Graviton mass bounds in very special relativity from binary pulsar’s gravitational waves

Massive Gravitons in Very Special Relativity: Theory and Observations

“…are the Minkowski tensor 𝜂 𝜇𝜈 , the derivative 𝜕 𝜇 and the VSR peculiar operator 𝑁 𝜇 = 𝑛 𝜇 𝑛•𝜕 . The exact expression of the quadratic operator 𝑂 𝜇𝜈 𝛼𝛽 , included in [17,18], is lenghty and intricated. However, at the moment of fixing a suited gauge, the equations of motion (e.o.m) simply becomes…”

“…Many of these complications, however, get simplified when considering both the conservation equation for the EMT and its (quasi-)periodicity. All the needed details can be found in [18].…”

“…with 𝛿 ≡ 𝑚 𝑔 Ω , 𝑇 ⊙ ≡ 𝐺 𝑀 ⊙ /𝑐 3 = 4.925490947 𝜇𝑠 [22] and the "tilde"-masses defined as m ≡ 𝑚/𝑀 ⊙ , with 𝑀 ⊙ being the solar mass. The functions 𝑓 (𝑁, 𝑒, 𝛿, n) [18], in general, are cumbersome combinations of the Bessel functions 𝐽 𝑁 depending on the VSR mass and preferred direction n. We do not include here their expressions for reasons of space. However, an important property is that they recover the GR limit [23] when…”