Gravity in General Relativity and Earth's Surface

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Discussion Overview

The discussion revolves around the concept of gravity in the context of General Relativity (GR) and its relation to the acceleration experienced at the surface of the Earth, specifically questioning whether there is a value equivalent to 9.8 m/s² in GR.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires if there is a value in General Relativity that corresponds to 9.8 m/s² at Earth's surface.
  • Another participant asserts that the proper acceleration at the surface is indeed 9.8 m/s².
  • A further contribution discusses the acceleration of a stationary observer in a spherically symmetric vacuum according to GR, providing a formula that approximates Newton's value when certain conditions are met.

Areas of Agreement / Disagreement

Participants present differing perspectives on the interpretation of gravity in GR, with no consensus reached on the implications of the discussed values.

Contextual Notes

The discussion includes assumptions about the conditions under which the approximations hold, particularly the relationship between the mass and radius in the provided formula.

Jerry Friedman
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Is there something in General Relativity whose value is 9.8 m/s2 at the surface of the Earth?
 
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Yes. The proper acceleration of the surface.
 
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Jerry Friedman said:
Is there something in General Relativity whose value is 9.8 m/s2 at the surface of the Earth?

The acceleration of the stationary observer in the spherically symmetric vacuum according to GR is ##a=\frac{m}{r^2\sqrt{1-2m/r}}## (up to a sign).

If ##r>>m## this is very close to Newtons value.
 
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Thank you, Orodruin and Mentz114. I may be back with another question.
 

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