, the fermion's wave function is expressed in terms of the Heun's Confluent functions. Finally, we are extending some previous investigations on the linearly independent fermionic modes solutions to the Mathieu's equation …
Simulation and experimental realization of acoustic black holes in analogue gravity systems have lead to a novel understanding of relevant phenomena such as Hawking radiation or superradiance. We explore here the possibility to use relativistic systems for simulating rotating black hole solutions and possibly get an acoustic analogue of a Kerr black hole. In doing so we demonstrate a precise relation between non-relativistic and relativistic solutions and provide a new class of vortex solutions for relativistic systems. Such solutions might be used in the future as a test bed in numerical simu…
In this paper, we show that the Hamiltonian approach to loop quantum gravity has a fermion doubling problem. To obtain this result, we couple loop quantum gravity to a free massless scalar and a chiral fermion field, gauge fixing the many fingered time gauge invariance by interpreting the scalar field as a physical clock. We expand around a quantum gravity state based on a regular lattice and consider the limit where the bare cosmological constant is large but the fermonic excitations have energies low in Planck units. We then make the case for identifying the energy spectrum in this approxima…
We investigate the consequences of the ambiguity of minimal coupling procedure for Einstein-Cartan gravity with Holst term and fermions. A new insight is provided into the nature and physical relevance of coupling procedures considered hitherto in the context of Ashtekar-Barbero-Immirzi formalism with fermions. The issue of physical effects of the Immirzi parameter in semi--classical theory is reinvestigated. We argue that the conclusive answer to the question of its measurability will not be possible until the more fundamental problem of nonuniqueness of gravity--induced fermion interaction i…
