Cosmological constant: a lesson from the effective gravity of topological weyl media

Topological matter with Weyl points, such as superfluid ³He-A, provide an explicit example where there is a direct connection between the properly determined vacuum energy and the cosmological constant of the effective gravity emerging in condensed matter. This is in contrast to the acoustic gravity emerging in Bose-Einstein condensates (S. Finazzi, S. Liberati, and L. Sindoni, Phys. Rev. Lett. 108, 071101 (2012); arXiv:1103.4841). The advantage of topological matter is that the relativistic fermions and gauge bosons emerging near the Weyl point obey the same effective metric and thus the effective gravity is more closely related to real gravity. We study this connection in the bi-metric gravity emerging in ³He-A, and its relation to the graviton masses, by comparison with a fully relativistic bi-metric theory of gravity. This shows that the parameter ??, which in ³He-A is the bi-metric generalization of the cosmological constant, coincides with the difference in the proper energy of the vacuum in two states (the nonequilibrium state without gravity and the equilibrium state in which gravity emerges) and is on the order of the characteristic Planck energy scale of the system. Although the cosmological constant ?? is huge, the cosmological term T _??? ^?? itself is naturally non-constant and vanishes in the equilibrium vacuum, as dictated by thermodynamics. This suggests that the equilibrium state of any system including the final state of the Universe is not gravitating.     

Towards the map of quantum gravity

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between loop quantum gravity, causal dynamical triangulations, Ho?ava–Lifshitz gravity, asymptotic safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincaré algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers.     

Newtonian versus relativistic nonlinear cosmology

Both for the background world model and its linear perturbations Newtonian cosmology coincides with the zero-pressure limits of relativistic cosmology. However, such successes in Newtonian cosmology are not purely based on Newton's gravity, but are rather guided ones by previously known results in Einstein's theory. The action-at-a-distance nature of Newton's gravity requires further verification from Einstein's theory for its use in the large-scale nonlinear regimes. We study the domain of validity of the Newtonian cosmology by investigating weakly nonlinear regimes in relativistic cosmology assuming a zero-pressure and irrotational fluid. We show that, first, if we ignore the coupling with gravitational waves the Newtonian cosmology is exactly valid even to the second order in perturbation. Second, the pure relativistic correction terms start appearing from the third order. Third, the correction terms are independent of the horizon scale and are quite small in the large-scale near the horizon. These conclusions are based on our special (and proper) choice of variables and gauge conditions. In a complementary situation where the system is weakly relativistic but fully nonlinear (thus, far inside the horizon) we can employ the post-Newtonian approximation. We also show that in the large-scale structures the post-Newtonian effects are quite small. As a consequence, now we can rely on the Newtonian gravity in analyzing the evolution of nonlinear large-scale structures even near the horizon volume.     

Ab initio many electron relativistic molecular DFS-calculations of inner shell MO-transitions

Using a relativistic molecular DFS code we have calculated a self-consistent many electron relativistic correlation diagram of the system Cl-Ar. The resulting energy for the 2pπ-1sσ transition is in complete agreement with the experimental results of Schuch et al./1/. This definitely confirms their claim that they are able to measure this quantity from interference structures observed in quasi-molecular K-X-ray spectra.     

Nonperturbative effects of the minimal length uncertainty on the relativistic quantum mechanics

We study the nonperturbative effects of the minimal length on the energy spectrum of a relativistic particle in the context of the generalized uncertainty principle (GUP). This form of GUP is consistent with various candidates of quantum gravity such as string theory, loop quantum gravity, and black-hole physics and predicts a minimum measurable length proportional to the Planck length. Using a recently proposed formally self-adjoint representation, we solve the generalized Dirac and Klein–Gordon equations in various situations and find the corresponding exact energy eigenvalues and eigenfunctions. We show that for the Dirac particle in a box, the number of the solutions renders to be finite as a manifestation of both the minimal length and the theory of relativity. For the case of the Dirac oscillator and the wave equations with scalar and vector linear potentials, we indicate that the solutions can be obtained in a more simpler manner through the self-adjoint representation. It is also shown that, in the ultrahigh frequency regime, the partition function and the thermodynamical variables of the Dirac oscillator can be expressed in a closed analytical form. The Lorentz violating nature of the GUP-corrected relativistic wave equations is discussed finally.     

