scholarly journals World Lines in Einstein's Elevator

2021 ◽  
Author(s):  
Mathieu Rouaud
Keyword(s):  
Black Hole ◽  
Special Relativity ◽  
Reference Frame ◽  
Large Scale ◽  
Thought Experiment ◽  
Michelson Interferometer ◽  
Free Fall ◽  
Classical Case ◽  
Frame Of Reference ◽  
Qualitative Aspect

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation. We consider a uniformly accelerated reference frame in rectilinear translation and we show that the trajectories of the particles are ellipses centered on the horizon of the events. The frame of reference is non-inertial, the space-time is flat, the metric is non-Minkowskian and the computations are performed within the framework of special relativity. Some experimental consequences are discussed such as trajectory deviation, desynchronization of a falling clock and the Michelson interferometer. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the box where the interest is above all theoretical and pedagogical. The study helps the student to become familiar with the concepts of metric, coordinate velocity, horizon, and, to do the analogy with the black hole.

scholarly journals World Lines in Einstein's Elevator

2021 ◽  
Author(s):  
Mathieu Rouaud
Keyword(s):  
Black Hole ◽  
Special Relativity ◽  
Large Scale ◽  
Thought Experiment ◽  
Free Fall ◽  
Classical Case ◽  
Frame Of Reference ◽  
Qualitative Aspect ◽  
Morley Experiment ◽  
Faster Than Light

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body, and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation. We consider a uniformly accelerated reference frame in rectilinear translation, and we show that the trajectories of the particles are semi-ellipses with the center on the event horizon. The frame of reference is non-inertial, the space-time is flat, the metric is non-Minkowskian, and the computations are performed within the framework of special relativity. Some experimental consequences are discussed, such as the deviation of trajectories, the desynchronization of a falling clock, the accelerated Michelson-Morley experiment, and, finally, an experiment where a paradox appears — a particle of matter seems to go faster than light. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical. The concepts of metric, coordinated velocity and horizon are discussed, and the analogy with the black hole is made.

scholarly journals World Lines in Einstein's Elevator

2021 ◽  
Author(s):  
Mathieu Rouaud
Keyword(s):  
Black Hole ◽  
Special Relativity ◽  
Large Scale ◽  
Thought Experiment ◽  
Free Fall ◽  
Classical Case ◽  
Frame Of Reference ◽  
Qualitative Aspect ◽  
Morley Experiment ◽  
Faster Than Light

We all have in mind Einstein’s famous thought experiment in the elevator where we observe the free fall of a body, and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation. We consider a uniformly accelerated reference frame in rectilinear translation, and we show that the trajectories of the particles are ellipses centered on the event horizon. The frame of reference is non-inertial, the space-time is flat, the metric is non-Minkowskian, and the computations are performed within the framework of special relativity. Some experimental consequences are discussed, such as the deviation of trajectories, the desynchronization of a falling clock, the accelerated Michelson-Morley experiment, and, finally, an experiment where a paradox appears — a particle of matter seems to go faster than light. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical and pedagogical. The study helps the student to become familiar with the concepts of metric, coordinate velocity, horizon, and, to do the analogy with the black hole.

scholarly journals Worldlines in the Einstein's Elevator

2021 ◽  
Author(s):  
Mathieu Rouaud
Keyword(s):  
Black Hole ◽  
Special Relativity ◽  
Reference Frame ◽  
Thought Experiment ◽  
Free Fall ◽  
Classical Case ◽  
Space Time ◽  
Frame Of Reference ◽  
Exact Calculation ◽  
Qualitative Aspect

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation. We consider a uniformly accelerated reference frame in rectilinear translation and we show that the trajectories of the particles are ellipses centered on the horizon of the events. The frame of reference is non-inertial, the space-time is flat, the metric is non-Minkowskian and the computations are performed within the framework of special relativity. The deviation, compared to the classical case, is important close to the horizon, but small in the box, and the interest is above all theoretical and pedagogical. The study helps the student to become familiar with the concepts of metric, coordinate velocity, horizon, and, to do the analogy with the black hole.

scholarly journals Einstein's Elevator: World Lines, Michelson-Morley Experiment and Relativistic Paradox

2021 ◽  
Author(s):  
Mathieu Rouaud
Keyword(s):  
Black Hole ◽  
Large Scale ◽  
Thought Experiment ◽  
Free Fall ◽  
Classical Case ◽  
Frame Of Reference ◽  
Qualitative Aspect ◽  
First Time ◽  
Morley Experiment ◽  
Faster Than Light

