In the framework of general relativity, it is not accurate to state that time "stops" at the speed of light. However, the theory does predict that time dilation becomes infinitely large as an object approaches the speed of light.
To understand this, let's consider the basic principles of general relativity. According to the theory, the presence of mass and energy curves the fabric of spacetime, causing objects to follow curved paths in the presence of gravity. In a flat spacetime (in the absence of gravitational fields), the theory reduces to special relativity.
In special relativity, time dilation occurs when an object moves relative to an observer. As the relative velocity increases, time appears to slow down for the moving object as observed by the stationary observer. This effect becomes more pronounced as the relative velocity approaches the speed of light.
General relativity builds upon this concept and extends it to include gravitational fields. In the presence of gravity, both the motion and gravitational field affect the flow of time. Gravitational time dilation occurs when an object is in a stronger gravitational field compared to another object in a weaker field.
In a flat spacetime, where there is no gravity, an object moving at the speed of light experiences infinite time dilation. This is a consequence of the Lorentz factor, which governs time dilation in special relativity. The Lorentz factor contains a term that approaches infinity as the relative velocity approaches the speed of light (v → c). Consequently, time dilation becomes infinitely large, and it would appear to an observer that time has "stopped" for the object moving at the speed of light.
However, it is essential to note that this is a theoretical prediction. In reality, massive objects with mass (such as particles with rest mass) cannot reach the speed of light due to the energy requirements and relativistic effects. The concept of time stopping at the speed of light is a theoretical limit based on the mathematics of special and general relativity.