Classical Gravitational Field Research Articles

Gravitational Field of a Self-Gravitating Continuous Medium and Dark Matter

A method to describe the hidden mass effect or dark matter has been proposed on the basis of a new general solution of the Poisson equation for the gravitational field strength in a continuous self-gravitating medium. This solution is a consequence of the theory of space and matter alternative to the general relativity. Conditions have been derived to distinguish between the cases where the obtained solution describes the classical Newtonian gravitational field and the cases where this solution leads to the hidden mass effect. The representation obtained for the gravitational field strength has been analyzed within the model of the dynamic equilibrium of disk galaxies and the possibility of describing the observed properties of the hidden mass effect within this approach has been discussed.

Effective graviton mass in de Sitter space

We calculate the effective mass of gravitational perturbations induced by the interaction of the classical gravitational field with quantum matter in the background of the Poincaré patch of de Sitter space. Using the Schwinger-Keldysh diagrammatic technique, the one-loop effective action is calculated, and it is shown that the graviton does not acquire mass for the most symmetric Bunch-Davies state. However, we have shown that even in this case, there is a nontrivial modification of the theory at one loop in the scalar sector of gravity. Published by the American Physical Society 2024

The semiclassical limit of quantum gravity and the problem of time

The question about the appearance of time in the semiclassical limit of quantum gravity continues to be discussed in the literature. It is believed that a temporal Schrödinger equation for matter fields on the background of a classical gravitational field must be true. To obtain this equation, the Born–Oppenheimer approximation for gravity is used. However, the origin of time in this equation is different in works of various authors. For example, in the papers of Kiefer and his collaborators, time is a parameter along a classical trajectory of gravitational field; in the works of Montani and his collaborators, the origin of time is introducing the Kuchař–Torre reference fluid; in the extended phase space approach, the origin of time is the consequence of existing of the observer in a fixed reference frame. We discuss and compare these approaches. To make the calculations transparent, we illustrate them with the model of a closed isotropic universe. In each approach, one obtains some Schrödinger equation for matter fields with quantum gravitational corrections, but the form of the equation and the corrections depend on additional assumptions which are rather arbitrary. None of the approaches can explain how time had appeared in the Early Universe, since it is supposed that classical gravity and, therefore, classical spacetime had already come into being.

Self-consistent equation for torsion arising as a consequence of the Dirac sea quantum fluctuations in external classical electromagnetic and gravitational fields

The quantum fluctuations of the Dirac field in external classical gravitational and electromagnetic fields are studied. A self-consistent equation for torsion is calculated, which is obtained using one-loop fermion diagrams.

Path integral formalism for the Jaynes–Cummings model in the presence of a classical homogeneous gravitational field

Path integral formalism for the Jaynes–Cummings model in the presence of a classical homogeneous gravitational field

Mechanism for the quantum natured gravitons to entangle masses

This paper points out the importance of the quantum nature of the gravitational interaction with matter in a linearized theory of quantum gravity induced entanglement of masses. We will show how the quantum interaction entangles the steady states of a closed system (eigenstates) of two test masses placed in the harmonic traps, and how such a quantum matter-matter interaction emerges from an underlying quantum gravitational field. We will rely upon quantum perturbation theory highlighting the critical assumptions for generating a quantum matter-matter interaction and showing that a classical gravitational field does not render such an entanglement. We will consider two distinct examples: one where the two harmonic oscillators are static, and the other where the harmonic oscillators are nonstatic. In both cases it is the quantum nature of the gravitons interacting with the harmonic oscillators that are responsible for creating an entangled state with the ground and the excited states of harmonic oscillators as the Schmidt basis. We will compute the concurrence as a criterion for the above entanglement and compare the two ways of entangling the two harmonic oscillators.

