On the Composition of Velocities in the Theory of Relativity. Allgemeine Dynamik. Online within the US. On the Theory of Aberration and the Principle of Relativity. Recent Researches on Space, Time, and Force. A Neglected Type of Relativity. The Second Postulate of Relativity. Anwendung der Lobatschefskijschen Geometrie in der Relativtheorie. Application of Lobachevskian Geometry in the Theory of Relativity. On the Electrodynamics of Minkowski. Die Relativtheorie und die Lobatschefskijsche Geometrie. The Theory of Relativity and Lobachevskian Geometry.

Erwiderung auf die Antwort des Hrn. Bucherer Online within the US. Elementare Elektronensysteme, Online within the US. Uniform Rotation and Lorentz Contraction. Zur elektromagnetischen Mechanik Online within the US. The Physical Aspect of Time. Is the Michelson Experiment Conclusive? Die Reflexion des Lichtes an bewegten Spiegeln. The Reflection of Light at Moving Mirrors. The Principle of Relativity. Erwiderung auf die Bemerkungen des Hrn. Bestelmeyer Online. Some General Remarks on the Relativity Principle. On the Theory of Relativity.

## General Relativity and Gravitation

Zu Herrn v. Ignatowskys Behandlung der Bornschen Starrheitsdefinition. Ignatowsky's Treatment of Born's Definition of Rigidity. The Common Sense of Relativity. Zum Ehrenfestschen Paradoxon. On Ehrenfest's Paradox. On the bearing of the Principle of Relativity on Gravitational Astronomy. Die Dynamik eines bewegten Gases in der Relativtheorie Online. On the Dynamics of the Theory of Relativity.

On an Experiment on the Optics of Moving Bodies.

### Journal History

Concerning Relativistic Statics. Energy and mass Online. Remarks on the Law of the Lever in the Theory of Relativity. The Evolution of Space and Time. The evolution of space and time Online , translated by J. Zur Theorie der Gravitation Online. Das Elementargesetz der Gravitation Online. Non-Newtonian Mechanics. The Mass of a Moving Body. Lorentz-Transformation Online in the US. Notiz zu vorstehender Abhandlung von Herrn F. Grundlagen einer Theorie der Materie I Online. Energy and mass II Online. On the Conception of the Current of Energy. On the Conception of the Current of Energy Online.

On the Theory of the Experiment of Trouton and Noble. Der freie Fall Online. Some Emission Theories of Light. On the Theory of the Michelson Experiment. The Space-time Manifold of Relativity. Zur Theorie des bewegten Spiegels Online. On the spacetime lines of a Minkowski world. Das Gravitationsfeld Online. Relativitaet und Gravitation. Erwiderung auf eine Bemerkung des Herrn A.

Einstein Online. Abraham Online. Bemerkungen zu A. Einsteins Erwiderung Online. On the Theory of Relativity: Analysis of the Postulates. Eine neue Gravitationstheorie Online. On electromagnetic induction and relative motion Online. On the Theory of Relativity: Philosophical Aspects. Zur Minkowskischen Mechanik Online. A proof of the constancy of the velocity of light. On the constancy of the velocity of light. The effect of dielectrics on unipolar induction Online. Schaposchnikow Online.

Zu Minkowskis Mechanik. Die Weltkonstante, die Systemmechanik Online. The demonstration of the luminiferous aether by an interferometer in uniform rotation. On the proof of the reality of the luminiferous aether by the experiment with a rotating interferometer. Bemerkungen zur Relativtheorie. Beitrag zur nichteuklidischen Interpretation der Relativtheorie.

Bemerkung zu P. Once Again: Sagnac Effect and Aether. Sagnac-Effekt und Emissionstheorie. Sagnac Effect and Emission Theory. Antwort auf eine Replik P. Harzers Online. Zur Frage der Symmetrie des elektromagnetischen Spannungstensors Online. Die neue Mechanik Online. Neuere Gravitationstheorien Online. Eine Bemerkung zum Dopplerschen Effekt. On the energy and den Radius of the electron Online. Relativity and Electrodynamics Online within the US.

Unipolar induction and electron theory Online. On the Experiment of F. Lorentz Contraction. Online in the US. La transformation de Lorentz-Einstein et le temps universel de M. The Lorentz-Einstein transformation and the universal time of Ed. Elementary geometric representation of the formulas of the special theory of relativity. An elementary geometrical representation of the transformation formulas of the special theory of relativity. Sagnac Online. Graphical representation of the four-dimensional space-time universe. Remarques au sujet de la Note de Prunier Online.

