Newtonian Gravitational Potential Research Articles

Collapse of neutrino wave functions under Penrose gravitational reduction

Models of spontaneous wave function collapse have been postulated to address the measurement problem in quantum mechanics. Their primary function is to convert coherent quantum superpositions into incoherent ones, with the result that macroscopic objects cannot be placed into widely separated superpositions for observably prolonged times. Many of these processes will also lead to loss of coherence in neutrino oscillations, producing observable signatures in the flavor profile of neutrinos at long travel distances. The majority of studies of neutrino oscillation coherence to date have focused on variants of the continuous state localization model, whereby an effective decoherence strength parameter is used to model the rate of coherence loss with an assumed energy dependence. Another class of collapse models that have been proposed posit connections to the configuration of gravitational field accompanying the mass distribution associated with each wave function that is in the superposition. A particularly interesting and prescriptive model is Penrose’s description of gravitational collapse which proposes a decoherence time τ determined through Egτ∼ℏ, where Eg is a calculable function of the Newtonian gravitational potential. Here we explore application of the Penrose collapse model to neutrino oscillations, reinterpreting previous experimental limits on neutrino decoherence in terms of this model. We identify effects associated with both spatial collapse and momentum diffusion, finding that the latter is ruled out in data from the IceCube South Pole Neutrino Observatory so long as the neutrino wave packet width at production is σν,x≤2×10−12 m. Published by the American Physical Society 2024

A Causal Net approach to Relativistic Quantum Mechanics and Gravitation

In this paper we discuss a causal network model to describe quantum mechanics and gravittation, where space–time is built solely from point events and connecting probabilities. A causal net provides a representation which combines the quantum complementary features of both partticles and waves as each vertex on the causal net represents a possible point event or particle observation. Simultaneity on the causal net is defined by hyperplanes of equivalent proper time. The causal net model when constructed in Minkowksi space–time is shown to lead to a formulation for relativistic quantum mechanics including the Dirac equation. In a curved Riemann space–time the causal paths of the causal net are geodesics and in the local Lorentz frame the net probabilities and the Dirac formalism are preserved. The variation of space–time density of events in the causal paths modifies the metric and provides a space–time curvature leading to the Hilbert action associated with general relativity. Consideration of the Schwarzchild metric shows that in classical limit the perturbation in the density of possible events is proportional to the Newtonian gravitational potential.

The manipulation of photon blockade via Newtonian gravity

We theoretically investigate the model of a quadratically coupled optomechanical system with a Newtonian gravitational potential in the weak-driving regime, where the optical cavity is driven by an external laser. The steady state of the whole system is treated in the framework of a few-photon subspace. We find that the conventional single-photon blockade, nonstandard types of single-photon blockade, two-photon blockade, and photon-induced tunneling can be induced by gravity when the quadratic optomechanical coupling strength remains constant. Moreover, we find that gravitational potential energy can compensate for the lack of quadratic optomechanical coupling for observation photon blockade. In particular, the photon stream with super-Poissonian distribution can be converted into a sub-Poissonian, antibunching photon stream by changing the driving detuning when the gravitational potential energy is included. These results show that the gravity has potential for realizing the manipulation of photon blockade in a quadratically coupled optomechanical system.

Exact conservation laws for neural network integrators of dynamical systems

The solution of time dependent differential equations with neural networks has attracted a lot of attention recently. The central idea is to learn the laws that govern the evolution of the solution from data, which might be polluted with random noise. However, in contrast to other machine learning applications, usually a lot is known about the system at hand. For example, for many dynamical systems physical quantities such as energy or (angular) momentum are exactly conserved. Hence, the neural network has to learn these conservation laws from data and they will only be satisfied approximately due to finite training time and random noise. In this paper we present an alternative approach which uses Noether's Theorem to inherently incorporate conservation laws into the architecture of the neural network. We demonstrate that this leads to better predictions for three model systems: the motion of a non-relativistic particle in a three-dimensional Newtonian gravitational potential, the motion of a massive relativistic particle in the Schwarzschild metric and a system of two interacting particles in four dimensions.