Validity of semiclassical limit to quantum gravity in two-mode oscillating quantized massive scalar field quantum cosmology

Semiclassical Einstein equations are used to describe the interaction of the back-reaction of the classical gravitational field with quantum matter fields in semiclassical gravity. We in our previous studies have made use of the semiclassical approximation to demonstrate the phenomenon of particle production, often called preheating/reheating of the universe, which occurs after the inflationary epoch during the oscillatory phase of two-mode quantized scalar field of chaotic inflationary model. During this oscillatory phase, back-reaction effects from the created particles, on account of the quantum nature of the states considered, could be significant and one might be concerned about the validity of the semiclassical approximation in these two-mode quantum optical states. The validity of the semiclassical approximation in these states is examined and it is presented how the magnitude of states parameter draws limit on the applicability and reliability of semiclassical theory of gravity. It is argued that semiclassical theory to gravity is a good approximation for states which are closer to coherent states i.e., with coherent parameters greater than unity and with squeezed parameter much smaller than unity.

Quantum mechanical rotation of a photon polarization by Earth\u2019s gravitational field

We describe the quantum mechanical rotation of a photon state, the Wigner rotation—a quantum effect that couples a transformation of a reference frame to a particle’s spin, to investigate geometric phases induced by Earth’s gravitational field for observers in various orbits. We find a potentially measurable quantum phase of the Wigner rotation angle in addition to the rotation of standard fame, the latter of which is computed and agrees well with the geodetic rotation. When an observer is in either a circular or a spiraling orbit containing non-zero angular momentum, the additional quantum phase contributes 10−6 degree to 10−4 degree respectively, depending on the altitude of the Earth orbit. In the former case, the additional quantum phase is dominant over the near-zero classical geodetic rotation. Our results show that the Wigner rotation represents a non-trivial semi-classical effect of quantum field theory on a background classical gravitational field.

Gravitational decoherence: A nonrelativistic spin 1/2 fermionic model

In a previous work [L. Asprea, G. Gasbarri, and A. Bassi, Gravitational decoherence: A general nonrelativistic model, Phys. Rev. D 103, 104041 (2021).] we derived a quantum master equation for the dynamics of a scalar bosonic particle interacting with a weak, stochastic and classical gravitational field. As standard matter is made of fermions, such an equation should be suitably extended to describe more relevant experimental situations. Here we derive a nonrelativistic model for the gravitational decoherence of spin 1/2 particles. We enrich the treatment by also considering a coupling with an external classical electromagnetic field. We comment on the differences with the scalar bosonic model and we describe the regimes in which they become negligible.

Coupling of quantum gravitational field with Riemann and Ricci curvature tensors

The theoretical problem of establishing the coupling properties existing between the classical and quantum gravitational field with the Ricci and Riemann curvature tensors of General Relativity is addressed. The mathematical framework is provided by synchronous Hamilton variational principles and the validity of classical and quantum canonical Hamiltonian structures for the gravitational field dynamics. It is shown that, for the classical variational theory, manifestly-covariant Hamiltonian functions expressed by either the Ricci or Riemann tensors are both admitted, which yield the correct form of Einstein field equations. On the other hand, the corresponding realization of manifestly-covariant quantum gravity theories is not equivalent. The requirement imposed is that the Hamiltonian potential should represent a positive-definite quadratic form when performing a quadratic expansion around the equilibrium solution. This condition in fact warrants the existence of positive eigenvalues of the quantum Hamiltonian in the harmonic-oscillator representation, to be related to the graviton mass. Accordingly, it is shown that in the background of the deSitter space-time, only the Ricci tensor coupling is physically admitted. In contrast, the coupling of quantum gravitational field with the Riemann tensor generally prevents the possibility of achieving a Hamiltonian potential appropriate for the implementation of the quantum harmonic-oscillator solution.

Gravitational decoherence: A general nonrelativistic model

We derive a general quantum master equation for the dynamics of a scalar bosonic particle interacting with a weak, stochastic and classical external gravitational field. The dynamics predicts decoherence in position, momentum and energy. We show how our master equation reproduces the results present in the literature by taking appropriate limits, thus explaining the apparent contradiction in their dynamical description. Our result is relevant in light of the increasing interest in the low energy quantum-gravity regime.

