# Gravitational force in different dimensions

• pavi_elex
In summary, Gravitational force differs in different dimensions. In 2+1 dimensions, gravitational force is equal to the mass of the object multiplied by the distance between the two objects. In 3+1 dimensions, gravitational force is equal to the mass of the object multiplied by the distance between the two objects and the cosine of the angle between the two objects' vectors. In 4+1 dimensions, gravitational force is equal to the mass of the object multiplied by the distance between the two objects and the cosine of the angle between the two objects' vectors and the cosine of the angle between the object's vector and the event horizon's direction.
pavi_elex
How Gravitational force differs in different dimensions.
what it would be for four dimensions, two dimensions and one dimension.
Give me the formula of Gravitational force in n dimension space.
If it is described well (complete derivation) in other web site, send me the link.

Look at chapter 3 (including exercises and problems) from A First Course in String Theory by Barton Zwiebach.

(2+1)D:
http://arxiv.org/abs/gr-qc/9503024
Lectures in (2+1)-Dimensional Gravity
Steven Carlip
"Work on (2+1)-dimensional gravity dates back at least to 1963 [1], and occasional articles appeared over the next twenty years [2, 3, 4]. But credit for the recent growth of interest should probably go to two groups: Deser, Jackiw, and ’t Hooft [5,6,7], who examined the classical and quantum dynamics of point sources, and Witten [8, 9, 10], who rediscovered and explored the representation of (2+1)-dimensional gravity as a Chern-Simons theory.*
*The Chern-Simons representation was first pointed out, I believe, by Achucarro and Townsend."

(2+1)D versus (3+1)D:
http://arxiv.org/abs/gr-qc/9905087
An Introduction to Spin Foam Models of Quantum Gravity and BF Theory
John C. Baez
"In particular, general relativity in 3 dimensions is a special case of BF theory, while general relativity in 4 dimensions can be viewed as a BF theory with extra constraints. ... unlike BF theory, general relativity in 4 dimensions has local degrees of freedom."

(3+1)D versus (4+1)D:
http://arxiv.org/abs/hep-th/0608012
Black Rings
Roberto Emparan, Harvey S. Reall
"A black ring is a five-dimensional black hole with an event horizon of topology S1 x S2. We provide an introduction to the description of black rings in general relativity and string theory. Novel aspects of the presentation include a new approach to constructing black ring coordinates and a critical review of black ring microscopics. "

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For space dimension D=3, 4, ... it's U(r) ~ 1/rD-2;

Basically this can be understood via solving a Poisson equation for the D-dim. laplacian. Doing this in momentum space one finds a Greens function ~ 1/k². The potential U(r) is the Fourier transform of this Greens function which is ~ 1/rD-2, therefore the force is div U(r) ~ 1/rD-1.

This calculation is exact in D-dim. Maxwell theory, but only approx. valid in ART as one has to use the Newtonian limit in order to arrive at the Poisson equation.

## 1. What is meant by "gravitational force in different dimensions"?

Gravitational force in different dimensions refers to the concept of how gravity behaves in spaces with more or less than the three dimensions we experience in our everyday lives. This can include theories about higher dimensions beyond our three-dimensional world or the effects of gravity on objects in lower-dimensional spaces.

## 2. How does gravity behave in higher dimensions?

In theories about higher dimensions, gravity is often described as a curvature of space-time caused by the presence of mass. In these theories, gravity can be thought of as a force that pulls objects towards each other in a higher-dimensional space.

## 3. Can gravity exist in lower dimensions?

In lower-dimensional spaces, such as a two-dimensional plane, the concept of gravity becomes more complex. While some theories suggest that gravity may exist in lower dimensions, it may behave differently than in our three-dimensional world. For example, in a two-dimensional space, the force of gravity may be inversely proportional to the distance squared, rather than the distance cubed as in our three-dimensional world.

## 4. How does the strength of gravity change in different dimensions?

The strength of gravity is determined by the amount of mass present and the distance between objects. In higher dimensions, the strength of gravity may be affected by the number of dimensions present, as well as the curvature of space-time. In lower dimensions, the strength of gravity may also be influenced by the structure of the space itself.

## 5. What are the implications of understanding gravity in different dimensions?

Understanding how gravity behaves in different dimensions can have significant implications for our understanding of the universe and the laws of physics. It can also potentially lead to new technologies and advancements in fields such as space travel and astronomy. Additionally, studying gravity in different dimensions can help scientists develop a more complete theory of gravity that can unify with other fundamental forces in the universe.

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