The speed of light is a fundamental constant denoted by 'c' in the theory of relativity. According to Albert Einstein's theory of general relativity, the presence of a massive body, such as a black hole, can affect the local geometry of spacetime, which in turn can influence the behavior of light.
Near a massive body like a black hole, the curvature of spacetime becomes significant. As a result, the path of light traveling near a black hole is curved due to the gravitational field. This phenomenon is known as gravitational lensing.
To calculate the speed of light with respect to an observer at rest near a massive body, we need to consider the local effects of gravity on light. In general relativity, the speed of light is still considered constant, but the observed speed of light can vary due to the gravitational field.
The observer near a black hole will measure the speed of light to be the same as its standard value, 'c,' in their local frame of reference. However, when the light is observed from a distance, it will appear to be affected by the gravitational field. This means that an observer far away from the black hole will perceive the light as moving slower due to the gravitational redshift caused by the intense gravitational field near the black hole.
Physically, this implies that the gravitational field of a black hole can cause a change in the observed properties of light, including its frequency and energy. It demonstrates the influence of gravity on the behavior of electromagnetic waves and confirms the predictions of general relativity in the presence of massive objects.