arXiv subjects

Lydia Bieri

Publications and source records attributed to Lydia Bieri.

30 records · Page 2Linked to original sources

arXiv2015

Gravitational wave memory in de Sitter spacetime

We examine gravitational wave memory in the case where sources and detector are in an expanding cosmology. For simplicity, we treat the case where the cosmology is de Sitter spacetime, and discuss the possibility of generalizing our results to the case of a more realistic cosmology. We find results very similar to those of gravitational wave memory in an asymptotically flat spacetime, but with the magnitude of the effect multiplied by a redshift factor.

gr-qc↗

arXiv2015

Gravitational Waves and Their Memory in General Relativity

General relativity explains gravitational radiation from binary black hole or neutron star mergers, from core-collapse supernovae and even from the inflation period in cosmology. These waves exhibit a unique effect called memory or Christodoulou effect, which in a detector like LIGO or LISA shows as a permanent displacement of test masses and in radio telescopes like NANOGrav as a change in the frequency of pulsars' pulses. It was shown that electromagnetic fields and neutrino radiation enlarge the memory. Recently it has been understood that the two types of memory addressed in the literature as `linear' and `nonlinear' are in fact two different phenomena. The former is due to fields that do not and the latter is due to fields that do reach null infinity.

gr-qc↗

arXiv2014

Asymptotic properties of solutions of the Maxwell Klein Gordon equation with small data

We prove peeling estimates for the small data solutions of the Maxwell Klein Gordon equations with non-zero charge and with a non-compactly supported scalar field, in $(3+1)$ dimensions. We obtain the same decay rates as in an earlier work by Lindblad and Sterbenz, but giving a simpler proof. In particular we dispense with the fractional Morawetz estimates for the electromagnetic field, as well as certain space-time estimates. In the case that the scalar field is compactly supported we can avoid fractional Morawetz estimates for the scalar field as well. All of our estimates are carried out using the double null foliation and in a gauge invariant manner.

math.AP↗

arXiv2014

Examination of a simple example of gravitational wave memory

We examine a simple example of gravitational wave memory due to the decay of a point particle into two point particles. In the case where one of the decay products is null, there are two types of memory: a null memory due to the null particle and an ordinary memory due to the recoiling timelike particle. In the case where both decay products are timelike, there is only ordinary memory. However, this ordinary memory can mimic the null memory in the limit where one of the decay products has a large velocity.

gr-qc↗

arXiv2014

A perturbative and gauge invariant treatment of gravitational wave memory

We present a perturbative treatment of gravitational wave memory. The coordinate invariance of Einstein's equations leads to a type of gauge invariance in perturbation theory. As with any gauge invariant theory, results are more clear when expressed in terms of manifestly gauge invariant quantities. Therefore we derive all our results from the perturbed Weyl tensor rather than the perturbed metric. We derive gravitational wave memory for the Einstein equations coupled to a general energy-momentum tensor that reaches null infinity.

gr-qc↗

arXiv2013

An electromagnetic analog of gravitational wave memory

We present an electromagnetic analog of gravitational wave memory. That is, we consider what change has occurred to a detector of electromagnetic radiation after the wave has passed. Rather than a distortion in the detector, as occurs in the gravitational wave case, we find a residual velocity (a "kick") to the charges in the detector. In analogy with the two types of gravitational wave memory ("ordinary" and "nonlinear") we find two types of electromagnetic kick.

gr-qc↗

arXiv2013

Neutrino Radiation Showing a Christodoulou Memory Effect in General Relativity

We describe neutrino radiation in general relativity by introducing the energy-momentum tensor of a null fluid into the Einstein equations. Investigating the geometry and analysis at null infinity, we prove that a component of the null fluid enlarges the Christodoulou memory effect of gravitational waves. The description of neutrinos in general relativity as a null fluid can be regarded as a limiting case of a more general description using the massless limit of the Einstein-Vlasov system. The present authors with co-authors have work in progress to generalize the results of this paper using this more general description. Gigantic neutrino bursts occur in our universe in core-collapse supernovae and in the mergers of neutron star binaries.

gr-qc↗

arXiv2012

The Electromagnetic Christodoulou Memory Effect and its Application to Neutron Star Binary Mergers

Gravitational waves are predicted by the general theory of relativity. It has been shown that gravitational waves have a nonlinear memory, displacing test masses permanently. This is called the Christodoulou memory. We proved that the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves, enlarging the permanent displacement of test masses. In experiments like LISA or LIGO which measure distances of test masses, the Christodoulou memory will manifest itself as a permanent displacement of these objects. It has been suggested to detect the Christodoulou memory effect using radio telescopes investigating small changes in pulsar's pulse arrival times. The latter experiments are based on present-day technology and measure changes in frequency. In the present paper, we study the electromagnetic Christodoulou memory effect and compute it for binary neutron star mergers. These are typical sources of gravitational radiation. During these processes, not only mass and momenta are radiated away in form of gravitational waves, but also very strong magnetic fields are produced and radiated away. Moreover, a large portion of the energy is carried away by neutrinos. We give constraints on the conditions, where the energy transported by electromagnetic radiation is of similar or slightly higher order than the energy radiated in gravitational waves or in form of neutrinos. We find that for coalescing neutron stars, large magnetic fields magnify the Christodoulou memory as long as the gaseous environment is sufficiently rarefied. Thus the observed effect on test masses of a laser interferometer gravitational wave detector will be enlarged by the contribution of the electromagnetic field. Therefore, the present results are important for the planned experiments.

astro-ph.CO↗

arXiv2012

Who discovered the expanding universe?

