Question

What would the Penrose Diagram look like that represented a black hole (call it Black Hole-B), inside of a massive black hole (Black Hole-A), in our universe?

and, as inside of the Penrose diagram for BH-A (PD-1), would be attached to the upper diagonal edge of our universe's Penrose Diagram (PD-0), a) Would the Penrose diagram for BH-B (PD-2), lie along the upper diagonal edge of PD-1, (the Penrose Diagram for BH-A)?

and, since radial Space-Like direction lines? in PD-0 become Time-like in PD-1, and vice versa, would they then switch back in PD-2 and revert back to the way they were in our own universe?

Answer 1

A Penrose diagram of a black hole within another would be nested, with Black Hole-B's diagram inside that of Black Hole-A, attached to the universe's Penrose diagram. The interaction of space-like and time-like dimensions in such an arrangement is speculative and lacks empirical evidence.

Step-by-step explanation:

The question revolves around the complex concept of a Penrose diagram, which is a two-dimensional diagram capturing the causal relations between different points in spacetime. It specifically addresses the scenario of having one black hole inside another and how the Penrose diagram would represent such a system. This involves discussions of event horizons, singularity, spacetime curvature, and potentially the reversal of the characteristics of the space-like and time-like directions within nested black holes.

A Penrose diagram for Black Hole-B (within Black Hole-A) would be complex. If one were theoretically constructing such a diagram, PD-2 (for Black Hole-B), would indeed be nested within PD-1 (for Black Hole-A), which is in turn attached to the larger context of the universe's Penrose diagram (PD-0). The nature of space-like and time-like directions would depend on the precise metrics of the black holes and their relative arrangements.

Regarding space-time distortion, it is established that near a massive object like a black hole, space is stretched and time dilated. If a black hole were to exist within another black hole, this stretching and dilation would be more severe due to compounded gravitational fields. However, whether the space-like and time-like dimensions would revert in PD-2 as they were in PD-0 is speculative since there is no experimental evidence or detailed theoretical model for such a scenario.