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The “surface” of a black hole is the radius at which the escape velocity equals the speed of light. This spherical surface is known as the event horizon. The radius of the event horizon is the Schwarzschild radius.

Nothing within the event horizon can escape the black hole. When an object is far away from a black hole, the gravity that it feels is no different from a star of a similar total “mass”. It is only when you get close that you could get “sucked in”.

The gravitational effects (tidal forces) of a black hole are unnoticeable outside of a few Schwarzschild radii .

Example 1

Calculate the event horizon of the supermassive black hole in the center of our Galaxy? The mass of the SMBH is 3 million masses of the Sun (that is 3x10⁶ M_sun ).

We are going to use the version of the Schwarzschild radius equation that is expressed in masses of the Sun (we will use this equation on the exam and the homework):

r_{sch}\ {\approx
}\ {\text{3 km}}({{\frac{M_{BH }}{m_{sun}})=}}\ {\text{3 km}}({\frac{3\ {\bullet}\ 10^6M_{sun}}{M_{sun}})}

r_{sch}=9\ {\bullet}\ 10^6 \ {\text{km}}

Notice that the Schwarzschild radius (or the event horizon) of the SMBH in the center of our Galaxy is significantly smaller than the Solar system (about 5 times smaller).

Example 2

Calculate the event horizon of a stellar-mass black hole with the mass of 3 M_sun .

r_{sch}\ {\approx
}\ {\text{3 km}}({{\frac{M_{BH }}{m_{sun}})=}}\ {\text{3 km}}({\frac{3M_{sun}}{M_{sun}})}

r_{sch}=9 {\text{km}}

Whoa, that is pretty close to the black hole!

Q: What is the difference between a black hole’s event horizon and its Schwarzschild radius? And its actual radius?

A: Schwarzschild radius is the radius at which the escape speed from the black hole equals the speed of light. Event horizon is the spherical surface (a black hole should be spherical just like the star from which it was formed) whose radius is the Schwarzschild radius. It is not a real surface in a sense that we can touch and feel it, but more of a zone within which nothing can escape the black hole.

The actual black hole must be much smaller than the Schwarzschild radius, but we do not know its true size. The black hole itself is usually called the singularity . So far, we thought of the size of the singularity to be close to zero. It is a spherical region at the center of the event horizon and its size is thought to be 10^-35 m (notice that this is significantly smaller than the size of a proton; proton size is ~10^-16 m). This is the place where the gravitational tidal field becomes infinity .

[The number given is Planck length – a set of constants in the universe where

(Planck length )² ={\hbar}cG/{c^3}

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