On Gravitational Shock Waves in Curved Spacetimes

TL;DR

This paper extends the theory of gravitational shock waves to include matter fields and cosmological constants, providing explicit examples in various black hole and cosmological spacetimes, including string-inspired solutions.

Contribution

It generalizes previous work by Dray and 't Hooft to more complex spacetimes with matter and cosmological constant, offering explicit solutions and examples.

Findings

Derived conditions for shock waves in matter-filled spacetimes

Provided explicit examples in black hole and cosmological backgrounds

Extended analysis to string-inspired gravitational solutions

Abstract

Some years ago Dray and 't Hooft found the necessary and sufficient conditions to introduce a gravitational shock wave in a particular class of vacuum solutions to Einstein's equations. We extend this work to cover cases where non-vanishing matter fields and cosmological constant are present. The sources of gravitational waves are massless particles moving along a null surface such as a horizon in the case of black holes. After we discuss the general case we give many explicit examples. Among them are the $d$-dimensional charged black hole (that includes the 4-dimensional Reissner-Nordstr\"om and the $d$-dimensional Schwarzschild solution as subcases), the 4-dimensional De-Sitter and Anti-De-Sitter spaces (and the Schwarzschild-De-Sitter black hole), the 3-dimensional Anti-De-Sitter black hole, as well as backgrounds with a covariantly constant null Killing vector. We also address the analogous problem for string inspired gravitational solutions and give a few examples.