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I have lagrangian like this:

(1)

And I am going to consider the equations of motion of the fields by varying the action related to this lagrangian with respect to and .

But I am still confused with these things:

From eq. (1) I can see that the Planck Mass is set to 1, but what does this mean?

What will happen if scalar potensial is zero,

What's the difference between scalar Ricci and

After getting the equations of motion of the fields, I have to solve them (Einstein equation and scalar fields), but I have no clue why I picked this lagrangian, does anyone can explain me why?

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# Lagrangian for black hole

Can you offer guidance or do you also need help?

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