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Bogdan Bancia. From special relativity to general relativity. Why space and time are curved in gravitational field?. Ad Astra, 2019.

Abstract: Let's consider the standard representation of relativity theory. We have two reference frames S(x,t) at rest and S'(x',t') moving with the speed v. This time we consider S' in accelerated motion (simulating the gravitational field), so we have dv.

We write the Lorent's transformation x=f(x',t',v) Equation(1) and rewrite this equation as x/t'=f(v) Equation(2) with x'=0 ( the point we study is in the origin of S', for simplicity).

When we differentiate both sides of Equation(2) we get dx/dt'=g(v)dv Equation(3), where g(v) is another function of v. If we represent g(v) we get a curve meaning that space is curved in gravitational field.

By replacing in Equation (3) dv=dx/dt and dv=dx'/dt' we get the following equations
dt/dt'=g(v) and dx/dx'=g(v) Equations (4), so both space and time are curved in gravitational field

Keywords: general relativity

Posted by Bogdan Bancia

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