scholarly journals From Maximal Force to the Field Equations of General Relativity

2021 ◽  
Author(s):  
C Sivaram ◽  
Arun Kenath ◽  
Christoph Schiller
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Elastic Constant ◽  
Gravitational Wave ◽  
Special Relativity ◽  
Field Equations ◽  
Maximal Force ◽  
Wave Measurements ◽  
Maximal Speed

We point out that field equations of general relativity are implied by a maximal force given by c4/4G, analogous to the way that special relativity is implied by a maximal speed given by c. We present some of the arguments for this equivalence. The maxi-mal force naturally plays the role of an elastic constant for space-time. Implications of the maximal force for gravitational wave measurements, cosmology and black holes are highlighted. Quantum aspects of the maximal force are discussed.

The stellar graveyard

2019 ◽  
pp. 177-206
Author(s):  
Nils Andersson
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Neutron Stars ◽  
Gravitational Wave ◽  
Stellar Evolution ◽  
White Dwarfs ◽  
Supermassive Black Holes ◽  
Compact Objects ◽  
Fermi Gases ◽  
The 1950S

This chapter introduces the different classes of compact objects—white dwarfs, neutron stars, and black holes—that are relevant for gravitational-wave astronomy. The ideas are placed in the context of developing an understanding of the likely endpoint(s) of stellar evolution. Key ideas like Fermi gases and the Chandrasekhar mass are discussed, as is the emergence of general relativity as a cornerstone of astrophysics in the 1950s. Issues associated with different formation channels for, in particular, black holes are considered. The chapter ends with a discussion of the supermassive black holes that are found at the centre of galaxies.

General Relativity

2017 ◽  
Author(s):  
Nicholas Manton ◽  
Nicholas Mee
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Field Equation ◽  
Einstein Field Equation ◽  
Kerr Metric ◽  
Gravitational Lenses ◽  
Field Equations ◽  
Spacetime Geometry ◽  
Tests Of General Relativity ◽  
Rotating Black Holes

This chapter presents the physical motivation for general relativity, derives the Einstein field equation and gives concise derivations of the main results of the theory. It begins with the equivalence principle, tidal forces in Newtonian gravity and their connection to curved spacetime geometry. This leads to a derivation of the field equation. Tests of general relativity are considered: Mercury’s perihelion advance, gravitational redshift, the deflection of starlight and gravitational lenses. The exterior and interior Schwarzschild solutions are discussed. Eddington–Finkelstein coordinates are used to describe objects falling into non-rotating black holes. The Kerr metric is used to describe rotating black holes and their astrophysical consequences. Gravitational waves are described and used to explain the orbital decay of binary neutron stars. Their recent detection by LIGO and the beginning of a new era of gravitational wave astronomy is discussed. Finally, the gravitational field equations are derived from the Einstein–Hilbert action.

Berichte: Mach's Principle - A Critical Review

1973 ◽  
Vol 28 (3-4) ◽  
pp. 529-537 ◽  
Author(s):  
Michael Reinhardt
Keyword(s):  
General Relativity ◽  
Selection Rule ◽  
Inertial Mass ◽  
Physical Principle ◽  
Mach's Principle ◽  
Mach’S Principle ◽  
Field Equations ◽  
Basic Physical Principle ◽  
Theories Of Gravitation

AbstractAfter a short historical introduction it is discussed how far Mach's principle is incorporated into general relativity. The possible role of Mach's principle as a selection rule for the solutions of Einstein's field equations is summarized. Then follows a discussion of Math's principle in theories of gravitation other than Einstein's, mainly the Brans-Dicke theory. Finally the experiments on the isotropy of inertial mass and their consequence for Mach's principle are described. The conclusion is that Mach's principle, though an extremely stimulating thought, has at present little claim to be a basic physical principle.

scholarly journals Testing general relativity using gravitational wave signals from the inspiral, merger and ringdown of binary black holes

2017 ◽  
Vol 35 (1) ◽  
pp. 014002 ◽  
Author(s):  
Abhirup Ghosh ◽  
Nathan K Johnson-McDaniel ◽  
Archisman Ghosh ◽  
Chandra Kant Mishra ◽  
Parameswaran Ajith ◽  
...  
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Wave ◽  
Binary Black Holes

scholarly journals Gravitational waves — A review on the theoretical foundations of gravitational radiation

2018 ◽  
Vol 33 (14n15) ◽  
pp. 1830013 ◽  
Author(s):  
Alain Dirkes
Keyword(s):  
General Relativity ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Gravitational Radiation ◽  
Wave Zone ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Radiative Losses ◽  
Zone Field ◽  
Theoretical Foundations

In this paper, we review the theoretical foundations of gravitational waves in the framework of Albert Einstein’s theory of general relativity. Following Einstein’s early efforts, we first derive the linearized Einstein field equations and work out the corresponding gravitational wave equation. Moreover, we present the gravitational potentials in the far away wave zone field point approximation obtained from the relaxed Einstein field equations. We close this review by taking a closer look on the radiative losses of gravitating [Formula: see text]-body systems and present some aspects of the current interferometric gravitational waves detectors. Each section has a separate appendix contribution where further computational details are displayed. To conclude, we summarize the main results and present a brief outlook in terms of current ongoing efforts to build a spaced-based gravitational wave observatory.

