• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,075 questions , 2,226 unanswered
5,348 answers , 22,757 comments
1,470 users with positive rep
818 active unimported users
More ...

  Has the time-space curvature a complex form ; due to the complex form of time-space ?

+ 0 like - 0 dislike

It is necessary for time-space curvature to be considered :

1-Rellationship between time factor and space factor .

2-Existence of complex material (mass) to make complex curvature (due to complex form of space-time).

Why haven't considered ?

asked Apr 13, 2018 in Theoretical Physics by seyedmohammad mohammadi [ revision history ]
recategorized Nov 26, 2020 by Dilaton

If your spacetime manifold admits a complex structure, then you can use complex coordinates to express curvature forms. You can find it from the book "Geometry, Topology and Physics" by Nakahara.

3 Answers

+ 1 like - 0 dislike

The notion of complex curvature does exist: see https://hal.archives-ouvertes.fr/hal-02948386/

For instance, a complex circle with (complex) radius R has a (complex) radius of curvature equal to R (see page 17).

The author says the paper is to appear in the Journal of Symplectic Geometry.

answered Nov 26, 2020 by Clement (10 points) [ no revision ]
+ 0 like - 0 dislike

You are taking space time curvature way to literally. Think of it as as mass increases in a confined space -> harder for any single unit of such mass in that space to move -> unit of mass therefore must move slower because no room to move -> therefore it appears that time is slowing down for such mass (this is called both gravity and gravitational time dilation - one and the same thing). When things move in space time they are impacted by various differences in levels of mass in the "mass in a confined space" so things in space time slow and go faster accordingly - > this gives appearance of curves in space time.

answered Feb 11, 2019 by anonymous [ no revision ]
+ 0 like - 0 dislike

As I said before, the notion of complex curvature does exist.

One could imagine that there exists a complex metric such that the operator annihilation verifies Dirac or Klein Gordon equations associated with this metric while the operator creation would verify these same equations but for the conjugate metric.

share cite improve this answerfollow

answered Dec 20, 2020 by Clement (10 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights