# What is Rindler horizon: Definition and 12 Discussions

In relativistic physics, the coordinates of a hyperbolically accelerated reference frame constitute an important and useful coordinate chart representing part of flat Minkowski spacetime. In special relativity, a uniformly accelerating particle undergoes hyperbolic motion, for which a uniformly accelerating frame of reference in which it is at rest can be chosen as its proper reference frame. The phenomena in this hyperbolically accelerated frame can be compared to effects arising in a homogeneous gravitational field. For general overview of accelerations in flat spacetime, see Acceleration (special relativity) and Proper reference frame (flat spacetime).
In this article, the speed of light is defined by c = 1, the inertial coordinates are (X, Y, Z, T), and the hyperbolic coordinates are (x, y, z, t). These hyperbolic coordinates can be separated into two main variants depending on the accelerated observer's position: If the observer is located at time T = 0 at position X = 1/α (with α as the constant proper acceleration measured by a comoving accelerometer), then the hyperbolic coordinates are often called Rindler coordinates with the corresponding Rindler metric. If the observer is located at time T = 0 at position X = 0, then the hyperbolic coordinates are sometimes called Møller coordinates or Kottler–Møller coordinates with the corresponding Kottler–Møller metric. An alternative chart often related to observers in hyperbolic motion is obtained using Radar coordinates which are sometimes called Lass coordinates. Both the Kottler–Møller coordinates as well as Lass coordinates are denoted as Rindler coordinates as well.Regarding the history, such coordinates were introduced soon after the advent of special relativity, when they were studied (fully or partially) alongside the concept of hyperbolic motion: In relation to flat Minkowski spacetime by Albert Einstein (1907, 1912), Max Born (1909), Arnold Sommerfeld (1910), Max von Laue (1911), Hendrik Lorentz (1913), Friedrich Kottler (1914), Wolfgang Pauli (1921), Karl Bollert (1922), Stjepan Mohorovičić (1922), Georges Lemaître (1924), Einstein & Nathan Rosen (1935), Christian Møller (1943, 1952), Fritz Rohrlich (1963), Harry Lass (1963), and in relation to both flat and curved spacetime of general relativity by Wolfgang Rindler (1960, 1966). For details and sources, see § History.

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1. ### I Can time run backwards in an accelerating frame?

I'm trying to make sure I understand how the traveling twin tracks the time of his stationary earthbound sibling and the time of another stationary observer who's farther away. From what I've understood until now, it's pretty straightforward with the earthbound twin: In the traveler's frame, the...
2. ### I Definition of Rindler Horizon: A Global View

[Moderator's note: Thread spun off from previous one due to closure of the previous thread.] I have been thinking about this off and on, and though late to the thread, want to propose another way of looking at this that can be presented both at B level or A level. I post here at B level, and...
3. ### A Rindler Horizon Subtleties: Advanced Discussion

[Mentors' note: thread spun off from https://www.physicsforums.com/threads/equivalence-principle-and-rindler-horizons.1007879/] [Disclaimer] Definitely not B Level, but possibly of interest: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.100.084029 discusses the Rindler horizons of an...
4. ### B Coulomb force over Rindler horizon

Let's say a rocket carrying a positively charged balloon starts to accelerate with a constant proper acceleration at time t. After a long time another rocket carrying a positively charged balloon is launched. The crew of this rocket drives the rocket to a position right below the...
5. ### I Dimensionless Time: Rindler & Minkowski Spacetime

What does the dimensionless time in Rindler spacetime signifies? And how something dimensionless can be regarded as time and coupled up with proper distance in Minkowski spacetime? (Page 7: https://www.perimeterinstitute.ca/images/files/black_holes_and_holography_course_notes.pdf )
6. ### A Solution to the wave equation in Rindler coordinates

I have been reading these notes on Rindler coordinates for an accelerated observer. In Rindler coordinates, the hyperbolic motion of the observer is expressed through the coordinate transformation $$t=a^{-1}e^{a{{\xi}}}\sinh a{\eta}\\ {}x=a^{-1}e^{a{{\xi}}}\cosh a{\eta}.$$On a space-time...
7. ### Charge Dropping on Rindler Horizon: Coulomb Force Effects?

Let's say I keep on dropping electrons on one spot of a Rindler horizon. Does the charge of the spot increase without a limit? When the charge of the spot is very large, does the spot exert a Coulomb force on the electron I'm about to drop, causing the electron to start moving away from the...
8. ### Clarifying Black Hole Horizons: An Examination of Observer Perspectives

I am confused about black hole horizons and such common statements as "light cannot escape from inside the horizon". The way I currently understand it is as follows : 1. Horizons are always relative to an observer, and what is called "the black hole horizon" is just a shorthand for "the black...
9. ### Rindler Horizon and Lorentz contraction

Hello, Onhttp://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html website it says in the section "below the rocket, something strange is happening" that the distance of an object which passes the accelerating observer never increases -c2/α. I think this means, that the Rindler Horizon...
10. ### What Causes the Unexpected Limit in Rindler Horizon Calculations?

Greetings. For my own edification I calculated a set of the congruence of uniformly accelerated observers in flat spacetime in the spherical polar chart. These observers accelerate radially outwards from some ##r## so that their horizons are at the same position ##r_h##. This requires that...
11. ### Singularities and Rindler horizon

I am trying to understand things around singularities and related to this I have a question. What kind of singularity is Rindler horizon? Wikipedia (Rindler coordinates) says that: "The Rindler coordinate chart has a coordinate singularity at x = 0," But if Rindler coordinates are not...
12. ### Reaching the Rindler horizon in a finite proper time

Hi, I am trying to show that timelike geodesics reach the Rindler horizon (X=0) in a finite proper time. The spacetime line element is ds^{2} = -\frac{g^{2}}{c^{2}}X^{2}dT^{2}+dX^{2}+dY^{2}+dZ^{2} Ive found something helpful here...