Introduction to the mathematics of general relativity

<p>The mathematics of general relativity is complicated. In <a href="/facts/Isaac_Newton/4L7gTncN">Newton</a>'s theories of motion, an object's length and the rate at which time passes remain constant while the object <a href="/facts/Acceleration/UVDmjYvR">accelerates</a>, meaning that many problems in <a href="/facts/Classical_mechanics/ykG8upsN">Newtonian mechanics</a> may be solved by <a href="/facts/Algebra/nMdqczjo">algebra</a> alone. In <a href="/facts/Theory_of_relativity/qGHj3eTC">relativity</a>, however, an object's length and the rate at which time passes both change appreciably as the object's speed approaches the <a href="/facts/Speed_of_light/sKSQwdNx">speed of light</a>, meaning that more variables and more complicated mathematics are required to calculate the object's motion. As a result, relativity requires the use of concepts such as <a href="/facts/Vector_space/M1pxMLx2">vectors</a>, <a href="/facts/Tensor/pNjFo5tV">tensors</a>, <a href="/facts/Pseudotensor/CEW7VNgr">pseudotensors</a> and <a href="/facts/Curvilinear_coordinates/RQD7Cajd">curvilinear coordinates</a>.
</p><p>For an introduction based on the example of particles following <a href="/facts/Circular_orbit/sSFMzmBv">circular orbits</a> about a large mass, nonrelativistic and relativistic treatments are given in, respectively, <a href="/facts/Newtonian_motivations_for_general_relativity/7EFklYz4">Newtonian motivations for general relativity</a> and <a href="/facts/Theoretical_motivation_for_general_relativity/9HhShW4w">Theoretical motivation for general relativity</a>.
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Introduction to the mathematics of general relativity open-in-new

Introduction to the mathematics of general relativity