Gravitational field from photons

The gravitational field created by a single photon is determined by taking into account the relativistic mass of the photon as source of gravitational interaction. In addition, the total force (due to the above field) over an accelerated particle is calculated in the light of the general theory of relativity. Some aspects related to the photon as an ultrarelativistic particle are discussed.     

Photon Productions in a Gravitational Collapsing

We study a possible gravitational vacuum-effect, in which vacuum-energy variation is due to variation of gravitational field, vacuum state gains gravitational energy and releases it by spontaneous photon emissions. Based on the path-integral representation, we present a general formulation of vacuum transition matrix and energy-momentum tensor of a quantum scalar field theory in curved spacetime. Using analytical continuation of dimensionality of the phase space, we calculate the difference of vacuum-energy densities in the presence and absence of gravitational field. Using the dynamical equation of gravitational collapse, we compute the rate of vacuum state gaining gravitational energy. Computing the transition amplitude from initial vacuum state to final vacuum state in gravitational collapsing process, we show the rate and spectrum of spontaneous photon emissions for releasing gravitational energy. We compare our idea with the Schwinger idea for Sonoluminiescence and contrast our scenario with the Hawking effect.     

Estimation of the photon rest-mass from gravitational interaction

An estimation of the photon rest-mass is performed by considering a single photon under the action of a gravitational field. In fact, the wavelength dependence of this mass is expressed in analytical form in connection with the fact that the photon velocity depends upon wavelength.     

On Relativistic Generalization of Gravitational Force

In relativistic theories, the assumption of proper mass constancy generally holds. We study gravitational relativistic mechanics of point particle in the novel approach of proper mass varying under Minkowski force action. The motivation and objective of this work are twofold: first, to show how the gravitational force can be included in the Special Relativity Mechanics framework, and, second, to investigate possible consequences of the revision of conventional proper mass concept (in particular, to clarify a proper mass role in the divergence problem). It is shown that photon motion in the gravitational field can be treated in terms of massless refracting medium, what makes the gravity phenomenon compatible with SR Mechanics framework in the variable proper mass approach. Specifically, the problem of point particle in the spherical symmetric stationary gravitational field is studied in SR-based Mechanics, and equations of motion in the Lorentz covariant form are obtained in the relativistic Lagrangean problem formulation. The dependence of proper mass on potential field strength is derived from the Euler-Lagrange equations as well. One of new results is the elimination of conventional 1/r divergence, which is known to be not removable in Schwarzschild gravitomechanics. Predictions of particle and photon gravitational properties are in agreement with GR classical tests under weak-field conditions; however, deviations rise with potential field strength. The conclusion is made that the approach of field-dependent proper mass is perspective for development of SR gravitational mechanics and further studies of gravitational problems.     

Thomson scattering induced by gravitational waves

We investigate the effects of a weak gravitational wave, modelled as a gaussian wavepacket, on the polarization state of an electromagnetic field enclosed in a cavity. Our approach is semiclassical, in that the electromagnetic field is described as a quantum field, while the gravitational perturbation is treated classically, as a slightly curved background spacetime. Assuming that before the interaction the electromagnetic field has been prepared in a given polarization state, we show that – due to the gravitational scattering with the wave – some photons having different polarization states are found in the cavity at late times. Such polarization scattering has some resemblance with Thomson scattering, well-known in Quantum Electrodynamics: hence the motivation for the title. We give a numerical estimate of the resulting photon polarization spreading in the case of a typical gravitational burst from a final supernova rebound. We also briefly comment about the possible influence of such gravitational scattering on the Cosmic Microwave Background (CMB) polarization.     

Neutrino radiation in spherically-symmetric gravitational fields. III. Comparison with photon radiation fields

The gravitational properties of spherically-symmetric photon and neutrino radiation fields are compared and found to be identical. A model for the photon radiation field made up of incoherent radiation is first developed, equations for photons being required to satisfy Maxwell's equations.     