Physics and Geometry

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
General Relativity ◽  
Special Relativity ◽  
Symmetry Property ◽  
Maxwell's Equations ◽  
Theory Of Relativity ◽  
Relativistic Invariance ◽  
Henri Poincaré ◽  
Ongoing Debate ◽  
French Mathematician

This chapter concerns the ongoing debate about the meaning of Einstein's theory in the formative years, with particular attention to the relation between physics and geometry. It also compares Einstein's thinking on this issue with that of the French mathematician and philosopher Henri Poincaré and deals with the role of symmetry in the theory of relativity—one of Einstein's enduring legacies. The role of symmetry becomes evident, for instance, in the lecture on special relativity, in which it is shown how relativistic invariance, a symmetry property of the spacetime continuum, shapes Maxwell's equations and other laws of physics. In the period under consideration, the understanding of symmetry is deepened by the emergence of Emmy Noether's famous theorems, for which the theory of general relativity was an important source of inspiration.

scholarly journals Quasi-normal modes of static spherically symmetric black holes in f(R) theory

2020 ◽  
Vol 80 (1) ◽  
Author(s):  
Sayak Datta ◽  
Sukanta Bose
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Black Hole ◽  
Gravitational Wave ◽  
Normal Modes ◽  
Einstein Frame ◽  
Spherically Symmetric ◽  
Inhomogeneous Term ◽  
Binary Black Hole ◽  
Special Case

AbstractWe study the quasi-normal modes (QNMs) of static, spherically symmetric black holes in f(R) theories. We show how these modes in theories with non-trivial f(R) are fundamentally different from those in general relativity. In the special case of $$f(R) = \alpha R^2$$f(R)=αR2 theories, it has been recently argued that iso-spectrality between scalar and vector modes breaks down. Here, we show that such a break down is quite general across all f(R) theories, as long as they satisfy $$f''(0)/(1+f''(0)) \ne 0$$f′′(0)/(1+f′′(0))≠0, where a prime denotes derivative of the function with respect to its argument. We specifically discuss the origin of the breaking of isospectrality. We also show that along with this breaking the QNMs receive a correction that arises when $$f''(0)/(1+f'(0)) \ne 0$$f′′(0)/(1+f′(0))≠0 owing to the inhomogeneous term that it introduces in the mode equation. We discuss how these differences affect the “ringdown” phase of binary black hole mergers and the possibility of constraining f(R) models with gravitational-wave observations. We also find that even though the iso-spectrality is broken in f(R) theories, in general, nevertheless in the corresponding scalar-tensor theories in the Einstein frame it is unbroken.

scholarly journals Atomic X-ray spectroscopy of accreting black holes

2005 ◽  
Vol 83 (12) ◽  
pp. 1179-1242 ◽  
Author(s):  
D A Liedahl ◽  
D F Torres
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Accretion Disk ◽  
Accretion Disks ◽  
Strong Field ◽  
Electromagnetic Spectrum ◽  
Field Equations ◽  
X Ray ◽  
Physical Conditions ◽  
Luminous Objects

Current astrophysical research suggests that the most persistently luminous objects in the Universe are powered by the flow of matter through accretion disks onto black holes. Accretion disk systems are observed to emit copious radiation across the electromagnetic spectrum, each energy band providing access to rather distinct regimes of physical conditions and geometric scale. X-ray emission probes the innermost regions of the accretion disk, where relativistic effects prevail. While this has been known for decades, it also has been acknowledged that inferring physical conditions in the relativistic regime from the behavior of the X-ray continuum is problematic and not satisfactorily constraining. With the discovery in the 1990s of iron X-ray lines bearing signatures of relativistic distortion came the hope that such emission would more firmly constrain models of disk accretion near black holes, as well as provide observational criteria by which to test general relativity in the strong field limit. Here, we provide an introduction to this phenomenon. While the presentation is intended to be primarily tutorial in nature, we aim also to acquaint the reader with trends in current research. To achieve these ends, we present the basic applications of general relativity that pertain to X-ray spectroscopic observations of black hole accretion-disk systems, focusing on the Schwarzschild and Kerr solutions to the Einstein field equations. To this, we add treatments of the fundamental concepts associated with the theoretical and modeling aspects of accretion disks, as well as relevant topics from observational and theoretical X-ray spectroscopy.PACS Nos.: 32.30.Rj, 32.80.Hd, 95.30.Dr, 95.30.Sf, 95.85.Nv, 97.10.Gz. 97.80.Jp, 98.35.Mp, 98.62.Mw

Theory of Relativity, The

2018 ◽  
Author(s):  
Adam James Bradley
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Special Relativity ◽  
Particle Physics ◽  
Albert Einstein ◽  
Newtonian Mechanics ◽  
Theory Of Relativity ◽  
Speed Of Light ◽  
Nuclear Age ◽  
The Relationship

The Theory of Relativity is the name given to two separate theories put forth by Albert Einstein (1879–1955): ‘Special Relativity’ and ‘General Relativity’. When first published in 1905, Einstein’s ‘Theory of Special Relativity’ upended Newtonian Mechanics and was in agreement with James Clerk Maxwell’s equations of electromagnetism. The theory opened up new avenues for particle physics and is thought to have ushered in the nuclear age. Relativity was also used to predict the existence of black holes and other cosmological phenomena. Special Relativity, Einstein’s theory of small particles, includes possibly the world’s most famous physics equation: E=mc², which predicts the relationship between mass and energy where energy is equal to the mass of an object multiplied by the speed of light squared.

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