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Black Hole Surface Gravity Formula:
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Black hole surface gravity (κ) is a measure of the gravitational acceleration at the event horizon of a black hole. It represents the force that would be experienced by an object at the black hole's boundary, and is a key parameter in black hole thermodynamics.
The calculator uses the surface gravity formula:
Where:
Explanation: This formula derives from general relativity and describes the surface gravity at the event horizon of a Schwarzschild black hole.
Details: Surface gravity is fundamental to understanding black hole thermodynamics, particularly Hawking radiation. It relates directly to the black hole's temperature and plays a crucial role in studying black hole evaporation.
Tips: Enter the black hole mass in kilograms. The speed of light and gravitational constant are pre-filled with standard values but can be adjusted if needed. All values must be positive.
Q1: Why is surface gravity important for black holes?
A: Surface gravity determines the Hawking temperature of a black hole and is directly related to its thermodynamic properties, including entropy and radiation.
Q2: How does surface gravity relate to black hole size?
A: Interestingly, larger black holes have weaker surface gravity at their event horizons, while smaller black holes have stronger surface gravity.
Q3: Can we measure black hole surface gravity directly?
A: Direct measurement is not currently possible, but it can be calculated theoretically from a black hole's mass using this formula.
Q4: Does this formula work for all types of black holes?
A: This specific formula applies to non-rotating (Schwarzschild) black holes. Rotating (Kerr) black holes have a more complex surface gravity calculation.
Q5: What are typical values for black hole surface gravity?
A: Values vary dramatically with mass. A solar mass black hole has surface gravity around 1.5 × 10¹³ m/s², while supermassive black holes have much smaller values.