# Questions tagged [spacetime-dimensions]

Use this tag for dimensions of a manifold, typically the space-time. DO NOT USE THIS TAG for dimension of a physical quantity nor for the size of an object.

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### Multidimensional space and Newton's inverse square law deviation [duplicate]

Many times I have heard the physicist Michio Kaku saying that the deviation on Newton's inverse law could demonstrate the existence of multidimensional space, which could support one of the aspect of ...
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### Another dimensions [closed]

Just a science ponderer, and pretty much interested in physics. Please guide me if I am wrong. There have been many statements made by the physicists about the existence of other dimensions (...
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### Could black holes be a three dimensional object breaking through space time and falling 4th dimensionaly [closed]

I was thinking about general relativity and I was thinking about it in two dimensions where a heavy metal ball would be placed on a mesh fabric (this is just how I’m imagining it) and if the ball was ...
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### Thought experiment of 0 times infinity and dimensions [closed]

Take a cube at 1x1x1 and cut it in half. Take the 0.5x1x1 and cut it in half again. Eventually, you get an object that is 0x1x1. The object does not disappear. It instead now exists in the 2D world. ...
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### If the radius of a sphere is reduced by half due to relativistic length contraction, will the volume also be half?

We know that volume is cubicly proportional to radius of a sphere. But if the radius is become half due to relativistic Length contraction, it's being reduced from only one dimension, not three. And ...
1 vote
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### Are branes topological defects? How else could they be physical?

As far as I understand, the branes of brane cosmology are lower-dimensional "sub-manifolds" of some space. It was hard to imagine for me how such structure could exist and be physical. But ...
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### How many independent degrees of freedom does the metric tensor have in vacuum (at every point)?

A field of metric tensors fully characterises the curvature of a vacuum space-time. (For example, the spacetime between some single point masses which are themself not part of the manifold) The metric ...
1 vote
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### Writing a gravity equation

I need a maple cod to variation this action with respect to tensor metric $g_{\mu\nu}$. This called the Einstein equation. To obtain the Einstein equation, we vary the action with respect to the ...
1 vote
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### Could the universe be a topological defect in a higher space?

I am a mathematician with an undergrad understanding of physics. I recently learned of topological defects in quantum fields. It is an intriguing idea that there could be regions in our universe that, ...
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### Why is Spacetime described as flat even though we live in 3 dimensions of space?

I’ve always heard and seen diagrams that show spacetime as being “flat” or in 2 dimensions with curvature. How does this correspond to the 3 spacial dimensions that we perceive to exist in?
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### Can someone explain intuitively why "black rings" are possible in 4+1 dimensional gravity? [duplicate]

In 3+1 dimensional general relativity, all black holes must be topologically equivalent to a sphere. However in 4+1 dimensional gravity, this isn't the case, there Torus shaped black holes are ...
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### Does gravity exist in two spatial dimensions? [duplicate]

I've been studying anyons and was wondering if gravity exists in two spatial dimensions and how it affects these particles?
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### How does the lifetime and temperature of a black hole scale with mass in higher dimenstions?

I've tried to find out how the lifetime and temperature of a black hole scale with mass in a universe with more then 3 spatial dimensions. I've spent a while trying to look up an answer to this ...
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### The relationship between dimensionality and space [duplicate]

The number dimensions defined by new theories keep going up. Is there a limit as to how many dimensions the universe can have? Weird question. The curse of dimensionality in computer science ...
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### Trying to get a metric like $ds^2 = -e^{2H_0t} dt^2 + dx^2$ from a higher dimensional Minkowski spacetime

Since the 4D de Sitter spacetime can be found by slicing up a 5D Minkowski spacetime: de Sitter space from generalized Minkowski spacetime resulting in a metric like: $ds^2 = - dt^2 + e^{2H_0t} dx^2$ ...
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### Dimensionality of system vs dimensionality of space time

Suppose we work in GR, then space time is four dimensions, but, if we have a mechanical system with a high number of degree of freedoms, say five then how would we fit it into a four dimensional space ...
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### What is the definition of a dimension? [duplicate]

We live in a 3-dimensional world with time, but what even is a dimension? I've often heard that anything can be a dimension because the math works either way. If this was true then why is finding the ...
1 vote
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### Small and large extra dimension(s) of the physical space

Trying to make sense of small and large extra dimension(s) of phyiscal space in a simple intuitive example. Consider a two dimensional manifold like $\mathbb{R}^2$ and we are trying to add a small and ...
132 views

### What is the nonrelativistic limit of the Einstein field equations in arbitrary dimensions?

A standard exercise in essentially any introductory textbook on general relativity is to work out the non-relativistic limit of the 3+1D Einstein field equations. This is most commonly done in order ...
1 vote
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### Why must the stress-energy tensor be traceless in 2D classical general relativity?

It's easy to show that the Einstein tensor is always traceless in 1+1 spacetime dimensions; this is just a simple algebraic identity that follows directly from the definitions. The Einstein field ...
1 vote
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### How are poles and equators geometrically defined in a 3D matrix (curved space) that is a part of a 4D matrix (hyperspace)?

Our planet's surface is a curved 2D that has an infinite number of equators although we chose just one for vital geom. orientation purposes. Every of those equators has its 2 conjugate poles that can ...
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### Why don't the extra compact dimensions collapse on themselves?

Why are the extra compact dimensions stable and do not collapse? I know the anomaly cancellation is the reason why the extra dimensions are necessary. But I can not visulize how the anomaly ...
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### Would quantum gravity be renormalized if the number of spacetime dimensions decreased at small distances?

In the discussion below (bottom of page on link) if the number of dimensions of spacetime d was lower than 3 at small distances would a theory of quantum gravity be renormalizable? Is is possible that ...  I understand that gamma matrices can be real in $d = 8$ and with Euclidean signature, with minimal dimension $16\times16$. Does anybody know where I can find such a representation explicitly written?