Rindler horizons in the Schwarzschild spacetime

Abstract

We investigate the past and future Rindler horizons for radial Rindler trajectories in the Schwarzschild spacetime. We assume the Rindler trajectory to be linearly uniformly accelerated (LUA) throughout its motion, in the sense of the curved spacetime generalisation of the Letaw-Frenet equations. The analytical solution for the radial LUA trajectories along with its past and future intercepts $\mathcal{C}$ with the past null infinity ${\mathcal{J}}^{-}$ and future null infinity ${\mathcal{J}}^{+}$ are presented. The Rindler horizons, in the presence of the black hole, are found to depend on both the magnitude of acceleration $|a|$ and the asymptotic initial data $h$, unlike in the flat Rindler spacetime case wherein they are only a function of the global translational shift $h$. The horizon features are discussed. The Rindler quadrant structure provides an alternate perspective to interpret the acceleration bounds, $|a|\le |a{|}_b$ found earlier in arXiv:1901.04674.

arXiv commentv1. 20 pages, 6 figures; v2. 21 pages references added; v3. 24 pages, 9 figures, new section added, matches published version

References in corpus (9)

• Thermodynamical Aspects of Gravity: New insights
• Dark Energy and Gravity
• Entropy of Null Surfaces and Dynamics of Spacetime
• Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces
• Action principle for the Fluid-Gravity correspondence and emergent gravity
• Indistinguishability of thermal and quantum fluctuations
• Uniformly accelerated observer in a thermal bath
• Gravitational memory for uniformly accelerated observers
• Bound on Rindler trajectories in Black Hole spacetime

Cited by in corpus (4)

• Black hole shadow and acceleration bounds for spherically symmetric spacetimes
• Super-Penrose process for nonextremal black holes
• Particle decay, Oberth effect and a relativistic rocket in the Schwarzschild background
• A nested sequence of inequivalent Rindler vacua : Universal Relic Thermality of Planckian origin