More on gravitational memory

Two novel results for the gravitational memory effect are presented in this paper. We first extend the formula for the memory effect to solutions with arbitrary two surface boundary topology. The memory effect for the Robinson-Trautman solution is obtained in its standard form. Then we propose a new observational effect for the spin memory. It is a time delay of time-like free falling observers.Comment: v3: presentation improved, discussion extended, typos corrected, refs. added v4: typos correcte

Critical phenomena in gravitational collapse of Husain-Martinez-Nunez scalar field

We construct analytical models to study the critical phenomena in gravitational collapse of the Husain-Martinez-Nunez massless scalar field. We first use the cut-and-paste technique to match the conformally flat solution ($c=0$ ) onto an outgoing Vaidya solution. To guarantee the continuity of the metric and the extrinsic curvature, we prove that the two solutions must be joined at a null hypersurface and the metric function in Vaidya spacetime must satisfy some constraints. We find that the mass of the black hole in the resulting spacetime takes the form $M\propto (p-p^*)^\gamma$, where the critical exponent $\gamma$ is equal to $0.5$. For the case $c\neq 0$, we show that the scalar field must be joined onto two pieces of Vaidya spacetimes to avoid a naked singularity. We also derive the power-law mass formula with $\gamma=0.5$. Compared with previous analytical models constructed from a different scalar field with continuous self-similarity, we obtain the same value of $\gamma$. However, we show that the solution with $c\neq 0$ is not self-similar. Therefore, we provide a rare example that a scalar field without self-similarity also possesses the features of critical collapse.Comment: 14 pages, 6 figure

New electromagnetic memories and soft photon theorems

In this paper, we present a new type of electromagnetic memory. It is a `magnetic' type, or B mode, radiation memory effect. Rather than a residual velocity, we find a position displacement of a charged particle induced by the B mode radiation with memory. We find two types of electromagnetic displacement (ordinary and null). We also show that the null electromagnetic memory formulas are nothing but a Fourier transformation of soft photon theorems.Comment: v2: interpretation improved and typos fixed, refs adde

Black Hole Mass Formula Is a Vanishing Noether Charge

The Noether current and its variation relation with respect to diffeomorphism invariance of gravitational theories have been derived from the horizontal variation and vertical-horizontal bi-variation of the Lagrangian, respectively. For Einstein's GR in the stationary, axisymmetric black holes, the mass formula in vacuum can be derived from this Noether current although it definitely vanishes. This indicates that the mass formula of black holes is a vanishing Noether charge in this case. The first law of black hole thermodynamics can also be derived from the variation relation of this vanishing Noether current.Comment: 7 page