TIDAL FORCES NEAR BLACK HOLES IN A GRAVITATIONAL THEORY WITH LORENTZ SYMMETRY BREAKING

Abstract

It is generally accepted that the curvature of space-time is small near the event horizon of a large static black hole, and test particles can fall into it without being destroyed. However, in most cases, at a small distance from the event horizon, the curvature of the black hole can be so huge that the test particle will stretch and even collapse under the influence of tidal forces. Thus, any object that falls into black holes experiences huge tidal forces beyond the horizon. This is a result of the fact that the curvature is very large near black holes and almost zero near the horizon. When measurements are made in a static frame (which also becomes zero), the curvature components remain small. This means that all curvature invariants are small, and any perturbing corrections, such as charge, angular momentum, Ricci scalar, etc., can be neglected. However, in a freely falling frame (the reference frame of a distant asymptotic observer), the curvature components are very large. In our paper, we consider the influence of the perturbing parameter ℓ on the curvature invariants of black holes in the gravitational theory with Lorentz symmetry breaking. The results are compared with the Schwarzschild black hole solution, which can be obtained by substituting ℓ =0.