Exact Harmonic Metric for a Uniformly Moving Schwarzschild Black Hole

The harmonic metric for Schwarzschild black hole with a uniform velocity is presented. In the limit of weak field and low velocity, this metric reduces to the post-Newtonian approximation for one moving point mass. As an application, we derive the dynamics of particle and photon in the weak-field limit for the moving Schwarzschild black hole with an arbitrary velocity. It is found that the relativistic motion of gravitational source can induce an additional centripetal force on the test particle, which may be comparable to or even larger than the conventional Newtonian gravitational force.     

Spherical gravitational collapse with photon emission and a generalized Schwarzchild interior solution

The general dynamical equations for perfect fluid filled spheres with an outward flux of photons are derived. The vital role played by the energy density of the free gravitational field in accelerating photon production has been emphasized. It is pointed out that even when the material energy density is finite, the energy density of the free gravitational field can take infinitely large values resulting in vanishing surface area of the star. A generalized Schwarzschild interior solution with conformally flat geometry but with photon emission has been obtained. It is pointed out that the interior conformal coordinate system bears a strong resemblance to the exterior Krushkal coordinates. It is shown that for spherical star the invariant velocity of the fluid particles, falling towards the centre, is proportional to its radius suggesting that the outer envelopes collapse at a faster rate than the core part. It is shown that the interior radiating solution can be matched with generalized Schwarzchild exterior solution.     

Influence of a Classical Homogeneous Gravitational Field on Dissipative Dynamics of the Phase Damped Jaynes–Cummings Model under the Markovian Approximation

In this paper, we study the dissipative dynamics of the phase damped Jaynes–Cummings model under the Markovian approximation in the presence of a classical homogeneous gravitational field. The model consists of a moving two-level atom simultaneously exposed to the gravitational field and a single-mode traveling radiation field in the presence of a phase damping mechanism. We first present the master equation for the reduced density operator of the system under the Markovian approximation in terms of a Hamiltonian describing the atom-field interaction in the presence of a homogeneous gravitational field. Then, by making use of the super-operator technique, we obtain an exact solution of the master equation. Assuming that initially the radiation field is prepared in a Glauber coherent state and the two-level atom is in the excited state, we investigate the influence of gravity on the temporal evolution of collapses and revivals of the atomic population inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting statistics and quadrature squeezing of the radiation field in the presence of phase damping.     

Localization and Amplification of the Electromagnetic Field in a Globular Photonic Crystal

Using the wave equation, the electromagnetic field distribution is calculated in a globular photonic crystal on the basis of artificial opal in the [111] direction. The electromagnetic field is found to be localized at the edge of the photonic band gap in the first surface pore of the sample. The effect of pumping on a sample is estimated as well. The results open up prospects for the application of artificial opals to solve photon and gravitational conversion problems.     

广义相对论浅释(1)

本文用通俗的方法介绍了广义相对论的基本思想 ,并得到了史瓦西场时空弯曲的规律及质点在史瓦西场中自由运动的规律 ,从而解决了引力红移 ,CS原子钟环地球飞行后与地面上 CS原子钟的时差 ,行星进动 ,光子经过太阳表面时的偏转角 ,雷达回波延迟等问题 .     

Study of the photon’s pole structure in the noncommutative Schwinger model

The photon magnetic moment for radiation propagating in magnetized vacuum is defined as a pseudotensor quantity, proportional to the external electromagnetic field tensor. After expanding the eigenvalues of the polarization operator in powers of \(k^2\) , we obtain approximate dispersion equations (cubic in \(k^2\) ), and analytic solutions for the photon magnetic moment, valid for low momentum and/or large magnetic field. The paramagnetic photon experiences a redshift, with opposite sign to the gravitational one, which differs for parallel and perpendicular polarizations. It is due to the drain of photon transverse momentum and energy by the external field. By defining an effective transverse momentum, the constancy of the speed of light orthogonal to the field is guaranteed. We conclude that the propagation of the photon non-parallel to the magnetic direction behaves as if there is a quantum compression of the vacuum or a warp of space-time in an amount depending on its angle with regard to the field.     

