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Gravitational Redshift is a pivotal concept in the field of Astrophysics, a discipline within Physics, and is particularly important when studying phenomena like black holes. This tutorial explains the Gravitational Redshift experienced by light when it escapes from the gravity of a black hole, a cosmic object with gravity so strong that nothing, not even light, can escape from it. The following sections will detail the formula used to calculate this redshift, its significance, real-world applications, key contributors to the field, and interesting facts related to this concept.

Observed frequency of light at infinity (ν_{0}) = |
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ν_{0} = ν √1 - r_{s}/rν _{0} = √1 - /ν _{0} = √1 - ν _{0} = √ν _{0} = × ν _{0} = |

Calculator Input Values |

Frequency of light at the black hole's event horizon (ν) = |

Schwarzschild radius (r_{s}) = |

Distance from the center of the black hole (r) = |

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The gravitational redshift of a light beam from a black hole can be described using the formula derived from the Schwarzschild metric, which is a solution to the equations of general relativity. It relates the observed frequency of light at infinity (ν_{0}) to the frequency of light at the black hole's event horizon (ν), the Schwarzschild radius (r_{s}), and the distance from the center of the black hole (r). The formula is as follows:

ν_{0} = ν √(1 - r_{s}/r)

Where:

**ν**: The observed frequency of light at infinity (ν_{0}_{0}) represents the frequency of light as observed by an observer located far away from the gravitational influence of the black hole.**ν**: The frequency of light at the black hole's event horizon (ν) is the frequency of light emitted by a source near the black hole.**r**: The Schwarzschild radius (r_{s}_{s}) is directly proportional to the mass of the black hole. It represents the distance from the center of the black hole where the event horizon is located, beyond which no light can escape.**r**: The distance from the center of the black hole (r) is the radial distance at which the light is observed.

By using this formula, we can calculate the gravitational redshift experienced by light as it escapes the gravitational pull of a black hole.

Let's consider a black hole with a mass of 10^{10} kilograms and a Schwarzschild radius (r_{s}) of 10^{3} meters. If an observer is located at a distance (r) of 10^{4} meters from the center of the black hole and observes light with a frequency (ν) of 10^{15} Hz near the event horizon, we can calculate the observed frequency at infinity (ν_{0}).

ν_{0} = ν √(1 - r_{s}/r)

ν_{0} = (10^{15} Hz) √(1 - 10^{3} m / 10^{4} m)

ν

ν_{0} = (10^{15} Hz) √(1 - 0.1)

ν_{0} = (10^{15} Hz) √(0.9)

ν_{0} ≈ 9.49 × 10^{14} Hz

ν

ν

Therefore, the observed frequency of the light at infinity is approximately 9.49 × 10^{14} Hz.

This calculation demonstrates how the formula allows us to determine the frequency of light as observed by an observer located far away from a black hole, taking into account the gravitational redshift caused by the black hole's immense gravitational pull.

The principle of gravitational redshift was first predicted by Albert Einstein in his general theory of relativity published in 1915. The Schwarzschild metric, which is used to describe the gravitational field outside a spherical mass and used in deriving the formula for gravitational redshift, was provided by Karl Schwarzschild in 1916.

Though black holes are not encountered in our everyday lives, understanding the gravitational redshift has real-life applications in GPS technology. The clocks in GPS satellites are corrected for the effects of gravitational redshift to ensure precise location tracking.

Albert Einstein is the key figure in this field, with his general theory of relativity laying the groundwork for understanding gravitational redshift. Additionally, Karl Schwarzschild contributed significantly to the study of black holes and the effects of gravity on light.

- Gravitational redshift confirmed one of the key predictions of Einstein's theory of general relativity and solidified its acceptance in the scientific community.
- Observations of stars orbiting the black hole at the center of our galaxy provide one of the best experimental tests of general relativity.
- The study of gravitational redshift has played a key role in the development of modern GPS technology.

The concept of Black Hole Gravitational Redshift offers profound insights into the workings of our universe, particularly the behavior of light under extreme gravitational fields. Understanding and applying this knowledge has allowed us to refine technologies, confirm scientific theories, and expand our comprehension of the universe.

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