Lichtgeschwindigkeit und Statik des Gravitationsfeldes Online. Zur Theorie des statischen Gravitationsfeldes Online. Gibt es eine Gravitationswirkung, die der elektrodynamischen Induktionswirkung analog ist? On Einstein's theory of the stationary gravitation field Online. On a system of curves occurring in Einstein's theory of gravitation Online. Physikalische Grundlagen einer Gravitationstheorie Online. Archives des sciences physiques et naturelles ser. Mathematische Begriffsbildungen zur Gravitationstheorie.

On Hamilton's principle in Einstein's theory of gravitation. Die Grundlagen der Physik. Erste Mitteilung. Die Feldgleichungen der Gravitation Online. The Field Equations of Gravitation. The Foundation of the Generalised Theory of Relativity. Space, time, and gravitation Online. Die Grundlagen der Einsteinschen Gravitationstheorie Online. Planetary motion and the motion of the moon according to Einstein s theory Online. Einstein's theory of gravitation and its astronomical consequences Online. On the relativity of rotation in Einstein's theory Online.

Einstein's theory of gravitation and its astronomical consequences. Second paper Online. Zweite Mitteilung. On the relativity of inertia. Remarks concerning Einstein's latest hypothesis Online. On the curvature of space Online. Third paper Online. We outline the merits of and differences between the various quantities used for parameterizing noise curves and characterizing gravitational-wave amplitudes. We conclude by producing plots that consistently compare different detectors.

## Portal:Relativity

This paper addresses a simple question: how small can one make a gravitational source mass and still detect its gravitational coupling to a nearby test mass? We describe an experimental scheme based on micromechanical sensing to observe gravity between milligram-scale source masses, thereby improving the current smallest source mass values by three orders of magnitude and possibly even more. The two instruments are identical in design, and are specialized versions of a Michelson interferometer with 4 km long arms. As in Initial LIGO, Fabry—Perot cavities are used in the arms to increase the interaction time with a gravitational wave, and power recycling is used to increase the effective laser power.

In the most sensitive frequency region around Hz, the design strain sensitivity is a factor of 10 better than Initial LIGO. In addition, the low frequency end of the sensitivity band is moved from 40 Hz down to 10 Hz. All interferometer components have been replaced with improved technologies to achieve this sensitivity gain.

Much better seismic isolation and test mass suspensions are responsible for the gains at lower frequencies. Higher laser power, larger test masses and improved mirror coatings lead to the improved sensitivity at mid and high frequencies. Data collecting runs with these new instruments are planned to begin in mid The first observing run of Advanced LIGO spanned 4 months, from 12 September to 19 January , during which gravitational waves were directly detected from two binary black hole systems, namely GW and GW Confident detection of gravitational waves requires an understanding of instrumental transients and artifacts that can reduce the sensitivity of a search.

Studies of the quality of the detector data yield insights into the cause of instrumental artifacts and data quality vetoes specific to a search are produced to mitigate the effects of problematic data. In this paper, the systematic removal of noisy data from analysis time is shown to improve the sensitivity of searches for compact binary coalescences.

The output of the PyCBC pipeline, which is a python-based code package used to search for gravitational wave signals from compact binary coalescences, is used as a metric for improvement. GW was a loud enough signal that removing noisy data did not improve its significance. The present paper introduces the science, engineering, data analysis, and heritage of Gravity Probe B, detailed in the accompanying 20 CQG papers. Nonetheless distant observers would observe a gravitational mass due to appearance of a so-called gravitational sphere around the star.

We perform our analysis for several equations of state including purely hadronic configurations as well as hyperons and quark stars. Also the decrease in the mass bounded by star surface may cause the surface redshift to decrease in R 2 -gravity when compared to Einsteinian predictions. This effect is shown to hardly depend upon the observed gravitational mass.

We consider large gauge transformations of gravity and electromagnetism in asymptotically flat spacetime. Already at the classical level, we identify a canonical transformation that decouples the soft variables from the hard dynamics. We find that only the soft dynamics is constrained by BMS or large charge conservation.

Physically this corresponds to the fact that sufficiently long-wavelength photons or gravitons that are added to the in-state will simply pass through the interaction region; they scatter trivially in their own sector. This implies in particular that the large gauge symmetries bear no relevance to the black hole information paradox. We also present the quantum version of soft decoupling.

### Introduction

As a consistency check, we show that the apparent mixing of soft and hard modes in the original variables arises entirely from the long range field of the hard charges, which is fixed by gauge invariance and so contains no additional information. We calculate the 3-point amplitudes on these backgrounds and find that a notion of double copy remains in the presence of background curvature: graviton amplitudes on a gravitational plane wave are the double copy of gluon amplitudes on a gauge field plane wave.

This is non-trivial in that it requires a non-local replacement rule for the background fields and the momenta and polarization vectors of the fields scattering on the backgrounds. These encode a memory effect in the scattering amplitudes, which naturally double copies as well.