On the mechanics of photon rockets in the general theory of relativity

Generally covariant equations of motion of a photon rocket comprising all the basic dynamic and thermodynamic processes are derived and are written for the case of a weak gravitational field. The equations lead to results which agree with those obtained by other means.     

Resonance photons in a gravitational radiation field and the regularization problem for the energy-momentum tensor

The exact solutions of the relativistic kinetic equation for a photon gas subjected to the influence of a relativistic fluid and a gravitational radiation field are analyzed. Singular solutions describing resonance and entrained photons moving at a gravitational wave front are investigated. The problem of the divergence of the energy-momentum tensor in models admitting resonance photons is discussed.V. I. Ul'yanov (Lenin) State University, Kazan. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 70–75, October, 1994.     

On gravitational fluctuations of quantum vacuum interacting with photons

An upper bound for the photon mass is calculated by regarding photons under the action of a gravitational field within the framework of fluctuations in the quantum vacuum. Furthermore, some considerations upon zero-point energy are made in order to estimate interaction range in terms of distance.     

Finite temperature field theory with boundaries: The photon field

We calculate the deviations from Planckian form of the photon field finite temperature stress tensor in a manifold with boundary, due to scattering from the boundary. Familiar non-integrable divergences are found in the photon stress tensor as the boundary is approached and these are shown to be an inescapable consequence of initial calculational assumptions. Modifications of these assumptions are discussed which serve to remove the divergences and to illustrate the importance of the role played by surface gravitational actions.     

Is GW151226 really a gravitational wave signal?

Recently, the LIGO Scientific Collaboration and Virgo Collaboration published the second observation of a gravitational wave, GW151226 [Phys. Rev. Lett. 116, 241103(2016)], from a binary black hole coalescence with initial masses about 14 M and 8 M. They claimed that the peak gravitational strain was reached at about 450 Hz, the inverse of which is longer than the average time a photon stays in the Fabry-Perot cavities in the two arms.In this case, the phase-difference of a photon in the two arms due to the propagation of a gravitational wave does not always increase as the photon stays in the cavities. It might even be cancelled to zero in extreme cases. When the propagation effect is taken into account, we find that the claimed signal GW151226 almost disappears.     

Combining general relativity, massive QED and Very Long Baseline Interferometry to gravitationally constrain the photon mass

A constraint between the photon mass and the parameters γ (the deflection parameter determined by experimentalists) and ν (the photon frequency) is found by judiciously combining General Relativity and Massive QED. By adopting this scenario and by considering as inputs the most recent measurements of the solar gravitational deflection of radio waves obtained by means of the Very Long Baseline Interferometry, gravitational upper bounds on the photon mass are estimated.     

Testing fundamental physics with astrophysical transients

Explosive astrophysical transients at cosmological distances can be used to place precision tests of the basic assumptions of relativity theory, such as Lorentz invariance, the photon zero-mass hypothesis, and the weak equivalence principle (WEP). Signatures of Lorentz invariance violations (LIV) include vacuum dispersion and vacuum birefringence. Sensitive searches for LIV using astrophysical sources such as gamma-ray bursts, active galactic nuclei, and pulsars are discussed. The most direct consequence of a nonzero photon rest mass is a frequency dependence in the velocity of light propagating in vacuum. A detailed representation of how to obtain a combined severe limit on the photon mass using fast radio bursts at different redshifts through the dispersion method is presented. The accuracy of the WEP has been well tested based on the Shapiro time delay of astrophysical messengers traveling through a gravitational field. Some caveats of Shapiro delay tests are discussed. In this article, we review and update the status of astrophysical tests of fundamental physics.