Gravitational potential in spherical topologies

We study the properties of the Newtonian gravitational potential in a spherical Universe for different topologies. For this, we use the non-Euclidean Newtonian theory developed in Vigneron [On non-Euclidean Newtonian theories and their cosmological backreaction, Classical Quantum Gravity 39, 155006 (2022)]. describing Newtonian gravitation in a spherical or hyperbolic Universe. The potential is calculated for a point mass in all the globally homogeneous regular spherical topologies, i.e., whose fundamental domain is unique and is a platonic solid. We provide the exact solution and the Taylor expansion series of the potential at a test position near the point mass. We show that the odd terms of the expansion can be interpreted as coming from the presence of a nonzero spatial scalar curvature, while the even terms relate to the closed nature of the topological space. A consequence is that, compared to the point mass solution in a 3-torus, widely used in Newtonian cosmological simulations, the spherical cases all feature an additional attractive first order term dependent solely on the spatial curvature. The choice of topology only affects the potential at second order and higher. For typical estimates of cosmological scales (curvature and topology), the strongest topological effect occurs in the case of the Poincar\'e dodecahedral space, but in general the effect of curvature dominates over topology. We also provide the set of equations that can be used to perform $N$-body simulations of structure formation in spherical topologies.

Relaxation-time model for the post-Newtonian Boltzmann equation

The non-equilibrium contributions to the post-Newtonian hydrodynamic equations are determined from a relaxation-time model of the post-Newtonian Boltzmann equation. The Chapman- Enskog method is used to calculate the non-equilibrium distribution function. The components of the energy–momentum tensor are found from the knowledge of the non-equilibrium and the post-Newtonian equilibrium Maxwell–Jüttner distribution functions. The linearized field equations for the mass, momentum and internal energy densities coupled with the three Poisson equations of the post-Newtonian approximation are investigated by considering a plane wave representation of the fields. The constitutive equations for the viscous stress and heat flux vector are obtained and it is shown that the transport coefficients of shear viscosity and heat conductivity do depend on the Newtonian gravitational potential.

Constraints on Yukawa gravity parameters from observations of bright stars

In this paper we investigate a Yukawa gravity modification of the Newtonian gravitational potential in a weak field approximation. For that purpose we derived the corresponding equations of motion and used them to perform two-body simulations of the stellar orbits. In 2020 the GRAVITY Collaboration detected the orbital precession of the S2 star around the supermassive black hole (SMBH) at the Galactic Center (GC) and showed that it is close to the general relativity (GR) prediction. Using this observational fact, we evaluated parameters of the Yukawa gravity (the range of Yukawa interaction Λ and universal constant δ) with the Schwarzschild precession of the S-stars assuming that the observed values as indicated by the GRAVITY Collaboration will have a small deviation from GR prediction [1]. GR provides the most natural way to fit observational data for S-star orbits, however, their precessions can be fitted by Yukawa gravity. Our main goal was to study the possible influence of the strength of Yukawa interaction, i.e. the universal constant δ, on the precessions of S-star orbits. We analyze S-star orbits assuming different strength of Yukawa interaction δ and find that this parameter has strong influence on range of Yukawa interaction Λ. For that purpose we use parameterized post-Newtonian (PPN) equations of motion in order to calculate the simulated orbits of S-stars in GR and Yukawa gravity. Using MCMC simulations we obtain the best-fit values and uncertainties of Yukawa gravity parameters for S-stars. Also, we introduce a new criterion which can be used for classification of gravitational systems in this type of gravity, according to their scales. We demonstrated that performed analysis of the observed S-stars orbits around the GC in the frame of the Yukawa gravity represent a tool for constraining the Yukawa gravity parameters and probing the predictions of gravity theories.

Energy-Casimir method for the dynamical systems with modified gravitational potential

We discuss the evolution of an ensemble of mutually gravitating particles, which can repeatedly collide during their motion. The repulsive forces arise in the process of collision and contact interaction of the particles. This process can be described by two models. The first one is a classical model of rigid elastic or inelastic collision, using newtonian formula with a recovery coefficient. In the second model this interaction can be modeled by adding to the gravitational potential a potential of repulsive forces similar to Lennard-Jones intermolecular forces. For an infinite number of particles, the probability density function is determined by the Vlasov kinetic equation with a modified gravitational potential. This approach allows to replace the Vlasov-Boltzmann equation describing the evolution of a system with possible collisions by the Vlasov equation with a modified potential. It is useful for investigation of many-particles gravitating systems when taking under consideration the particle sizes. The 'Lennard-Jones type' potential improves the stability of computational process in comparison with newtonian gravitational potential. Using the energy-Casimir method, we justify the existence of nonlinearly stable steady states of the Vlasov equation with a modified gravitational potential.

