Light following a curved space5/20/2023 Whenever the spaceship fires its rockets the onboard accelerometers will show non zero acceleration and they will know that their path is in fact curved. In GR curved paths in spacetime are characterized by proper acceleration, which is the kind of acceleration which is measured by an accelerometer. Let's say, first, for simplicity, the target star location were fixed relative to your depature point Do you think if you were coasting though space, the spaceship would get you to the star without any course correction? In other words, do you think your spaceship would follow the same geodesic as the light, or would you follow a different one yet arrive at the star, or neither? Since light has a finite speed, as you approach the star you'd need to adjust the spaceship course to account for the smaller and smaller error in your visual location of the target, right? In addition, to these rather static curvature conditions, your example also includes a target star moving relative to your spaceship. The warping of spacetime curves the paths of the light rays and the trajectory of the spaceship. Light rays and coasting spaceships follow these curves which we call geodesics through this bent, stretched or compressed spacetime. In general relativity, matter, energy and pressure cause spacetime to bend, stretch or compress.to 'warp' or 'curve' to use two common terms. Hey Lavabug, It's difficult for me to pick just what aspect of gravity and curvature you are wondering about. What if the observer and ship were practically massless (but somehow still moved at v<<c, not sure if this is a non-sequitur on classical grounds), would he/she then be able to tell that the path was curved? (again without looking at background star motions) If the observer didn't know any GR/know that space was curved would he reasonably conclude that any steering he did was to correct any deflection from the Sun's gravity, and that the path was apparently straight? I presume if you had manual control over the ship's direction, you would progressively have to reorient the ship as the star changed position as you performed a close encounter with the Sun's gravitational field. If the observer did not look at the rest of the background stars and just did everything necessary to keep the spaceship pointed towards the target star, is there any way he/she would realize that the path being taken is not straight but in fact curved? Say an observer wanted to travel to the star from Earth and pointed his spaceship directly towards the star in question (at a speed v<<c). Then, given different black hole and wormhole metrics, we apply this method obtaining an excellent agreement with respect to the exact solutions in the original gravity framework by committing angular deviations below \(3^\) is met.Here goes a conceptual question that has been bugging me:Ĭonsider the famous eclipse experiment that shows the Sun's gravitational lensing effect, allowing a star that would otherwise be obscured by the Sun to be visible from Earth. Within this geometrical background, the photon geodesics are calculated. In other words, we pass from curved to flat space-times, where instead of the Einstein field equations, the Maxwell equations are solved. By applying a conformal transformation, we are able to consider an analogue gravity model, where curvature is encoded in the dielectric and magnetic properties of a medium. In this manuscript, we present an alternative method for calculating null geodesics in General Static Isotropic Metrics in General Relativity and Extended Theories of Gravity.
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