People often illustrate space-time curvature with an heavy ball curving a sheet but the heavy ball is curving the sheet because that heavy ball is pulled by Earth’s gravity but in space there is no gravity without space time bending,so while there is no gravity how is the space-time bent wherever there is mass?

In: Physics

The illustration of the ball on a sheet is grossly misleading. We reside in a four dimensional space, three spatial and one temporal (time). All of these are bent, but the temporal one is affected a little more, which happens to give rise to the time dilation effect of general relativity (not to be confused with time dilation in special relativity).

The thing with the curvature of space-time is that this IS what we call gravity. This is one of the important conclusions of Einsteins general relativity. Mass bends space. Mass does not exert an instantaneous force on another object. We can use the description of gravitational force to explain most phenomenon you can come across, but it’s not completely accurate.

This curvature can be calculated with the Einstein equations (Einstein tensors for curvature if anyone is interested) which consist of materia information. This means, if there is no materia, there is no curvature. This curvature is remarkable around large celestial bodies, like Earth. Space around the planet (and inside even) is curved which gives rise to the moons orbit around us, and us staying on Earth.

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