This page is response to possible objections to the Closed Timelike Curves and the Big Bang Theory
https://www.theinventorspot.com/science/cosmology/closed-timelke-curves-and-the-big-bang
Objection: Don’t universal rest frames and the complications of Lorentz transformations cause problems for wormholes?
Only in the context of special relativity (SR), which is rooted in the concept of flat spacetime and inertial motion without gravity. Wormholes and black holes, however, exist in the realm of general relativity (GR), where spacetime is heavily curved by gravity. Black Hole studies generally handle this by coordinate transformations within the general relativistic framework, rather than addressing Lorentz transformations specifically.
1. Universal Rest Frames in SR vs. GR:
o A universal rest frame is a concept tied to SR and flat spacetime. It does not exist in GR, where spacetime is curved, and the equations are covariant. Covariance means the equations remain valid under any smooth coordinate transformation, emphasizing that there is no preferred coordinate system or rest frame in GR.
2. Lorentz Transformations:
o In GR, Lorentz transformations only apply locally, in small regions where spacetime is approximately flat (tangent space). For example:
§ Near a black hole, the curvature of spacetime becomes so extreme that global definitions of "rest" and straightforward applications of Lorentz transformations are impossible.
§ Metrics like Schwarzschild or Reissner–Nordström describe spacetime geometries where global inertial frames are meaningless due to curvature and event horizons.
Admittedly, this is a problem if the Universe were as speculated in the infinitely large, all of space unfolded at once theories, This is because observers in different parts of such a universe would have different horizons that may not be compatible with each other.
I am suggesting that if we are in a black hole, or if our universe is indeed of the mass causing it to collapse into a black hole, and thus is curved enough to have the same properties, that everyone in our universe sees themselves as being at the center, and each point sees the same event horizon.
Objection: Our universe does not appear to be curved.
General relativity allows for the possibility of such large-scale spacetime curvature being imperceptible locally, much like Earth's curvature is undetectable to someone standing on its surface.
Theories suggesting that our universe might be inside a black hole often address the idea of scale by considering the properties of extremely large black holes. If a black hole were as large as the observable universe, the event horizon would be vast enough that the curvature of spacetime within it could appear almost flat to local observers, similar to how the large-scale structure of the universe appears flat to us. These theories explore the parallels between the cosmological horizon of the universe and the event horizon of a black hole, suggesting that the same general relativistic principles might govern both.