The authors found a shock-wave solution of the Einstein equation with nonvanishing cosmological constant. The solution is obtained by (anti-)de-Sitter boosting the Schwarzschild-(anti-)-de-Sitter metric. The solution can be regarded as an extension of the Aichelburg-Sexl geometry. It will be useful for calculation of graviton-exchange amplitudes.

In this paper, a protocol is proposed in which energy extraction from local vacuum states is possible by using quantum measurement information for the vacuum state of quantum fields. In the protocol, Alice, who stays at a spatial point, excites the ground state of the fields by a local measurement. Consequently, wavepackects generated by A' measurement propagate the vacuum to spatial infinity. Let us assume that Bob stays away from Alice and fails to catch the excitation energy when the wavepackets pass in front of him. Next Alice announces her local measurement result to Bob by classical communication. Bob performs a local unitary operation depending on the measurement result. In this process, positive energy is released from the fields to Bob's apparatus of the unitary operation. In the field systems, wavepackets are generated with negative energy around Bob's location. Soon afterwards, the negative -energy wavepackets begin to chase after the positive-energy wavepackets generated by Alice and form loosely bound states.

The real and imaginary parts of the relative complex permittivity (εr' and εr") were measured in the ranges of X-band frequencies (8.2 to 12.4 GHz) and between 1 and 10 GHz for graphite, carbon black and coal powders at room temperature so as to clarify the relation between the complex permittivities of carbonaceous materials and their characteristics, i.e., graphitization, porosity (i.e., specific surface area) and ash contained in coals. It is found that the complex permittivities increase with increasing crystallite size and specific surface area. It is also found that the dependency of the permittivities on the ash content seems be negligible within the range of the ash content in the present study.

It is argued that the diffeomorphism on the horizontal sphere can be regarded as a nontrivial asymptotic isometry of the Schwarzschild black hole. We propose a new boundary condition of asymptotic metrics near the horizon and show that the condition admits the local time-shift and diffeomorphism on the horizon as the asymptotic symmetry.

The partner mode with respect to a vacuum state for a given mode (like that corresponding to one of the thermal particles emitted by a black hole) is defined and calculated. The partner modes are explicitly calculated for a number of cases, in particular for the modes corresponding to a particle detector being excited by turn-on/turn-off transients, or with the thermal particles emitted by the accelerated mirror model for black hole evaporation. One of the key results is that the partner mode in general is just a vacuum fluctuation, and one can have the partner mode be located in a region where the state cannot be distinguished from the vacuum state by any series of local measurements, including the energy density. I.e., "information" (the correlations with the thermal emissions) need not be associated with any energy transport. The idea that black holes emit huge amounts of energy in their last stages because of all the information which must be emitted under the assumption of black-hole unitarity is found not necessarily to be the case.