Measurement of gravitational spin-orbit coupling in a binary-pulsar system

In relativistic gravity, a spinning pulsar will precess as it orbits a compact companion star. We have measured the effect of such precession on the average shape and polarization of the radiation from PSR B1534+12. We have also detected, with limited precision, special-relativistic aberration of the revolving pulsar beam due to orbital motion. Our observations fix the system geometry, including the misalignment between the spin and orbital angular momenta, and yield a measurement of the precession time scale consistent with the predictions of general relativity.     

Towards new tests of strong-field gravity with measurements of surface atomic line redshifts from neutron stars

In contrast to gravity in the weak-field regime, which has been subject to numerous experimental tests, gravity in the strong-field regime is largely unconstrained by observations. We show that gravity theories that pass solar system tests, but that diverge from general relativity in the strong-field regime, predict neutron stars with significantly different properties than their general relativistic counterparts. The range of redshfits of surface atomic lines predicted by such theories is significantly wider than the uncertainty introduced by our lack of knowledge of the equation of state of ultradense matter. Measurements of such lines with x-ray observatories can thus put new constraints on strong-field gravity.     

Aberration and the Fundamental Speed of Gravity in the Jovian Deflection Experiment

We describe our explicit Lorentz-invariant solution of the Einstein and null geodesic equations for the deflection experiment of 2002 September 8 when a massive moving body, Jupiter, passed within 3.7’ of a line-of-sight to a distant quasar. We develop a general relativistic framework which shows that our measurement of the retarded position of a moving light-ray deflecting body (Jupiter) by making use of the gravitational time delay of quasar’s radio wave is equivalent to comparison of the relativistic laws of the Lorentz transformation for gravity and light. Because, according to Einstein, the Lorentz transformation of gravity field variables must depend on a fundamental speed c, its measurement through the retarded position of Jupiter in the gravitational time delay allows us to study the causal nature of gravity and to set an upper limit on the speed of propagation of gravity in the near zone of the solar system as contrasted to the speed of the radio waves. In particular, the v/c term beyond of the standard Einstein’s deflection, which we measured to 20% accuracy, is associated with the aberration of the null direction of the gravity force (“aberration of gravity”) caused by the Lorentz transformation of the Christoffel symbols from the static frame of Jupiter to the moving frame of observer. General relativistic formulation of the experiment identifies the aberration of gravity with the retardation of gravity because the speed of gravitational waves in Einstein’s theory is equal to the speed of propagation of the gravity force. We discuss the misconceptions which have inhibited the acceptance of this interpretation of the experiment. We also comment on other interpretations of this experiment by Asada, Will, Samuel, Pascual–Sánchez, and Carlip and show that their “speed of light” interpretations confuse the Lorentz transformation for gravity with that for light, and the fundamental speed of gravity with the physical speed of light from the quasar. For this reason, the “speed of light” interpretations are not entirely consistent with a retarded Liénard–Wiechert solution of the Einstein equations, and do not properly incorporate how the phase of the radio waves from the quasar is perturbed by the retarded gravitational field of Jupiter. Although all of the formulations predict the same deflection to the order of v/c, our formulation shows that the underlying cause of this deflection term is associated with the aberration of gravity and not of light, and that the interpretations predict different deflections at higher orders of v/c beyond the Shapiro delay, thus, making their measurement highly desirable for deeper testing of general relativity in future astrometric experiments like Gaia, SIM, and SKA.     

