# Difference in Gravitational Waveforms for different objects?

This is an extension of one of my older questions:

How would the gravitational strain waveform look like for a planet in orbit with a star?

Let's say at some distance D there are two objects which are in binary inspiral. Both lets assume mass $M_1$ and $M_2$. And both these masses are sufficiently large and far away. Let's take three cases of these objects:

1) Two black holes in binary inspiral which will merge in the end.

2) A planet orbiting a star.

3) Two stars inspiral with each other.

I wanted to know if the individual properties of these bodies cause the gravitational waves ie Numerical Relativity Waveforms to look significantly different from each other? Like for example, the ringdown phase does not exist for both cases 2 and 3 in a numerical relativity waveform.

I wanted to know if there are any other factors that would cause the overall waveform to be different for these three cases. Assuming $M_1$ and $M_2$ where $M_1$ > $M_2$ . If there are any, how would the waveform differ?

What I'm trying to infer here is, are numerical relativity waveforms an outcome of just the mass of an object or does the property of the object come into question as well?

## 1 Answer

I am no experrt in Numerical relativity but NR will give you answer based on the mass distribution you provide to it (specifically:stress-energy tensor). For the case of black-holes its not clear what to provide. Cosmic censorship says that the tensor just depends on masses and spins. Which may very well be not right.

Your question is speculative for 2) and 3) as these systems will not produce detectable gravitational waves however it will merge at a frequency far below LIGO's sensitivity level (if that is your interest).

But assuming that strength does not matter. The tidal deformability is the first thing to consider. The Earth-moon system knows very well about tidal deformability. Moon was much closer but went farther away due to tidal forces. Its rotation is synced with its revolution for the same reason. The stuff that maked up planet along with the its masses will determine tidal deformation (and also the mututal distance).

• What I mean is, assuming the mass is sufficient enough, how does the numerical relativity waveform differ for these cases? As in shape or amplitude wise. If there are any discrepancies what causes them? – Rahul Aedula Jan 22 '18 at 12:44