# Are photons affected by "temporal gravity?"

Since objects follow geodesics in spacetime, that is the locally shortest path, it would seem to me that unless objects move, they do not trace any path at all. In other words, if I'm stationary on Earth, I should only be affected by the curvature of time, since I always move through time. But on the flipside, photons do not travel through time at all, and so my question is: are they only affected by the spatial curvature?

• unless objects move, they do not trace any path at all An object that is stationary in space is moving through spacetime. Nov 23, 2022 at 18:54
• the curvature of time Time does not have curvature. Spacetime has curvature, and the curvature tensor has components involving the time direction along with spatial directions. The $tttt$ component is zero. Nov 23, 2022 at 18:57
• photons do not travel through time at all They travel through the time of any observer. Nov 23, 2022 at 18:57
• @Ghoster Regarding your statement that time does not have curvature: It is often said that near Earth, 99.99% of gravity is due to time dilation and it is only near a black hole that space curvature accounts for 50% of gravity. Can you reconcile these for me? Nov 23, 2022 at 21:04
• @foolishmuse near Earth, 99.99% of gravity is due to time dilation That’s talking about the $tt$ component of the metric tensor. It represents time dilation, and it is the only important component in the Newtonian limit of GR. It isn’t talking about the Riemann curvature tensor. Nov 24, 2022 at 0:35