I Hawking After 54 Years Confirmed: BH surfaces don't shrink

[fresh_42]

TL;DR Summary

GW250114: Testing Hawking’s Area Law and the Kerr Nature of Black Holes

Abstract​

The gravitational-wave signal GW250114 was observed by the two LIGO detectors with a network matched-filter signal-to-noise ratio of 80. The signal was emitted by the coalescence of two black holes with near-equal masses $m_1=33.6_{-0.8}^{+1.2} M_{⊙}$ and $m_2=32.2_{-1. 3}^{+0.8} M_{⊙}$, and small spins $\chi_{1,2}\leq 0.26$ (90% credibility) and negligible eccentricity $e⁢\leq 0.03.$ Postmerger data excluding the peak region are consistent with the dominant quadrupolar (ℓ=|𝑚|=2) mode of a Kerr black hole and its first overtone. We constrain the modes’ frequencies to ±30% of the Kerr spectrum, providing a test of the remnant’s Kerr nature. We also examine Hawking’s area law, also known as the second law of black hole mechanics, which states that the total area of the black hole event horizons cannot decrease with time. A range of analyses that exclude up to five of the strongest merger cycles confirm that the remnant area is larger than the sum of the initial areas to high credibility.

Source: https://journals.aps.org/prl/abstract/10.1103/kw5g-d732

 

[PeterDonis]

Hawking’s area law, also known as the second law of black hole mechanics, which states that the total area of the black hole event horizons cannot decrease with time.

Note that this law only holds if energy conditions on the matter are satisfied. In the case of black hole mergers being observed by LIGO, they will be; but that's not the same as saying they always will be. This paper does not give evidence that black hole evaporation can't happen. It just shows that, as we already expected anyway, if black hole evaporation does happen, it happens on time scales many orders of magnitude longer than the time scale for black hole mergers.

 

[Filip Larsen]

I am trying to understand the meaning of Hawking's area law in simple terms and why it needs to be a law and not just a "natural" consequence.

If the area of a black hole is the geometric area of the event horizon, i.e. $A = 4\pi r^2$, and the radius of the event horizon is proportional to the enclosed mass, e.g. $r = 2Gm/c^2$, then we have BH area proportional to the square of the mass, $A = km^2$ with $k = \left( {4\sqrt{\pi}G} / {c^2} \right)^2$. If two such (simple) black holes merge their mass adds up, so I would expect the area of the combined BH to be $A_{12} = k(m_1 + m_2)^2 = k(m_1^2 + m_2^2) + 2k m_1 m_2$ which is clearly always bigger than the sum of the area of the two original BH with value $A_{1+2} = k(m_1^2+m_2^2)$, that is $A_{12} = A_{1+2} + 2k m_1 m_2$.

To the extend that the above simplifications holds, at least for the simple BH solutions, my question would now be if there is a simple explanation as to why Hawkin's area law need to be a law and not just seen as a "natural consequence"?

Skimming the paper linked in #1 (and reading the piece Arstechnica had on it) I understand the experimental confirmation is based on "matching" simulations of the merger with observations and thereby establish a credible model for the pre- and post-merge BH's allowing to "measure" the BH properties by simply extracting this from the model. If so, I guess my question above could also be formulated as:

Do such models used for simulations of BH merger's (A) have a "free parameter" that in one range would allow mergers where Hawkin's area law hold and another range where it does not, and the present experimental observations then "matched" this parameter to be in the "hold range"? Or is it more like (B) that all merger simulations always result in Hawking's area law being valid (as a result of the underlying dynamics) and the present experimental observations then "just" confirmed that the model can be matched observation in general?

It is not my understanding that (A) is the case but if this means (B) then again I am (again) puzzled as to why Hawkin's area law needs to be a law in the first place.

 

[Filip Larsen]

a simple explanation as to why Hawkin's area law need to be a law and not just seen as a "natural consequence"?

Reading the paper more slowly (after discovering that most of it is surprisingly readable even for people only vaguely aware of BH terms and theory) it does seems the authors did provide a nice explanation of what could theoretically break the area law:

The area law relies on three conditions. The first is the null-energy condition, a restriction on the properties of matter. It is violated, for example, by Hawking radiation which extracts energy from a black hole and causes its horizon to shrink —in this case, the area law is superseded by a generalized law that considers both the entropy of the black hole and that of the radiation . The second is the premise that the observed objects are black holes and weak cosmic censorship holds, i.e., no naked singularities. Alternative compact objects have modified entropy and violate the null-energy condition; their interactions could violate the area law. The third is general relativity; the area law can be violated in alternative theories . Testing the area law thus amounts to testing for physical behavior that violates at least one of these conditions.

So, I guess it is fair to say that the area law was historically speaking a law, but is now more seen as a theoretical consistent consequence under the stated assumptions?