Testing the first law of black hole mechanics with GW150914

Whether the first law of black hole mechanics is correct is an important question in black holes physics. Subjected to current limited gravitational wave events, we propose its weaker version that permits a relatively large perturbation to a black hole system and implement a simple test with the first event GW150914. Confronting the strain data with the theory, we obtain the constraint on the deviation parameter $\alpha =0.07\pm 0.11$, which indicates that this weaker version is valid at the 68% confidence level. This result implies that the first law of black hole mechanics may be correct.