Assessing the foundation and applicability of some dark energy fluid models in the Dirac–Born–Infeld framework

In this paper, we will deepen the understanding of some fluid models proposed by other authors for the description of dark energy. Specifically, we will show that the so-called (Modified) Berthelot fluid is the hydrodynamic realization of the free Dirac–Born–Infeld (DBI) theory and that the Dieterici fluid admits a nonrelativistic [Formula: see text]-essence formulation; for the former model the evolution of the scalar field will be written in terms of some cosmographic parameters. The latter model will also be tested using Machine Learning algorithms with respect to cosmic chronometers data, and results about the dynamics at a background level will be compared with those arising when other fluids (Generalized Chaplygin Gas and Anton-Schmidt) are considered. Due to some cosmic opacity effects, the background cosmology of universes filled by these inequivalent fluids, as they arise in physically different theories, may not be enough for discriminating among them. Thus, a perturbation analysis in the long-wavelength limit is carried out revealing a rich variety of possible behaviors. It will also be shown that the free DBI theory cannot account for flat galactic rotation curves, and therefore we derive an appropriate relationship between the scalar field potential and the brane tension for achieving this goal; this provides an estimate for the dark matter adiabatic speed of sound inside the halo consistent with other literature. A certain relationship between the Newtonian gravitational potential within the galaxy and the Lagrangian potential in the nonrelativistic regime for the (Modified) Berthelot fluid will also be enlightened.

Complementarity and causal propagation of decoherence by measurement in relativistic quantum field theories

Entanglement generation by Newtonian gravitational potential between objects has been widely discussed to reveal the quantum nature of gravity. In this paper, we perform a quantum field theoretical analysis of a slightly modified version of the gedanken experiment by Mari and co-workers. We show that decoherence due to the presence of a detector propagates with the speed of light in terms of a retarded Green's function, as it should be consistent with causality of relativistic field theories. The quantum nature of fields, such as quantum fluctuations or emission of gravitons expressed in terms of the Keldysh Green's function also play important roles in the mechanism of decoherence due to on-shell particle creation. We also discuss the trade-off relation between the visibility of the interference and the distinguishability of the measurement, known as the wave particle duality, in our setup.

Gravity at the tip of the throat

We study the gravitational signatures that arise from compactifying Type IIB supergravity on a compact space containing a Klebanov-Strassler warped throat. After reviewing the dimensional reduction of the 10d graviton and explicitly obtaining the equa- tions of motion for the 4d tensor hμν, vector hμn and scalar hmn modes, we find the masses and wavefunctions of the Kaluza-Klein tower of spin-2 states. We explore how the masses and wavefunctions depend on the balance between the strength of the warping and the size of the bulk, and how these relate to the range and strength of the interactions which correct the Newtonian gravitational potential. By computing the modified Newtonian potential for sources on a brane somewhere along the throat, and applying consistency constraints on the Klebanov-Strassler parameters, we obtain predictions for the phenomenological pa- rameter space. In the case of a fully warped throat, and depending on where the brane is along the throat, these predictions are narrow in range and consistent with current obser- vational and experimental constraints. We also begin an exploration of gravitational wave signatures of KK gravitons in warped throats, finding that strong warping can bring the corresponding frequencies down to the windows of current and proposed experiments.

Vorticity equation on surfaces with arbitrary topology embedded in three-dimensional Euclidean space

We derive the vorticity equation for an incompressible fluid on a two-dimensional surface with an arbitrary topology, embedded in three-dimensional Euclidean space and arising from a first integral of the flow, by using a tailored Clebsch parameterization of the velocity field. In the inviscid limit, we identify conserved surface energy and enstrophy and obtain the corresponding noncanonical Hamiltonian structure. We then discuss the formulation of the diffusion operator on the surface by examining two alternatives. In the first case, we follow the standard approach for Navier–Stokes equations on a Riemannian manifold and calculate the diffusion operator by requiring that flows corresponding to Killing fields of the Riemannian metric are not subject to dissipation. For an embedded surface, this leads to a diffusion operator, including derivatives of the stream function across the surface. In the second case, using an analogy with the Poisson equation for the Newtonian gravitational potential in general relativity, we construct a diffusion operator taking into account the Ricci scalar curvature of the surface. The resulting vorticity equation is two-dimensional, and the corresponding diffusive equilibria minimize dissipation under the constraint of curvature energy.