Non-Rotating Black Holes, Dark Matter and Dark Energy in a Unifying Theory

The theory here developed, makes use of the decomposition of matter (mass) in different spatial frequencies k’s using spatial Fourier transforms, and the posterior use of modified inverse Fourier transforms to construct an accurate description of the classical Newtonian gravitational field. Introducing the concept of quantization of the spatial frequency k, which means allowing only discrete values, such as km, 2km, 3km, leads to the appearance of extra gravitational force regions that occur at distances equally spaced apart in 2π/km. These areas of extra gravitational force decrease inscribed in an inverse of the distance envelope (1/r). The value of 2π/km can be adjusted to be of the order of kiloparsec (kpc), being this way a plausible explanation for the effect of the dark matter since this causes practically flat rotation curves for most of the galaxies. As these regions of extra gravitational force also have adjacent areas of negative values (repulsive gravitational force), it is possible to show that any mass placed in the gravitational field far from the galaxy center will acquire, on average, a null acceleration, thereby remains the “light push,” or in other words, the “mean luminosity density” between galaxies as an explanation for the accelerating expansion of the universe, today being considered mainly due to dark energy. Along with the article, it is showed that the effect of light push is sufficient to explain the expansion of the universe. The present work also explains the nonlinear behavior of gravitational fields near massive objects such as blackholes, not contradicting the theory of general relativity, instead giving a complementary description of how black holes work, even describing the gravitational field internally to it, which is not available in the GR theory.

Relativistic Gravitational Field and Invalidity of Singularity

A century of successful experiments on general relativity was unable to convince substantial scholars on the presence of “gravitational singularity”. Physically questionable outcomes of general relativity are due to the deployment of non-relativistic Newtonian gravitation. However, the nonrelativistic classical gravitational field equation can be utilized for the weak field with negligible error. The connection between inertia and mass is distinct for classical and relativistic mechanics. As per the equivalence principle, the connection between energy and spacetime should be identical for special and general relativity; the relativistic approach on the gravitational field will eliminate “gravitational singularity”. This theory aligned well with relativity and improved sturdiness to general relativity. The impacts of this model on general relativity experimental results are insignificant.

On the interaction between tripod-type four-level atom and one-mode field in the presence of a classical homogeneous gravitational field

In this paper, we investigate the effects of gravitational field on the dynamical behaviour of nonlinear atom–field interaction. We consider a moving tripod-type four-level atom interacting with a single mode field in the presence of a classical homogeneous gravitational field. The analytical solution of the model is calculated by using the Schrodinger equation for a coherent electromagnetic field and when the atom is in its excited state. The influence of the detuning parameter and the classical homogeneous gravitational field on the temporal behaviour of atomic inversion, Mandel Q-parameters, purity of the atomic system and concurrence is studied. Our proposal has many advantages over the previous optical schemes and can be realised in several multiple experiments, such as quantum gravity. The results show that the gravity parameter has an important effect on the properties of these phenomena. Finally, conclusions and some features and comments are given.

The gravitational magnetic component and its magnetic effects in linearized theory of gravity

According to the General Relativity (GR), under the approximation of the weak field, the weak gravitational field not only contains the classical Newtonian gravitational field, but also contains a gravitomagnetic (GM) field analogous to the concept of magnetic field, and the name of GM field borrows the basic idea of the magnetic field in electrodynamics. In order to study the physical properties of GM field and its associated effects, firstly, we use a similarity transformation method to decompose the gravitomagnetic component from the second-order tensor field in linearized Einstein field equation and define the concept of the GM field. Then, on this basis, we consider a circular microtube model with uniform velocity fluids (or superfluids), and study the distribution characteristics of the far GM field by this special model. We use a simpler approximation approach to improve the previous calculation method of the GM field in these kind of rings model, the result shows that the distribution characteristic of the far GM field in this model is analogous to the magnetic field produced by a dipole, it is a good correspondence between this microtube model and the dipole model. After that, we have studied the dynamic characteristics of GM field by analogizing the properties of magnetic field, and studied the test particles’ tracks in the linear time-varying GM field and the cosine time-varying GM field in the first time. In addition, in order to improve the previous research methods of ‘gravitational induction’ and ‘frame dragging’ in the GR, we have designed a circular microtube model which has a double-layer structure and with the accelerating flow fluid (or superfluids), we use simpler mathematics than before to explain these two effects by this special model. In conclusion, this work provides some new methods for the study of GM field and its associated effects.