A virial theorem for relativistic plasmas

We obtain a tensor form of the virial theorem for a relativistic charged thermodynamic perfect fluid. As a particular application, we consider the equilibrium of a spherically symmetric charged dust cloud.     

Axial anomalies of Lifshitz fermions

We compute the axial anomaly of a Lifshitz fermion theory with anisotropic scaling z = 3 which is minimally coupled to geometry in 3+1 space‐time dimensions. We find that the result is identical to the relativistic case using path integral methods. An independent verification is provided by showing with spectral methods that the η‐invariant of the Dirac and Lifshitz fermion operators in three dimensions are equal. Thus, by the integrated form of the anomaly, the index of the Dirac operator still accounts for the possible breakdown of chiral symmetry in non‐relativistic theories of gravity. We apply this framework to the recently constructed gravitational instanton backgrounds of Hořava–Lifshitz theory and find that the index is non‐zero provided that the space‐time foliation admits leaves with harmonic spinors. Using Hitchin's construction of harmonic spinors on Berger spheres, we obtain explicit results for the index of the fermion operator on all such gravitational instanton backgrounds with SU(2) × U(1) isometry. In contrast to the instantons of Einstein gravity, chiral symmetry breaking becomes possible in the unimodular phase of Hořava–Lifshitz theory arising at λ = 1/3 provided that the volume of space is bounded from below by the ratio of the Ricci to Cotton tensor couplings raised to the third power. Some other aspects of the anomalies in non‐relativistic quantum field theories are also discussed.     

Why gravity experiments are so exciting

Being the most fundamental interaction gravity not only describes a particular interaction between matter, but also covers issues like the notion of space and time, the role of the observer and the relativistic measurement process. Gravity is geometry and, as a consequence, allows for the existence of black holes, non-trivial topologies, a cosmological big bang, time-travel, warp drive, and other phenomena not known from non-relativistic physics. Here we present the experimental basis of General Relativity, in particular its foundations encoded in the Einstein Equivalence Principle and its predictions in the weak and strong gravity regime. We discuss various routes to search for effects possibly signaling effects of the looked for quantum theory of gravity. We lay emphasis on assumptions to be tested which are only rarely discussed in the literature like tests of Newton’s axioms, tests of conservation laws, etc. We propose an experiment testing the order of time derivatives in the equation of motion.     

Solitons in collisionless cold plasma

The relativistic nonlinear self-consistent equations for a collisionless plasma with stationary ions are transformed into a form appropriate for finding exact analytic solutions. It is shown that for an axial system with planar geometry, the two-dimensional stationary equations for this system can be reduced to the sh-Gordon equation. The exact solution of this equation describing the charge-density equilibrium configuration is obtained, the solution having sharp transverse boundaries and a soliton form in longitudinal direction. The generalization to the nonstationary case is considered in an perturbative approach.     

A microinstability code for a uniform magnetized plasma with an arbitrary distribution function

We have developed a very general computer code for studying microinstabilities in a uniform magnetized plasma. Employing a new algorithm to perform two-dimensional numerical integrals in the conductivity tensor, the code can handle an arbitrary distribution function given by either an analytical function or numerical values on a momentum space grid and solve the full dispersion relation for an arbitrary propagation angle in either a non-relativistic or relativistic plasma except for a highly relativistic plasma (energy 1 MeV). The results for cyclotron-maser instability and whistler-wave instability are presented to illustrate the validity of the method.     

Neutrino oscillation phase dynamically induced by scalar-tensor gravity

We show that the shift of quantum mechanical phase can depend on the nonminimal coupling of scalar-tensor gravity. This fact could constitute a further test to discriminate among the various relativistic theories of gravity. Consequences on atmospheric, solar and astrophysical neutrinos are discussed.     

