Gravitational Physics
Theoretical Physics

Team leader: Mátyás Vasúth

Dániel Barta#, Károly Zoltán Csukás#, Máté Ferenc
Egri-Nagy#, István Rácz, László Somlai

# Ph.D. student   The main research areas of the Gravitational Physics Research Group are related to the study of gravitational phenomena. In addition to field theory research, other areas such as numerical and post-Newtonian general relativity, experimental gravitational wave data analysis and their related algorithms and developing multi-core computer procedures play a significant role. The group's research interest is motivated by gravitational wave physics, since we are a member of the Virgo Collaboration operating the European Virgo gravitational wave detector. In connection with the data evaluation tasks of the gravitational wave observations restarted in the autumn of 2015, our group participates in using the data analysis packages of the LIGO-Virgo collaboration.


The members of the Gravitational Physics Research Group of the Wigner RCP have solid
background in experimental and theoretical physics, in particular, general relativity and/or
particle physics. They also have experience in developing optimal numerical algorithms and
coding these algorithms into efficient computer procedures that can run on grid and GPU
clusters. One of the main motivation of our research interest originates in gravitational
wave (GW) physics as our group is a member of the Virgo Scientific Collaboration operating
the Virgo detector, the European gravitational wave observatory. The scientific results of
last year are summarized below.

Gravitational wave data analysis.


Interferometric gravitational wave detectors such as
LIGO and Virgo are sensitive to compact astrophysical objects with time-varying quadrupole
moment. The start of the advanced LIGO detectors in fall of 2015 has opened the very
interesting era of gravitational wave astronomy. The first direct detection of GWs and their
subsequent observation have important consequences on various fields of science and
modern technology. It opens a totally new window to the Universe as our current
knowledge is entirely based on observations of electromagnetic radiation. Despite its
weakness gravity is believed to be the dominant force governing the evolution of
astrophysical objects and the entire cosmos. With the help of the developing GW astronomy
scientists will be able to probe the nature of dark energy and matter and, in turn, increase
our knowledge about the universe considerably. Joining not only to the European efforts but
also the international LIGO-Virgo collaboration our research projects aimed to analyze
important and interesting compact binary sources of GWs and study the astrophysical and
cosmological implications of the observations.
For ground-based interferometric GW detectors compact binary systems of low mass black
holes are the most important sources for detection considering their present sensitivity. The
dynamics and the emitted radiation of these binaries are commonly described by the post-
Newtonian expansion. Specific waveform templates are ready for offline searches and
parameter estimation studies for these kind of sources within the software package of the
LIGO-Virgo Collaboration, e.g. the PyCBC and GstLAL packages. In data analysis processes
the matched template filtering method is considered to be the most optimal one for the
identification of theoretically predicted waveforms that are significantly suppressed by a
noisy background. Matched filtering for compact binary sources are implemented in the
PyCBC software package. The members of the Gravitational Physics Research Group have
learnt the use of the PyCBC toolkit and we are utilizing this knowledge during the upcoming
GW observations. Using Institutional computational resources we are performing data
analysis runs on Wigner Cloud. We have successfully installed clusters of virtual machines
and set up a Condor task manager system. From a central computer all of the virtual
machines are accessible through Condor. Test result for running basic PyCBC scripts are
successful. As an important application we have implemented high precision waveform
match calculations for a wide range of the parameter space using in-built PyCBC waveforms.
Reduced basis for GWs. — The large dimensionality of the parameter space for binary
sources makes GW searches, parameter estimation, and modeling expensive and
computationally unsuitable with most of the methods. This problem is called the “curse of
dimensionality”, and, as a solution, the reduced basis approach was introduced in GW
physics. We have developed an interpolation technique for the reduction of the required
gravitational waveforms. For a given parameter space of compact binary systems it is
possible the appropriately choose a system of basis waveforms in a way that an arbitrary
gravitational waveform can be faithfully represented by this basis. The method is available
for circular binaries. In our work we have demonstrated the applicability of this procedure
for binaries on eccentric orbit resulting in the reduction of the required computational

The effect of the cosmological constant.

— The presence of a non-zero cosmological
constant Λ makes the Universe globally a de Sitter space-time. The smallness of the
cosmological constant may imply that it is unobservable except at large distances.
Gravitational waves of the first direct detection fit to the current ΛCDM cosmological model
and to Einstein’s prediction of gravitational waves. In the linearized approximation of
general relativity, the metric tensor is the sum of the flat metric and a perturbative term,
which can be interpreted as the sum of gravitational waves and background perturbation
involving Λ. In order to study the effect of the cosmological constant on the linearized
theory a different gauge choice was considered. This allowed us to write the equations of
motion in terms of the two perturbation part separately and order by order in Λ. With these
equations the earlier results of gravitational waveforms calculated in the usual transversetraceless
gauge can be used to study the effect of the cosmological constant Λ. It was shown
that the presence of the cosmological constant modifies both the phase and the amplitude
of the original quadrupole GW signal.
Continuous gravitational waves. — Within the science exchange program of the
NewCompStar EU COST action our Polish colleague Michal Bejger visited our department for
3 weeks. Our common interest is in the analysis of continuous GWs. These waves are
produced by systems that have almost constant and well-defined frequency. Example of
these are rotating single stars with a large mountain or other irregularity. These sources are
expected to produce weak gravitational waves since they evolve over longer periods of time
and are usually less catastrophic than sources producing inspiral or burst gravitational
waves. The aim of our project was to develop a new version of an all-sky data-analysis
pipeline which was initially developed by the Polish Virgo-POLGRAW group aiming at a
targeted search for almost-monochromatic gravitational-wave signals from rotating, nonsymmetric,
isolated neutron stars. During our joint work we have enhanced the existing GPU
implementation of the pipeline. Our initial discussions led to riding the code of dead parts,
obsolete dependencies, etc. making it generally more flexible. In hope of acquiring a larger
user base, we have moved from GCC/Linux/CUDA-only support to using open standards,
such as C11 and OpenCL.

