To calculate the time dilation near a black hole, we can use the concept of gravitational time dilation. The gravitational time dilation near a massive object like a black hole is described by the following equation:
Δt' = Δt √(1 - (2GM)/(rc^2))
Where: Δt' is the time interval experienced by an observer near the black hole, Δt is the time interval experienced by a distant observer (far away from the black hole), G is the gravitational constant, M is the mass of the black hole, r is the distance from the center of the black hole, c is the speed of light in a vacuum.
Given that the black hole in question has a mass of 10 quadrillion solar masses, we can assume its mass to be approximately 10^17 times the mass of the Sun (since 1 solar mass ≈ 2 × 10^30 kilograms). Let's denote M as the mass of the black hole, where M = 10^17 times the mass of the Sun.
To calculate the time dilation near the black hole, we need to specify the distance from the center of the black hole. The equation above shows that time dilation depends on the distance from the black hole. As you move closer to the black hole, the time dilation becomes more significant.
If you provide the distance from the center of the black hole, I can help you calculate the time dilation experienced at that location.