## Relativity in Combinatorial Gravitational Fields

**Authors:** Linfan Mao

A combinatorial spacetime (CGj t) is a smoothly combinatorial manifold C underlying a
graph G evolving on a time vector t. As we known, Einstein's general relativity is suitable
for use only in one spacetime. What is its disguise in a combinatorial spacetime?
Applying combinatorial Riemannian geometry enables us to present a combinatorial
spacetime model for the Universe and suggest a generalized Einstein's gravitational
equation in such model. For finding its solutions, a generalized relativity principle,
called projective principle is proposed, i.e., a physics law in a combinatorial spacetime
is invariant under a projection on its a subspace and then a spherically symmetric multisolutions
of generalized Einstein's gravitational equations in vacuum or charged body
are found. We also consider the geometrical structure in such solutions with physical
formations, and conclude that an ultimate theory for the Universe maybe established
if all such spacetimes in R3. Otherwise, our theory is only an approximate theory and
endless forever.

**Comments:** 12 pages

**Download:** **PDF**

### Submission history

[v1] 20 Mar 2010

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