With the contribution of Tuan Máté Nguyen our group is actively engaged in the
development of analysis software for the analysis group in Rome. The Rome group have
concluded that the bottleneck in their Wolfram Mathematica script toolchain was the
Hough-transform they implemented in Mathematica’s own scripting language, hence the
goal of its acceleration was set. First time around a native C++ implementation was devised,
both serial and parallel. The results are positive and can be put to use immediately. Further
collaboration may target a GPU-parallel implementation as well as porting other parts of the

Neutron star interiors

— Neutron stars (NS) are interesting and important sources of
gravitational waves. Despite of the fact that the present sensitivity of GW observatories
does not allow the detection of neutron star coalescences future upgrades will enable the
analyzation of such processes. The most intense part of the observed GW signal is coming
from the merger part of the coalescence carrying essential information about the neutron
star characteristics and the merger itself. In our work we have analyzed neutron star
interiors of ideal and non-ideal fluids. Assuming spherical symmetry the metric tensor is
time dependent and the equations characterizing the neutron star interior are decouple to
the TOV equation and a differential equation for the time evolution of the radius. For a twocomponent
polytrophic equation of state we have analyzed the Mass-Radius relation for
neutron stars. The analysis was extended to other equation of states. Without GW
observation of neutron stars present bounds for NS mass and radius can limit the parameter
ranges of possible equation of states.

Matra Gravitational and Geophysical Laboratory

— The lower frequency bound of present
Advanced GW observatories are around 20 Hz. The fundamental limitations at low
frequency of the sensitivity are given by the seismic noise, the related gravitational gradient
noise (so-called Newtonian noise) and the thermal noise of the mirrors. To circumvent these
limitations new infrastructures are necessary: an underground site for the detector, to limit
the effect of the seismic noise, and cryogenic facilities to cool down the mirrors to directly
reduce the thermal vibration of the test masses. To accurately predict the seismic noise
variation and behavior it is inevitable to perform long term seismic monitoring
underground. The Mátra Gravitational and Geophysical Laboratory was constructed 88 m
deep below the surface in an unused mine near Gyöngyösoroszi in 2016. In a collaboration
of several Institutes the aim of the Laboratory is to perform long term seismic, infrasound
and electromagnetic noise measurements, and monitor the variation of the cosmic muon
flux. The members of our group were involved in the preparation of the first data taking
period between March and August, 2016. In preparation for the subsequent measurements,
we have performed preliminary unification of the measured data coming from different

Constraint equations as evolutionary systems

— Seven decades ago the constrains of
Einstein's theory of gravity were converted to a semilinear elliptic system by the seminal
work of Lichnerowicz and York. All the currently applied techniques developed to solve the
constraints are based on this approach which, as it involves conformal rescaling of the basic
variables, also referred as the conformal method. A new alternative approach was proposed
which endows the constraints with a radically new evolutionary character. In particular, it is
shown that the constraints may be put either to a parabolic-hyperbolic system or to a
strongly hyperbolic system subsided by an algebraic relation. The proposed new approach is
expected to yield new techniques to solve the constraints, because local (in some cases
global) existence and uniqueness of solutions to these evolutionary systems are guaranteed.
Numerical relativity research. — In hope of investigating the perturbations of near
spherically symmetric processes on various space-times we are developing a numerical
library keen in making use of series expansion of spin-weighted spherical harmonics. We
would like to simulate the perturbations of spinning black holes with unprecedented
accuracy. The solution of the arising constraint equations have been accounted for with CPU
parallel calculations. Our future plans involve devising the equations governing the
evolution in a similar formalism as well completing the GPU-accelerated back-end of the

Concurrently to previous efforts and consulting with members of the GPU-Lab we are
working on a visualization module to GridRipper, the subject of our theoretical work. Our
aim is to develop a ray caster (in the computer graphics sense), to visualize various
volumetric density functions, implemented in a fully templated manner in modern C++ for
maximum flexibility. Similar to other developments in the Lab, his work is relying on
portable and open standards.


— The announcement of the first direct detection of gravitational waves in
February 2016, 100 years after Einstein’s original prediction, was generated a very intense
public interest and attention to this research field. Our group members were actively
participated in the preparation of the Press Kit for the announcement. Moreover, we have
given several scientific and public lectures, radio interviews about the first direct detection
of gravitational waves and its implications.
In 2016 our group members were actively participated in the organization of the national
scientific conference “100 éves az általános relativitáselmélet” in Budapest.

OTKA K 115434: Developing and applying new methods to solving the Cauchy problem in
general relativity (I. Rácz, 2015-2019)

International cooperation
Virgo Scientific Collaboration (M. Vasúth, D. Barta, M.F. Egri-Nagy, L. Somlai)
NewCompStar EU COST MP1304 action, (Hungarian Representatives: G.G. Barnaföldi – QCD
Topic Leader WG2, M. Vasúth, 2013-2017)

Long term visitor
Michal Bejger (M.F. Egri-Nagy, 3 weeks)


1. Rácz I: Constraints as evolutionary systems. CLASSICAL QUANT GRAV 33:(1) 015014/1-
18 (2016)