相对论重离子碰撞的趋平衡问题

从相对论ＢＵＵ理论出发,研究了１ＧｅＶ／ｕ能区重离子碰撞全局和局域平衡性质．研究结果表明,在该能区平均场对反应动力学过程仍有相当的作用;对有限核系统的反应动力学过程的时间演化的研究表明,有限核系统未能达到全局平衡,在中心区基本达到局域平衡．因而在该能区的重离子碰撞中引入完全热平衡概念时,需谨慎考虑．The equilibration in relativistic heavy ion collisions for systems 16 O+ 16 O, 40 Ca+ 40 La and 139 La+ 139 La is studied with RBUU theory. We have found that the mean field still plays a role in addition to the collision term in the equilibration process in relativistic heavy ion collisions at energy around 1 GeV/u. For finite systems, the systems do not reach complete equilibrium. But at the center zone, the local equilibrium is almost reached.     

Post-newtonian parameters from alternative theories of gravity

Alternative theories of gravity have been recently studied in connection with their cosmological applications, both in the Palatini and in the metric formalism. The aim of this paper is to propose a theoretical framework (in the Palatini formalism) to test these theories at the solar system level and possibly at the galactic scales. We exactly solve field equations in vacuum and find the corresponding corrections to the standard general relativistic gravitational field. On the other hand, approximate solutions are found in matter cases starting from a Lagrangian which depends on a phenomenological parameter. Both in the vacuum case and in the matter case the deviations from General Relativity are controlled by parameters that provide the Post-Newtonian corrections which prove to be in good agreement with solar system experiments.     

Post-Newtonian spin and angular momentum of bounded systems

We generalize the newtonian expressions for the orbital angular momentum of a two-body system, and for the spin of each body, by introducing corresponding definitions in the post-Newtonian approximation of fully conservative theories of gravity. Using this definition of the spin and assuming that the bodies rotate rigidly and that the equations of motion are Hamiltonian, we show that in fully conservative theories of gravity the spin of each body undergoes a relativistic precession about the direction of the orbital angular momentum, as a consequence of the local equations of motion for a perfect fluid.Visiting scientist to the Max-Planck-Institut für Physik und Astrophysik. On leave of absence from the Astronomy Department, University of Thessaloniki, Greece.     

Magnetic properties of a relativistic plasma

On the basis of thermodynamic functions calculated in closed form, the magnetic properties of an equilibrium relativistic plasma in fields of arbitrary magnitude are studied in both the Boltzmann and quantum cases. It is shown that, for a relativistic degenerate gas of free electrons, the de Haas-van Alphen effect will remain.     

Gravimagnetism,causality, and aberration of gravity in the gravitational light-ray deflection experiments

Experimental verification of the existence of gravimagnetic fields generated by currents of matter is important for a complete understanding and formulation of gravitational physics. Although the rotational (intrinsic) gravimagnetic field has been extensively studied and is now being measured by the Gravity Probe B, the extrinsic gravimagnetic field generated by the translational current of matter is less well studied. The present paper uses the post-Newtonian parametrized Einstein and light geodesics equations to show that the extrinsic gravimagnetic field generated by the translational current of matter can be measured by observing the relativistic time delay and/or light deflection caused by the moving mass. We prove that the extrinsic gravimagnetic field is generated by the relativistic effect of the aberration of the gravity force caused by the Lorentz transformation of the metric tensor and the Levi–Civita connection. We show that the Lorentz transformation of the gravity field variables is equivalent to the technique of the retarded Lienard–Wiechert gravitational potentials predicting that a light particle is deflected by gravitational field of a moving body from its retarded position so that both general-relativistic phenomena—the aberration and the retardation of gravity—are tightly connected and observing the aberration of gravity proves that gravity has a causal nature. We explain in this framework the 2002 deflection experiment of a quasar by Jupiter where the aberration of gravity from its orbital motion was measured with accuracy 20%. We describe a theory of VLBI experiment to measure the gravitational deflection of radio waves from a quasar by the Sun, as viewed by a moving observer from the geocentric frame, to improve the measurement accuracy of the aberration of gravity to a few percent.