Gravitational wave memory: A new approach to study modified gravity

It is well known that two types of gravitational wave memory exist in general relativity (GR): the linear memory and the nonlinear, or Christodoulou, memory. These effects, especially the latter, depend on the specific form of the Einstein equation. It can then be speculated that, in modified theories of gravity, the memory can differ from the GR prediction and provides novel phenomena to study these theories. We support this speculation by considering scalar-tensor theories, for which we find two new types of memory: the T memory and the S memory, which contribute to the tensor and scalar components of a gravitational wave, respectively. Specifically, the former is caused by the burst of energy carried away by scalar radiation, while the latter is intimately related to the no scalar hair property of black holes in scalar-tensor gravity. We estimate the size of these two types of memory in gravitational collapses and formulate a detection strategy for the S memory, which can be singled out from tensor gravitational waves. We show that (i) the S memory exists even in spherical symmetry and is observable under current model constraints, and (ii) while the T memory is usually much weaker than the S memory, it can become comparable in the case of spontaneous scalarization.

Figure 1

The stationary interior and exterior scalar field profile of an $M=10M_{\odot }$ and $R=100M_{\odot }$ Newtonian star for different values of ${\beta }_0$.

Figure 2

Scales of T memory and S memory from gravitational collapse of an $M=10M_{\odot }$, $R=100M_{\odot }$, $\epsilon =0.1$, and $r=10\mathrm{kpc}$ Newtonian star.

Figure 3

The effective angular pattern function ${\mathcal{F}}_3(\widehat{\mathrm{\Omega }})$ for network H-L-V (upper panel) and ${\mathcal{F}}_4(\widehat{\mathrm{\Omega }})$ for network H-L-V-K (lower panel) as a function of $\widehat{\mathrm{\Omega }}$, the direction of the source. The $x$ axis is the longitude as observed on Earth and the $y$ axis the latitude.

Figure 4

Discoverable curves of S memory from a collapsing star with $M=10M_{\odot }$, $R=100M_{\odot }$, and $r=10\mathrm{kpc}$ for second generation detectors (red) and third generation detectors (green). The current constraints on the model parameters are from the Cassini Mission (grey), PSR $\mathrm{J}1738+0333$ (orange), and PSR $\mathrm{J}0348+0432$ (blue).