Mass is negligible inside an atom and hence so must conventional gravity. This is why spacetime curvature is normally ignored. Is spacetime confirmed to be flat inside the atom?
Following articles show that the spacetime is flat inside atom.
Periodic relativity: the theory of gravity in flat space time
https://arxiv.org/abs/0707.4539v11
Hydrogen spectra using Einstein's field equations
Ch. 4 in the book
"The wave equation: An overview"
https://novapublishers.com/shop/the-wave-equation-an-overview/
https://www.researchgate.net/publication/338621783_Hydrogen_Spectra_Using_Einstein%27s_Field_Equations
It depends at what scale inside the atom you mean : space time becomes an ever-shifting quantum foam at very small scales. If you are looking at the scale of a few picometers, space time is still flat , but if you approach the Planck scale, then spacetime becomes something else entirely.
We don’t know for sure what’s inside an atom, possibly not even if we are allowed to speak of inside and outside from a possible (3D, 4D, 6D, 7D, 10D) dimensional point of view. For example iSpace-theory (able to derive constants of nature from integer geometric first principles) predicts or requires an integer Calaby-Yau style 10D spacetime 3D+6D+1D discretized (!) time for it’s model, so from such model your answer would be an atom (it’s 7D subspace-time it is embedded in, to be precise) would be perfectly flat from an inside point of view - think LEGO - yet infinite as being a closed subspace) while 4D relativistic spacetime such 6D integer Calaby-Yau closed subspaces would be relativistic bendable from a continuum point of view, embedding or consisting of such subspaces to the standard rules of Relativity. Maybe the question needs to be a bit precised with respect to such model(s), which you had likely not on mind when stating it?
I am not sure that I understand the question. If a wandering black hole passes through the atom (yes, it can, if it is sufficiently small), then the spacetime inside the atom cannot be flat while it is passing. Of course, the passing can rip the atom apart, but not necessarily. Naturally, very tiny black holes can spontaneously arise at the Planck scale, but they may not be significant.
Dear Shantikumar Nair ,
The question is not well asked... because if we consider our dimention time... we will have touble. in the event that we project the question on our dimensions, considrer the Sun as the biggest 'atom' of our sollar system you can imagine your answer onto the present analogy...
Regards,
Laszlo
Shantikumar Nair Sir,
As you are aware that curvature of spacetime continuum is a mathematical construct, and certainly will not have any physical significance in our 3-D space, the way you are imagining. Its effect in 3-D space, if visible, is likely to be in entirely different form rather than as curvature of 3-D space.
Coming back to the question: "Can spacetime be curved significantly inside an atom?"
Even if I answer it in the affirmative, which I imagine is the correct answer, the challenge(s) in front of you would be
1. What do you understand/mean by the word 'significantly' in the question?
2. How would you measure this 'curve' obviously in 4-D space?
3. In the explanation of this mathematical distortion the words 'massive objects' has often been used. Would you consider an atom 'a massive object' in the same sense also needs to be decided.
Regards
Space-time inside an atom is inhomogeneous (due to the concentration of matter in the nucleus and the electron) and anisotropic (due to the space rotation). According to the basics of General Relativity, these factors produce some curvature in the internal space-time of the atom.
For example, the lifetime of the atom of orthopositronium and parapositronium (the time duration before they annihilate) is different.
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