wormholes can not be taken seriously without having a quantum gravity.

Piyali Bhar I agree with Hinnerk Albert that wormholes cannot be taken seriously but for different reasons. Popular descriptions of black holes suggest that there is a singularity at the centre of the black hole. This is not a necessary requirement from a mathematical or a physical point of view.

It is a much better conclusion that a black hole forms when there is a sufficient density of matter that an event horizon forms outside the surface of the massive object. Using the Schwarzschild radius formula it is easy to show that a neutron star of greater than 3.4 solar masses will have an event horizon outside the surface of the star.

This hypothesis is supported by the fact that all black holes are all greater than 3.4 solar masses and all observed neutron stars are smaller than 3.4 solar masses. Given that the idea of a singularity at the centre of a black hole is false, this also rules out the possibility of a worm hole. However, wormholes are a very entertaining piece of science fiction.

Data Black Holes

Richard

Richard Lewis i am absolutely convinced, that the singularity of a black hole, or better, that the mass of a star forming a black hole.by crushing to a point and hence giving an infinite density, signals the end of validity of general relativity at the Planck length

Hinnerk Albert Many people do think that black holes contain a singularity and that has been the accepted scientific view for many years. Unfortunately we can't look inside a black hole to find out. The idea of a star collapsing to a black hole is plausible for the smaller black holes of less than say 100 solar masses but this idea does not work for the supermassive black holes at the centre of a galaxy.

I would prefer to avoid singularities if at all possible as these are places where the laws of physics break down. As you mentioned it would mean the end of the validity of the Einstein equations of general relativity at the very small scale.

I would prefer to stay with the validity of GR everywhere and go with the more natural explanation for black holes which is that they contain a dense massive object.

Richard

Thank you Richard Lewis Hinnerk Albert for your valuable comments

Richard Lewis but there is nothing, at least in gr, that prevents massive stars to crush to a point, i.e., infinite density, and that means end of validity of gr.

Einstein spoke of the need to rid the theory of singularities. I completely agree with him. This is the mathematically meaningless part of solving the Einstein equation.

Preprint Einstein's Last Will

By the way, Einstein urged not to get carried away with modifications of the theory.

Valery Borisovich Morozov that's it.

Singularities are a defect in the Einstein equation. It doesn't work for large fields.

The defect can be eliminated only by replacing the gravitational field equation with a new one

Preprint Exact equation of gravity field based on Einstein's separati...

Valery Borisovich Morozov that's it.

Now there are no singularities in the universe

In 1915, Einstein divided the left side of his gravity field equation (the Ricci tensor) into two tensors, one of which turned into zero at a certain choice of coordinates. The feature of this part of the Ricci tensor suggests that this equation part is related to the gravity field because it is known that only a gravity field metric can be reduced to zero by a coordinates transformation. This allows to introduce the energy-momentum tensor of the gravity field into the Einstein equation. The new equation is asymptotically equivalent to the Einstein equation at low energy of the gravity field. In addition, the local law of conservation of momentum energy follows directly from this equation. The covariance of this equation is proved. The computational solution of the equation is given for ݃଴଴. This solution can change our understanding of behavior of gravitational fields near their sources. In contrast to the Schwarzschild solution here, ݃଴଴ does not change the sign, which would make it meaningless; instead, when it reaches an extreme zero value, it grows rapidly. This feature is seen on a sphere with a radius slightly larger than the Schwarzschild radius.

Preprint Exact equation of gravity field based on Einstein's separati...