Entangling quantum fields via a classical gravitational interaction

We consider the coupling of quantum fields to classical gravity in the formalism of ensembles on configuration space, a model that allows a consistent formulation of interacting classical and quantum systems. Explicit calculations show that there are solutions for which two initially independent quantum fields evolve into an entangled state, even though their interaction occurs solely via a common classical gravitational field. Thus in contrast to recent suggestions, an observed generation of entanglement would not provide a definitive test of the nonclassical nature of gravity.

Minisuperspace model of compact phase space gravity

The kinematical phase space of classical gravitational field is flat (affine) and unbounded. Because of this, field variables may tend to infinity leading to appearance of singularities, which plague Einstein's theory of gravity. The purpose of this article is to study the idea of generalizing the theory of gravity by compactification of the phase space. We investigate the procedure of compactification of the phase space on a minisuperspace gravitational model with two dimensional phase space. In the affine limit, the model reduces to the flat de Sitter cosmology. The phase space is generalized to the spherical case, and the case of loop quantum cosmology is recovered in the cylindrical phase space limit. Analysis of the dynamics reveals that the compactness of the phase space leads to both UV and IR effects. In particular, the phase of re-collapse appears, preventing the universe from expanding to infinite volume. Furthermore, the quantum version of the model is investigated and the quantum constraint is solved. As an example, we analyze the case with the spin quantum number $s=2$, for which we determine transition amplitude between initial and final state of the classical trajectory. The probability of the transition is peaked at $\Lambda=0$.

The classical double copy in maximally symmetric spacetimes

The classical double copy procedure relates classical asymptotically-flat gravitational field solutions to Yang-Mills and scalar field solutions living in Minkowski space. In this paper we extend this correspondence to maximally symmetric curved spacetimes. We consider asymptotically (A)dS spacetimes in Kerr-Schild form and construct the corresponding single and zeroth copies. In order to clarify the interpretation of these copies, we study several examples including (A)dS-Schwarzschild, (A)dS-Kerr, black strings, black branes, and waves, paying particular attention to the source terms. We find that the single and zeroth copies of stationary solutions satisfy different equations than those of wave solutions. We also consider how to obtain Einstein-Maxwell solutions using this procedure. Finally, we derive the classical single and zeroth copy of the BTZ black hole.

An application of information theory to stochastic classical gravitational fields

The objective of this study lies on the incorporation of the concepts developed in the Information Theory (entropy, complexity, etc.) with the aim of quantifying the variation of the uncertainty associated with a stochastic physical system resident in a spatiotemporal region. As an example of application, a relativistic classical gravitational field has been considered, with a stochastic behavior resulting from the effect induced by one or several external perturbation sources. One of the key concepts of the study is the covariance kernel between two points within the chosen region. Using this concept and the appropriate criteria, a methodology is proposed to evaluate the change of uncertainty at a given spatiotemporal point, based on available information and efficiently applying the diverse methods that Information Theory provides. For illustration, a stochastic version of the Einstein equation with an added Gaussian Langevin term is analyzed.

Ghirardi-Rimini-Weber model with massive flashes

I introduce a modification of the Ghirardi-Rimini-Weber (GRW) model in which the flashes (or collapse space-time events) source a classical gravitational field. The resulting semi-classical theory of Newtonian gravity preserves the statistical interpretation of quantum states of matter in contrast with mean field approaches. It can be seen as a discrete version of recent proposals of consistent hybrid quantum classical theories. The model is in agreement with known experimental data and introduces new falsifiable predictions: (1) single particles do not self-interact, (2) the $1/r$ gravitational potential of Newtonian gravity is cut-off at short ($\lesssim 10^{-7}$m) distances, and (3) gravity makes spatial superpositions decohere at a rate inversely proportional to that coming from the vanilla GRW model. Together, the last two predictions make the model experimentally falsifiable for \emph{all} values of its parameters.