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Register a new userDeflection angle with electromagnetic interaction and gravitational-electromagnetic dual lensing
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The trajectory deflection and gravitational-electromagnetic dual lensing (GEL) of charged signal in general charged static and spherically symmetric spacetimes are considered in this work. We showed that the perturbative approach previously developed for neutral particles can be extended to the electromagnetic interaction case. The deflection angle still takes a (quasi-)series form and the finite distance effect of both the source and observer can be taken into account. Comparing to pure gravitational case, the apparent angles of the images in the GEL, their magnifications and time delay all receive the electromagnetic corrections starting from the first non-trivial order. The sign and relative size of the leading corrections are determined by $sim frac{Q}{M}frac{q}{E}$ where $M,~Q,~q,~E$ are the spacetime mass and charge, and signal particle charge and energy respectively. It is found that for $qQ>0$ (or $<0$), the electromagnetic interaction will decrease (or increase) the deflection angle, and in GEL the impact parameters, apparent angles, magnifications and total travel time for each image. The time delay is increased for small $beta$ and $qQ>0$, and otherwise always increased regardless the sign of $qQ$. The results are then applied to the deflection and GEL of charged protons in cosmic rays in Reissner-Nordstrom, charged dilaton and charged Horndeski spacetimes.
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In this review paper we investigate the connection between gravity and electromagnetism from Faraday to the present day. The particular focus is on the connection between gravitational and electromagnetic radiation. We discuss electromagnetic radiation produced when a gravitational wave passes through a magnetic field. We then discuss the interaction of electromagnetic radiation with gravitational waves via Feynman diagrams of the process $graviton + graviton to photon + photon$. Finally we review recent work on the vacuum production of counterpart electromagnetic radiation by gravitational waves.
Wave propagation of field disturbances is ubiquitous. The electromagnetic and gravitational are cousin theories in which the corresponding waves play a relevant role to understand several related physical. It has been established that small electromagnetic waves can generate gravitational waves and vice versa when scattered by a charged black hole. In the realm of cylindrical spacetimes, we present here a simple nonlinear effect of the conversion of electromagnetic to gravitational waves reflected by the amount of mass extracted from them.
A perturbative method to compute the deflection angle of both timelike and null rays in arbitrary static and spherically symmetric spacetimes in the strong field limit is proposed. The result takes a quasi-series form of $(1-b_c/b)$ where $b$ is the impact parameter and $b_c$ is its critical value, with coefficients of the series explicitly given. This result also naturally takes into account the finite distance effect of both the source and detector, and allows to solve the apparent angles of the relativistic images in a more precise way. From this, the BH angular shadow size is expressed as a simple formula containing metric functions and particle/photon sphere radius. The magnification of the relativistic images were shown to diverge at different values of the source-detector angular coordinate difference, depending on the relation between the source and detector distance from the lens. To verify all these results, we then applied them to the Hayward BH spacetime, concentrating on the effects of its charge parameter $l$ and the asymptotic velocity $v$ of the signal. The BH shadow size were found to decrease slightly as $l$ increase to its critical value, and increase as $v$ decreases from light speed. For the deflection angle and the magnification of the images however, both the increase of $l$ and decrease of $v$ will increase their values.
The renewed serious interest to possible practical applications of gravitational waves is encouraging. Building on previous work, I am arguing that the strong variable electromagnetic fields are appropriate systems for the generation and detection of high-frequency gravitational waves (HFGW). The advantages of electromagnetic systems are clearly seen in the proposed complete laboratory experiment, where one has to ensure the efficiency of, both, the process of generation and the process of detection of HFGW. Within the family of electromagnetic systems, one still has a great variety of possible geometrical configurations, classical and quantum states of the electromagnetic field, detection strategies, etc. According to evaluations performed 30 years ago, the gap between the HFGW laboratory signal and its level of detectability is at least 4 orders of magnitude. Hopefully, new technologies of today can remove this gap and can make the laboratory experiment feasible. The laboratory experiment is bound to be expensive, but one should remember that a part of the cost is likely to be reimbursed from the Nobel prize money ! Electromagnetic systems seem also appropriate for the detection of high-frequency end of the spectrum of relic gravitational waves. Although the current effort to observe the stochastic background of relic gravitational waves is focused on the opposite, very low-frequency, end of the spectrum, it would be extremely valuable for fundamental science to detect, or put sensible upper limits on, the high-frequency relic gravitational waves. I will briefly discuss the origin of relic gravitational waves, the expected level of their high-frequency signal, and the existing estimates of its detectability.
The behaviour of a test electromagnetic field in the background of an exact gravitational plane wave is investigated in the framework of Einsteins general relativity. We have expressed the general solution to the de Rham equations as a Fourier-like integral. In the general case we have reduced the problem to a set of ordinary differential equations and have explicitly written the solution in the case of linear polarization of the gravitational wave. We have expressed our results by means of Fermi Normal Coordinates (FNC), which define the proper reference frame of the laboratory. Moreover we have provided some gedanken experiments, showing that an external gravitational wave induces measurable effects of non tidal nature via electromagnetic interaction. Consequently it is not possible to eliminate gravitational effects on electromagnetic field, even in an arbitrarily small spatial region around an observer freely falling in the field of a gravitational wave. This is opposite to the case of mechanical interaction involving measurements of geodesic deviation effects. This behaviour is not in contrast with the principle of equivalence, which applies to arbitrarily small region of both space and time.
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