Who discovered the expanding universe? Was it Hubble, or Lemaître, or was it just the end result of a long series of investigations? In this article we summarise the main steps and contributions that led to one of the most exciting discoveries ever made, of which Lemaître was the principal architect. In 1927 he combined his dynamical solutions of the Einstein equations with astronomical observations to conclude that the universe is expanding. He derived the linear velocity-distance relationship and calculated the first numerical value of what later was called the "Hubble constant". His discovery paper of 1927 was written in French and in 1931 it was translated into English and published in Monthly Notices. However, the translation omits the section where Lemaître computed the "Hubble constant". Why was that done, and who was responsible? We do not speculate on this question, but present in a very condensed way the facts along the path of discovery. The documented details from primary sources can be found in our book "Discovering the Expanding Universe".

physics.hist-ph↗

arXiv2011

The Electromagnetic Christodoulou Memory Effect in Neutron Star Binary Mergers

Gravitational waves are predicted by the general theory of relativity. In [6] D. Christodoulou showed that gravitational waves have a nonlinear memory. We proved in [3] that the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In the present paper, we study this electromagnetic Christodoulou memory effect and compute it for binary neutron star mergers. These are typical sources of gravitational radiation. During these processes, not only mass and momenta are radiated away in form of gravitational waves, but also very strong magnetic fields are produced and radiated away. Thus the observed effect on test masses of a laser interferometer gravitational wave detector will be enlarged by the contribution of the electromagnetic field. Therefore, the present results are important for the planned experiments. Looking at the null asymptotics of spacetimes, which are solutions of the Einstein-Maxwell (EM) equations, we derived in [3] the electromagnetic Christodoulou memory effect. Moreover, our results allow to answer astro- physical questions, as the knowledge about the amount of energy radiated away in a neutron star binary merger enables us to gain information about the source of the gravitational waves.

math.DG↗

arXiv2010

Null Asymptotics of Solutions of the Einstein-Maxwell Equations in General Relativity and Gravitational Radiation

We prove that for spacetimes solving the Einstein-Maxwell (EM) equations, the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In [5] D. Christodoulou showed that gravitational waves have a nonlinear memory. He discussed how this effect can be measured as a permanent displacement of test masses in a laser interferometer gravitational wave detector. Christodoulou derived a precise formula for this permanent displacement in the Einstein vacuum (EV) case. We prove in Theorem 6 that for the EM equations this permanent displacement exhibits a term coming from the electromagnetic field. This term is at the same highest order as the purely gravitational term that governs the EV situation. On the other hand, in Chapter 3, we show that to leading order, the presence of the electromagnetic field does not change the instantaneous displacement of the test masses. Following the method introduced by D. Christodoulou in [5] and asymptotics derived by N. Zipser in [8] and [9], we investigate gravitational radiation at null infinity in spacetimes solving the EM equations. We study the Bondi mass loss formula at null infinity derived in [9]. We show that the mass loss formula from [9] is compatible with the one in Bondi coordinates obtained in [4]. And we observe that the presence of the electromagnetic field increases the total energy radiated to infinity up to leading order. Moreover, we compute the limit of the area radius at null infinity in Theorem 7.

math.DG↗

arXiv2009

An Extension of the Stability Theorem of the Minkowski Space in General Relativity

In this paper, we sketch the proof of the extension of the stability theorem of the Minkowski space in General Relativity done explicitly in previous work by the present author. We discuss solutions of the Einstein vacuum (EV) equations. We solve the Cauchy problem for more general, asymptotically flat initial data than in the pioneering work `The Global Nonlinear Stability of the Minkowski Space' of D. Christodoulou and S. Klainerman or than in any other work. Moreover, we describe precisely the asymptotic behaviour. Our relaxed assumptions on the initial data yield a spacetime curvature which is not bounded in $L^{\infty}(M)$. As a major result, we encounter in our work borderline cases, which we discuss in this paper as well. The fact that certain of our estimates are borderline in view of decay indicates that the conditions in our main theorem are sharp in so far as the assumptions on the decay at infinity on the initial data are concerned. Thus, the borderline cases are a consequence of our relaxed assumptions on the data. They are not present in the other works, as all of them place stronger assumptions on their data. We work with an invariant formulation of the EV equations. Our main proof is based on a bootstrap argument. To close the argument, we have to show that the spacetime curvature and the corresponding geometrical quantities have the required decay. In order to do so, the Einstein equations are decomposed with respect to specific foliations of the spacetime. This result generalizes the work `The Global Nonlinear Stability of the Minkowski Space' of D. Christodoulou and S. Klainerman.

gr-qc↗