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1

When two black holes collide and merge into one, a lot of energy is sent out as gravitational waves. This energy spreading out without bound represents an increase in entropy, along with any increase due to the final BH surface area being greater than the sum of the original two. If we had an exact solution to Einstein's field equation describing this, we ...

35

You missed something: the gravitational waves. A black hole merger spacetime contains gravitational waves leaving the merger at the speed of light. Time reversal reverses time across the entire spacetime, and this converts those escaping gravitational waves into a converging gravitational wave front, as well as the black holes into white holes. These waves ...

9

Yes, to the same extent as falling egg violates time reversal symmetry (have you seen a broken egg spontaneously jump from the floor to your cup?). This is called "second law of thermodynamics" and it is not time-symmetric.

0

OP got a point: Zee presumably only meant orthochronous Lorentz transformations when he claimed that the sign of $x^0$ [...] do not change. Nevertheless, eq. (I.3.23) in Zee's book is directly derived from the previous equation $$D(x-y)~=~\int_{\mathbb{R}^4}\! \frac{d^4k}{(2\pi)^4} \frac{e^{ik\cdot(x-y)}}{k^2-m^2+i\epsilon}, \tag{I.3.22}$$ which is ...

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Weinberg vol 1 Eqs (2.6.7) to (2.6.12) for $P$ and $T$.

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