Sphaleron bound in some nonstandard cosmology scenarios

In the first scenario, we revise the upper bound of the cutoff scale of the dimension-six potential Higgs operator required for a successful electroweak baryogenesis in the case of a modified expansion history caused by the existence of a noninteracting scalar field at the time phase transition happens. The upper bound 860[Formula: see text]GeV of the cutoff scale in the conventional case can be improved to 1[Formula: see text]TeV in the modified expansion case under certain conditions. In the second scenario, we consider the Randall–Sundrum type II model. We show that the lower bound of the five-dimensional Planck scale in this model, which is determined from the validity of Newtonian gravitational potential at small distance, turns out to be crucial in eliminating this model as a viable candidate to satisfy the sphaleron bound; however, again modifying the expansion history by including a noninteracting scalar field at the electroweak scale can then make this model satisfy the sphaleron bound with a certain parameter space.

Nonrelativistic Boson stars as N-body quantum systems

In this work, we show that the structural configuration of a collection of generic nonrelativistic bosons forming a gravitationally bound Bose–Einstein condensate can be interpreted as a nonrelativistic boson star. With the approach followed in this work, we can analyze with a concise and straightforward procedure the equilibrium properties of nonrelativistic boson stars viewed as a Bose–Einstein condensate. The system’s behavior is obtained by analyzing its fundamental constituent properties, i.e. the associated single-particle properties. Additionally, we show that by expressing the corresponding Newtonian gravitational potential, under certain circumstances, as a harmonic oscillator potential one, we can describe the conditions in which the nonrelativistic boson star can form equilibrium configurations. In order to analyze the boson star’s structural configuration, we employ four different ansätzes commonly used in the literature. These ansätzes allow us to compare the cloud’s structural properties of the boson star, which leads us to obtain several gravitational equilibrium configurations from compact objects matching the size of typical stars to gigantic systems comparable to the size of galaxy cluster dark matter halos. Finally, we show that these ansätzes predict, qualitatively speaking, the same structural and gravitational equilibrium configurations for different values of the parameters involved.

Jeans instability in an expanding universe with dissipation

Jeans instability is analyzed in an expanding universe within the framework of BGK model of the Boltzmann equation and Poisson equations. The background is characterized by a comoving Maxwellian distribution function and a spacetime Newtonian gravitational potential which satisfy the BGK model of the Boltzmann–Poisson equations without the necessity to invoke “Jeans swindle.” The perturbations of the distribution function and Newtonian gravitational potentials from their background states are represented by plane waves of small amplitudes and a differential equation for the density contrast is determined. The density contrast differential equation was solved numerically and it is shown: (i) Jeans instability is characterized by perturbation wavelengths larger than Jeans wavelength where the density contrast grows with time. The growth of the density contrast is less accentuated for the case where the particle collisions are considered due to an energy dissipation; (ii) for perturbation wavelengths smaller than Jeans wavelength the density contrast has an oscillatory behavior in time and the oscillations for the case where the collisions are taken into account fade away in time due to the energy dissipation.

Constraining modified gravity with quantum optomechanics

We derive the best possible bounds that can be placed on Yukawa- and chameleon-like modifications to the Newtonian gravitational potential with a cavity optomechanical quantum sensor. By modelling the effects on an oscillating source-sphere on the optomechanical system from first-principles, we derive the fundamental sensitivity with which these modifications can be detected in the absence of environmental noise. In particular, we take into account the large size of the optomechanical probe compared with the range of the fifth forces that we wish to probe and quantify the resulting screening effect when both the source and probe are spherical. Our results show that optomechanical systems in high vacuum could, in principle, further constrain the parameters of chameleon-like modifications to Newtonian gravity.

IS GRAVITATIONAL VACUUM ENERGY RENORMALIZEDIN NEUTRON STAR BINARY?