## Classical and Quantum Gravity - IOPscience

In this paper, we study constant-roll inflation in gravity. We take two different approaches, one that relates gravity to well-known scalar models of constant-roll and a second that examines the constant-roll condition in gravity directly. With regard to the first approach, by using well-known techniques, we find the gravity that realizes a given constant-roll evolution in the scalar—tensor theory.

We also perform a conformal transformation in the resulting gravity and find the Einstein frame counterpart theory.

As we demonstrate, the resulting scalar potential is different in comparison to the original scalar constant-roll case, and the same applies for the corresponding observational indices. Moreover, we discuss how cosmological evolutions that can realize constant-roll to constant-roll era transitions in the scalar-tensor description can be realized by vacuum gravity. With regard to the second approach, we examine the effects of the constant-roll condition on the inflationary dynamics of vacuum gravity directly. We present in detail the formalism of constant-roll gravity inflationary dynamics and we discuss the inflationary indices for this case.

We use two well-known gravities in order to illustrate our findings: the R 2 model and a power-law gravity in vacuum. As we demonstrate, in both cases the parameter space is enlarged in comparison to the slow-roll counterparts of the models and, in effect, the models can also be compatible with the observational data.

Finally, we briefly address the graceful exit issue. A number of very different approaches to quantum gravity contain a common thread, a hint that spacetime at very short distances becomes effectively two dimensional.

- 13.7 Einstein’s Theory of Gravity.
- General Relativity Still Making Waves!
- General Relativity and Gravitation.

In particular, the linearized Schwarzschild metric is obtained as a solution. It arises from a quasi-static would-be massive graviton mode, and slowly decreases during the cosmic expansion. For the dynamical scalar modes, non-linear effects must be taken into account. We argue that they lead to non-Ricci-flat metric perturbations with very long wavelengths, which would be perceived as dark matter from the GR point of view. We consider here a possible pointing jitter in the light beam sent from the emitter.

We show how the resulting phase noise depends on the quality of the wavefront due to the incident beam impinging on the telescope and due to the imperfections of the telescope itself. Namely, we numerically assess the crossed influence of various defects aberrations and astigmatisms , inherent to a real telescope with pointing fluctuations. Specifically, we consider modifications to their boundary conditions, to the bulk metric, and to bulk quantum matter fields. These include familiar properties such as smeared versions of the quantum focusing conjecture and the generalized second law, as well as new constraints on i metric and matter perturbations in spacetimes close to vacuum and ii the bulk stress tensor in generic not necessary close to vacuum spacetimes.

This latter constraint is highly reminiscent of a quantum energy inequality. Systematic errors in the calibration parameters lead to systematic errors in the GW strain estimate, and hence to systematic errors in the astrophysical parameter estimates in a particular GW signal. In this work we examine this effect for a GW signal similar to GW, both for a low-power detector operation similar to the first and second Advanced LIGO observing runs and for a higher-power operation with detuned signal extraction. We set requirements on the accuracy of the calibration such that the astrophysical parameter estimation is limited by errors introduced by random detector noise, rather than calibration systematics.

We also examine the impact of systematic calibration errors on the possible detection of a massive graviton. We then present a comparison of ABK charges with other notions of de Sitter charges. We compare ABK charges with counterterm charges, showing that they differ only by a constant offset, which is determined in terms of the boundary metric alone. We also compare ABK charges with charges defined by Kelly and Marolf at spatial infinity of de sitter spacetime. When the formalisms can be compared, we show that the two definitions agree.

Finally, we express Kerr—de Sitter metrics in four and five dimensions in an appropriate Fefferman—Graham form. Gravitational waves GWs have a great potential to probe cosmology. We review early universe sources that can lead to cosmological backgrounds of GWs. We begin by presenting proper definitions of GWs in flat space-time and in a cosmological setting section 2.

Following, we discuss the reasons why early universe GW backgrounds are of a stochastic nature, and describe the general properties of a stochastic background section 3. We then review in detail early universe GW generation mechanisms, as well as the properties of the GW backgrounds they give rise to. We classify the backgrounds in five categories: GWs from quantum vacuum fluctuations during standard slow-roll inflation section 5 , GWs from processes that operate within extensions of the standard inflationary paradigm section 6 , GWs from post-inflationary preheating and related non-perturbative phenomena section 7 , GWs from first order phase transitions related or not to the electroweak symmetry breaking section 8 , and GWs from general topological defects, and from cosmic strings in particular section 9.

The phenomenology of these early universe processes is extremely rich, and some of the GW backgrounds they generate can be within the reach of near-future GW detectors. A future detection of any of these backgrounds will provide crucial information on the underlying high energy theory describing the early universe, probing energy scales well beyond the reach of particle accelerators.

The starting point for each such unification scenario is a particular formalism for general relativity. We review what has been done in the literature on each of these unification schemes, and compare and contrast their achievements to those of the better developed Kaluza—Klein scenario.