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body, and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation, and for the first time the worldlines equations are given. We consider a uniformly accelerated reference frame in rectilinear translation, and we show that the trajectories of the particles are semi-ellipses with the center on the event horizon. The frame of reference is non-inertial, the space-time is flat, and the computations are performed within the framework of special relativity. Some experimental consequences are discussed, especially the experiment with the accelerated Michelson-Morley interferometer is solved, and we described an experiment where a new relativistic paradox appears --- a particle of matter seems to go faster than light. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical. The concepts of metric, coordinated velocity and horizon are discussed, and the analogy with the black hole is made.

What is the meaning of the pullback Schwarzschild metric?

2019 ◽  
Author(s):  
Matheus Pereira Lobo
Keyword(s):  
Black Hole ◽  
Thought Experiment ◽  
Schwarzschild Metric

We propose a thought experiment regarding the pullback Schwarzschild metric, considering that there is no interior of a black hole.

scholarly journals Gaseous Disks in the Nuclei of Elliptical Galaxies

1997 ◽  
Vol 163 ◽  
pp. 620-625 ◽  
Author(s):  
H. Ford ◽  
Z. Tsvetanov ◽  
L. Ferrarese ◽  
G. Kriss ◽  
W. Jaffe ◽  
...  
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Angular Momentum ◽  
Accretion Disks ◽  
Large Scale ◽  
Elliptical Galaxies ◽  
Central Mass ◽  
Massive Black Holes ◽  
Radio Jets

AbstractHST images have led to the discovery that small (r ~ 1″ r ~ 100 – 200 pc), well-defined, gaseous disks are common in the nuclei of elliptical galaxies. Measurements of rotational velocities in the disks provide a means to measure the central mass and search for massive black holes in the parent galaxies. The minor axes of these disks are closely aligned with the directions of the large–scale radio jets, suggesting that it is angular momentum of the disk rather than that of the black hole that determines the direction of the radio jets. Because the disks are directly observable, we can study the disks themselves, and investigate important questions which cannot be directly addressed with observations of the smaller and unresolved central accretion disks. In this paper we summarize what has been learned to date in this rapidly unfolding new field.

scholarly journals Hayden-Preskill decoding from noisy Hawking radiation

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ning Bao ◽  
Yuta Kikuchi
Keyword(s):  
Black Hole ◽  
Quantum State ◽  
Hawking Radiation ◽  
Thought Experiment ◽  
Natural Question ◽  
Early Radiation

Abstract In the Hayden-Preskill thought experiment, the Hawking radiation emitted before a quantum state is thrown into the black hole is used along with the radiation collected later for the purpose of decoding the quantum state. A natural question is how the recoverability is affected if the stored early radiation is damaged or subject to decoherence, and/or the decoding protocol is imperfectly performed. We study the recoverability in the thought experiment in the presence of decoherence or noise in the storage of early radiation.

scholarly journals Circum-nuclear molecular disks: Role in AGN fueling and feedback

2019 ◽  
Vol 15 (S359) ◽  
pp. 312-317
Author(s):  
Francoise Combes
Keyword(s):  
Black Hole ◽  
Angular Momentum ◽  
High Resolution ◽  
Large Scale ◽  
Active Galaxy ◽  
Small Scale ◽  
Massive Black Hole ◽  
Molecular Outflows ◽  
Molecular Outflow

AbstractGas fueling AGN (Active Galaxy Nuclei) is now traceable at high-resolution with ALMA (Atacama Large Millimeter Array) and NOEMA (NOrthern Extended Millimeter Array). Dynamical mechanisms are essential to exchange angular momentum and drive the gas to the super-massive black hole. While at 100pc scale, the gas is sometimes stalled in nuclear rings, recent observations reaching 10pc scale (50mas), may bring smoking gun evidence of fueling, within a randomly oriented nuclear gas disk. AGN feedback is also observed, in the form of narrow and collimated molecular outflows, which point towards the radio mode, or entrainment by a radio jet. Precession has been observed in a molecular outflow, indicating the precession of the radio jet. One of the best candidates for precession is the Bardeen-Petterson effect at small scale, which exerts a torque on the accreting material, and produces an extended disk warp. The misalignment between the inner and large-scale disk, enhances the coupling of the AGN feedback, since the jet sweeps a large part of the molecular disk.

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