The vacuum energy of fluctuating quantum fields has been intensively studied by analyzing boundary conditions on the objects. By treating the two star components, making up of a wide neutron star (NS) binary with orbital separation of , as two Dirichlet point particles on the radial line, we calculate the quantum vacuum energy of fluctuating gravitational fields, arising from the Newtonian gravitational scalar potential and a gravitational vector potential that leads to the spiral-in orbital motion of the system. It is found that the stress tensor, which is responsible for the fluctuations of gravitational fields, gives rise to a finite quantum vacuum energy inside the binary system, i.e., in the region of . Accordingly, both objects making up of the binary are imposed by an additionally finite and attractive stress of . While outside the system, , the gravitational vacuum energy consists of a divergent term , resulting from the free Greens function without any presence of gravitational sources, and a term of that disappears when the distance is far away from the sources. However, the gravitational Casimir force imposed on NS binary is a finite one, because the fluctuating gravitational fields vanish on the star, on which the stress tensor appears discontinuity.

Inspiraling corrugation-induced quantum effects on neutron star binary plane

We use the path-integral formula and investigate some dynamical quantum effects induced by the inspiraling lateral corrugation of orbital plane in gravitationally bound neutron star (NS) binaries, with orbital separation of 109 m. Based on Dewitt's approach, we calculate the gravitational Casimir energy cost of the binary plane, which consists of statically gravitational effects and deformation-induced effects. It is found that the static effects include a term coming from the self-gravity of the orbital plane and the contribution of Newtonian gravitational potential of the binary system. While the deformation-induced effect also results from two parts, i.e. the instability of orbital binding energy, scaling as 1(R−r)2, and the dynamically Casimir energy cost of the orbital binding energy, decaying as 1(R−r)4. The dynamically gravitational Casimir phenomena and the corresponding energy cost modify the spiral-in orbital motion of the binary and thus the frequency of released gravitational waves (GWs). We consider the mechanical response of two NS components and qualitatively study the corrections to the orbital motion of the system and the GW frequencies. It is found that the dynamical Casimir effects exert a dissipative force on the binary plane, depending on the frequency of GWs. The resultant dissipation may enhance with the decaying separation and increasing GW frequencies, which subsequently accelerates the orbital decay of the binary. However, the dissipation rate just has an order of 10−70 eV/s. So the corrections to the dynamics of NS binaries are very marginal, by considering the wide separation, the cosmological coalescence time, and low-frequency GWs of the system.

Graviton corrections to the Newtonian potential using invariant observables

We consider the effective theory of perturbative quantum gravity coupled to a point particle, quantizing fluctuations of both the gravitational field and the particle’s position around flat space. Using a recent relational approach to construct gauge-invariant observables, we compute one-loop graviton corrections to the invariant metric perturbation, whose time-time component gives the Newtonian gravitational potential. The resulting quantum correction consists of two parts: the first stems from graviton loops and agrees with the correction derived by other methods, while the second one is sourced by the quantum fluctuations of the particle’s position and energy-momentum, and may be viewed as an analog of a “Zitterbewegung”. As a check on the computation, we also recover classical corrections which agree with the perturbative expansion of the Schwarzschild metric.

The Relation between General Relativity’s Metrics and Special Relativity’s Gravitational Scalar Generalized Potentials and Case Studies on the Schwarzschild Metric, Teleparallel Gravity, and Newtonian Potential

This paper shows that gravitational results of general relativity (GR) can be reached by using special relativity (SR) via a SR Lagrangian that derives from the corresponding GR time dilation and vice versa. It also presents a new SR gravitational central scalar generalized potential V=V(r,r.,ϕ.), where r is the distance from the center of gravity and r.,ϕ. are the radial and angular velocity, respectively. This is associated with the Schwarzschild GR time dilation from where a SR scalar generalized potential is obtained, which is exactly equivalent to the Schwarzschild metric. Thus, the Precession of Mercury’s Perihelion, the Gravitational Deflection of Light, the Shapiro time delay, the Gravitational Red Shift, etc., are explained with the use of SR only. The techniques used in this paper can be applied to any GR spacetime metric, Teleparallel Gravity, etc., in order to obtain the corresponding SR gravitational scalar generalized potential and vice versa. Thus, the case study of Newtonian Gravitational Potential according to SR leads to the corresponding non-Riemannian metric of GR. Finally, it is shown that the mainstream consideration of the Gravitational Red Shift contains two approximations, which are valid in weak gravitational fields only.