Areax

Two black holes merge into Areax, and her horizon-crown is bigger than both of theirs put together. It always is.

The Physics

In classical general relativity the total event-horizon area of black holes can never decrease. So when two black holes merge, the final horizon must be larger than the two original horizons combined, even though energy is radiated away as gravitational waves. For a spinning (Kerr) black hole the area depends on its mass and spin.

A_final ≥ A₁ + A₂, Kerr: A = 8π (GM/c²)² (1 + √(1 − χ²))

• A: horizon area (m²)
• G: gravitational constant (m³ kg⁻¹ s⁻²)
• M: black-hole mass (kg)
• c: speed of light (m/s)
• χ: dimensionless spin, 0 to 1

Stephen Hawking proved the theorem in 1971; the gravitational-wave event GW250114 (2025) found the final area larger than the initial area at 4.4σ in the collaboration's reference analysis (LIGO–Virgo–KAGRA, Phys. Rev. Lett. 135, 111403), a far stronger test than GW150914 (Isi et al. 2021).

Honest caveat: It is a classical result: Hawking radiation lets black holes shrink, very slowly.

On the shirt

Front: Areax, the pixel-art character, with the title. Back: both area equations, the GW150914 and GW250114 tests, the classical-only caveat and three sources. Printed on a unisex tee.