Is it possible to say we are inside a black hole?

Question

Why I am asking is because I read about it on the internet. But if that is true, does it imply the following?

If one is inside a black hole than he could be seen as trapped in a space-time observation point from which space in any direction would seem moving away from, or expanding. In fact, stars, galaxies and other stuff closer to the black hole center would be effectively moving away from the observation point, since there, at their location, space-time stretches at a higher rate; while stars galaxies and other stuff more far away than the observation point from the center of the black hole would instead only apparently move far away but it is really the observation point moving away from them.

Our universe, that really looks like an expanding universe, could be instead a contracting/stretching one.

Being inside a black hole would also provide an idea of why does the light travel at a speed which is the limit speed for anything else. This could be somehow related to the rate at which space-time is stretched (maybe light speed being equal to the actual rate at which space time stretches at our space-time state or position?). However this would imply that at another location, far away from the observation point the stretching rate would be different and therefore also the light speed. This would be generally true but only for an outside observer, which is in a different space-time state; this since the observer located at the far away position would experience a the same space-time state in which the light is moving and therefore measure the same light speed.

Also, if we are inside a black hole, do we anyway need to account for black matter to explain why the universe holds together? Could this be explained by the gravity (whatever it is) of the black hole itself?

Gravitational waves, couldn't this be described as vibrations of the giant black hole bubble containing us which reacts to internal explosions/implosions?

The big bang theory would change in a "big Implosion Theory" and inflation would not be needed to explain the rate of expansion of the initial formation of the universe but instead the otherwise inexplicable initial rate of expansion could be theorized by the presence a completely different space-time state at the beginning of the implosion where all space is concentrated in one point and is gradually stretching inward at what is a different light speed for us at the present space time state.

Another question that could find an answer if the theory is true is: "when did time begin?" Well, by defining time as the entity which describes a rate of change in state of any object, one needs at least another reference point to define a change. Therefore more than one single point, which is how a black hole starts: as a singular point. Lets suppose this points starts shrinking inward, so it becomes a black hole; that is when time starts. Before that, inside the single point, there is no reason to define time. One could say: "Well there must have been a time before that, before the formation of the black hole itself and also a time outside the black hole must exist"; and that would be true, but it is irrelevant for anything inside the black hole itself; for which time started together with the black hole shrinking.

One last thing, is the universe infinite? Based on this idea yes, since the black hole is shrinking (by which i mean stretching the space-time at its interior) faster than anything can escape it and it is pulling in stuff at the same time.

The theory of "being inside a black hole" seems to me quite appealing. I would really like to hear what you think about it. And please, understand I am an amateur, do not focus on the details of my questions; instead, if you want, give me your impressions on the big picture.

Thanks for reading!

Answer 1

There is a lot in this question, and some of this is not answerable or I don't think the writer of the question has some of the right concept of things. However, it is not entirely impossible that the universe is in some respect the physical product of a black hole. The Maldecena $\rm AdS/CFT$ correspondence might suggest that our universe is the result of a black hole in $10$ or $11$ dimensions.

To start let us look at the complementary relationship between black holes and $\rm AdS$ spacetime. The condition for an accelerated observer near the horizon is given by a constant radial distance. We then consider the Reissnor-Nordstrom metric $$ \mathrm ds^2~=~\left(1~-~\frac{2m}{r}~+~\frac{Q^2}{r^2}\right)~\mathrm dt^2~-~\left(1~-~\frac{2m}{r}~+~\frac{Q^2}{r^2}\right)^{-1}~-~r^2~\mathrm d\Omega^2 $$ as a simple form of this type of problem. The proper distance from the horizon is $$ \rho = \int ~\mathrm dr \sqrt{g_{rr}} = \int \frac{\mathrm dr}{\sqrt{1 - 2m/r + Q^2/r^2}} $$ with low and upper limits on integration $r_+$ and $r$. The result is $$\begin{align} \rho &= m~ \log\left[\sqrt{r^2 - 2mr + Q^2} + r - m\right] + \sqrt{r^2 - 2mr + Q^2}\\ & = m ~\log\left[\sqrt{r^2 - 2mr + Q^2} + r - m\right] + r \sqrt{g_{tt}} - \Lambda\,.\end{align} $$ Here $\Lambda$ is a large number evaluated within an infinitesimal distance from the horizon We write the metric at this position $$ \mathrm ds^2 = \left(1 - \frac{2m}{r(\rho)} + \frac{Q^2}{r(\rho)^2}\right)~\mathrm dt^2 - \mathrm d\rho^2 - r(\rho)^2~\mathrm d\Omega^2. $$ With the near horizon condition we may set $r^2 - 2mr + Q^2 \simeq 0$ in the log so that $$ \rho \simeq m~ \log(r - m) + r \sqrt{g_{tt}} – \Lambda. $$ The divergence of the log cancels the arbitrarily large $\Lambda$ $$ \rho/r_+ =~ \sqrt{g_{tt}}. $$ We now write the metric as $$ \mathrm ds^2 = \frac{\rho^2}{r_+^2}~\mathrm dt^2 - \mathrm d\rho^2 - m^2~\mathrm d\Omega^2 $$ We may now observe that $\mathrm d\rho^2 = \mathrm dr^2/g_{tt}^2$ and substitute in $\rho/m$ for $g_{tt}$ for $r_+ = m$ and obtain $$ \mathrm ds^2 = \left(\frac{\rho}{m}\right)^2~\mathrm dt^2 - \left(\frac{m}{\rho}\right)^2dr^2 - m^2~\mathrm d\Omega^2. $$ Or $$ \mathrm ds^2 = \left(\frac{\rho}{m}\right)^2~\mathrm dt^2 - \left(\frac{m}{\rho}\right)^2 ~\mathrm d\rho^2 - m^2~\mathrm d\Omega^2~~ {\rm for}~~ \rho \simeq r. $$ This is the metric for $\rm AdS_2$ in the $(t, r)$ variables and a sphere $S^2$ of constant radius $= m$ in the angular variables. The $\rm Ads_2$ spacetime has the form illustrated in this diagram:

This is considerably easier to see than the approach taken by Carroll and Randall, which employs the kerr metric and admittedly is a more exact derivation. The extremal condition on a black hole result in an anti-de Sitter spacetime. In $10$ dimensions this is $\rm AdS_5\times S^5$ in the $\rm AdS/CFT$ correspondence. This connects with the $\rm AdS$ black hole which reduces by a dimension and the $\rm CFT$ information in the anti-de Sitter spacetime is also on the horizon of the black hole. The BPS limit of an extremal black hole will then define the conformal or quantum field theory on the boundary.

From this perspective it is then possible in a way that our universe is inside or a result of a black hole. This anti-de Sitter spacetime is clearly not the spacetime of our universe, but it could serve as the inflationary spacetime that generates efolding regions of transient rapid inflation that our observable universe is an example of.